searl 20th century counterpoint

J3y the Same ^Author

THE MUSIC OF I.ISZT

TWENTIETH CENTURYCOUNTERPOINT

A Guide for Students by

HUMPHREY SEARLE

NEW YORKJohn de Graff Inc.

Copyright 1954 by Vifilliams and Jforgate Ltd*

in Great Britain

Printed in Great Britain

CONTENTSPAGE

PREFACE Vli

ACKNOWLEDGEMENTS ix

CHAP.

I INTRODUCTION I

II THE DEVELOPMENT OF CHROMATIC COUNTERPOINT 7

III STRAVINSKY AND EXPANDED DIATONICISM 22

IV MILHAUD AND POLYTONALTTY 32

V BART6K. AND THE FREE USE OF DISSONANCE 44

VI mNDEMTTH AND DIATONICISED CHROMATICISM 55

VII SCHOENBERG AND TWELVE-TONE COMPOSITION Jl

VIII SOME INDEPENDENTS Il8

IX CONCLUSION A NEW HYPOTHESIS 132

POSTSCRIPT, 1954 147

BIBLIOGRAPHY 15!

DISCOGRAPHY 153

INDEX 157

PREFACE

THIS book is sub-titled "A Guide for Students"; that is to say,it is not primarily intended for scholars or musicologists, whocan find fuller information on the subject elsewhere. I

remember, when a student myself^ finding it difficult, if not

impossible, to bridge the gulf between the traditional harmonyand counterpoint taught in most colleges of music and themusic that was actually being written by contemporarycomposers especially as one of the justly respected professorsat the college where I was studying was famed for his use of

parallel fifths and polytonal counterpoint in his own works.This book, then, is an attempt to bridge that gul an attemptto show how modern composers have come to write as they do,and perhaps to point out new paths which the student, if

interested, may care to follow up for himself,

This book is, therefore, not a complete"guide to modern

music " it is only intended as a land of signpost on the way;nor is it a discussion of the Hundred Best ContemporaryComposers. Apart from limitations ofspace, such a compendiumcould easily degenerate into a mere catalogue of names andworks. What I have attempted to do is to single out a numberof composers who represent various different tendencies in

modern music, and to discuss their work in some detail. I havealso tended" to concentrate on those who have gone to theextremes rather than those who have chosen the middle path;this means, of course, that a good many well-known anddistinguished composers are not mentioned at all, whereas someothers who are less well known and more rarely performed find

a place here. This is not intended to imply any criticism of the

former; as composers and musicians many ofthem are certainlyof far greater importance than some of those discussed here.

But I have concentrated on the extremists because I feel it is

important for the student to know the furthest that has been

gone in any particular direction; whether he will wish to go so

far himself is his own affair, but at any rate he should knowvii

viii AUTHOR'S PREFACE

where the limits lie. And I have approached the subject morefrom the point ofview of technical interest than musical value;what a student needs to acquire is technique and confidence in

self-expression but nobody can make him into a genius if the

spark is not there already.In the final chapter, greatly daring, I have attempted to

outline a method ofharmonic analysis which may be applicableto most types ofmodern music. I am aware that it is an outlineand not a complete system; but I feel that one should bewareof too much rigidity in matters of this kind, and if the ideasthere put forward may be of service to another in the construc-tion of a more detailed system of analysis, they will not havebeen put forward in vain.In conclusion, I should like to thank Mr. Richard Gorer for

many helpful suggestions during the preparation of this book.

H.S.London

ACKNOWLEDGEMENTSThanks are due to the following for permission to reproduce

copyright material:

PURCEIX: Royal Music Library.REGER: Messrs. Bote and Bock, Berlin.

STRAUSS: "Thus Spake Zarathustra." Hinrichsen Edition Ltd,"Ein Heldenleben." F. E. C. Leuckhart, Munich.

MAHLER: By arrangement \vith Universal Edition (London)Limited.

STRAVINSKY: Messrs. Boosey & Hawkes, and J. & W. Chester("Les Noces" and "Histoire du Soldat"); United MusicPublishers Ltd.

MILHAUD: By arrangement with Universal Edition (Alfred A.Kalmus, London).

BART6K: Messrs. Boosey & Hawkes; Quartet No. i, Zeno-mukiado, Vdllalat, Budapest.

HZNDBMTTH: Messrs. Schott & Co.SCHOENBERG: Universal Edition, Wilhelm Hansen Musik-

fbrlag (Serenade), Bomart Music Publications*, Editions

L'Arche, Messrs. G. Schirmer Inc.

BERG: By arrangement with Universal Edition (Alfred A.Kalmus, London).

WEBERN: By arrangement with Universal Edition (Alfred A.Kalmus, London).

KRJENEK: Messrs. O. Schirmer, Inc. and Messrs. Chappell & Co.BUSONI: Messrs. Breitkopf & Hartel; British and Continental

Music Agencies.VAN DIEREN: Oxford University Press.

SZYMANOWSXI: By arrangement with Universal Edition (AlfredA. Kalmus, London).

JANA&EK: Universal Edition, Hudebni Matice.IVES: Arrow Music Press, Inc.; Mercury Music Corpn.VARSE: Messrs. Curwen & Sons Ltd.VALEN: Norsk Musikforlag (Quartet No. 2): Harold Lyches

Musikfbrlag.STOGKHAUSEN: By arrangement with Universal Edition

(London) Limited.

*For "A Survivor fiom WaraaV.

CHAPTER I

INTRODUCTION

Is it really possible to give any general rules for moderncontrapuntal writing? To many people modern music seems to

be in a state of complete anarchy; there are so many methodsand systems that it would appear hardly practicable to find anycommon factor between them. We get composers who spice upnormal diatonic writing with a skilful use of dissonance, like

Stravinsky, those who go in for polytonality, like Milhaud, thosewho use peculiar scales derived from folk music, like Bart6k, andthose, like Schoenberg and Hindemith, who have invented their

own systems of composition and laid down rules which are

chiefly followed by their own disciples. These are the maintendencies in contemporary music; but there are many others,and many composers borrow ideas from each or aU of themethods outlined above. Yet no one would seriously pretendthat there are no rules at all; composers must instinctively feel

what sounds good and what bad. Our purpose then is to tryand discover why modern composers write as they do infact to find what method there is (if any) in their variegatedmadness.A student who wishes to become a composer is compelled

(if he goes to a college of music) to spend a great deal of time

writing counterpoint exercises in the styles of Palestrina andBach. He may object to this as a waste of time, pointing out

(quite correctly) that all modern composers are continuallybreaking the rules which he is so carefully taught to observe.But in fact he is not wasting his time; by doing these exerciseshe is merely re-living the process ofmusical history. IfPalestrinaand Bach had not existed there would have been no Bart6k or

Schoenberg; every composermust learn all the lessons ofthe pastbefore he can embark on new developments himself. In factthere is no break between modern music and that of the past;every element in every work, written by every composer of

2 TWENTIETH CENTURY COUNTERPOINT

today has developed out of some feature of the music of his

predecessors. It is only by understanding this that one can hopeto dissect or analyse the different tendencies in modern music;in fact, before embarking on a study of contemporary counter-

point it is absolutely essential for the student to have a thoroughknowledge of the procedure of past generations. It is no goodtrying to start reading a detective story in the middle, when onehas no ideawho is the detective, who are the potential criminals,or even who has been murdered.

I am therefore assuming that readers of this book will have agood knowledge of classical harmony and counterpoint up to,

say, Wagner's day. Where do we go from there? We must first

try to place ourselves in perspective with the musical history ofthe last four hundred years. This period may be divided intothree great epochs. The first, beginning in the fifteenth century,and ending with the death of Bach in 1750, may be called apolyphonic period, in the sense that in general counterpointrather than harmony was the dominant factor. The second,which covers the period of the Viennese classics and also theromantic composers, ended about 1910; this was primarily aharmonic period, with the reverse tendency to its predecessor.Our modern age is again predominantly contrapuntal; andthere are reasons for this, as there are indeed for the predomi-nant characteristics of the two previous epochs. TTiese arebound up with the question of tonality, which is perhaps themost formidable problem which we have to face in this

enquiry.The period before Bach saw the gradual dissolution of the

seven medieval church modes, on which music had previouslybeen based, and their fusion into the major and minor diatonicscales; hence it was in a sense a transitional epoch. The periodfrom 1750 to 1910, on the other hand, was a static period,based on the firm tonality of the major and minor scales, andit was only towards the end of the period that chromaticismgradually began to undermine these scales. Our modern periodis again a transitional one, in which the diatonic scale ofsevea notes phis five "accidentals" is gradually being replacedby a twelve-note scale which has not yet taken a definite

We shall ofcourse be considering this question of tonality in

INTRODUCTION 3

more detail as we proceed; but I should merely like to sayat this point that in general a transitional age seems to be

predominantly contrapuntal, whereas a static age seems to

be predominantly harmonic. Harmony and counterpoint areof course the obverse and reverse sides of the medal, a-n.d it is

impossible to treat them as separate entities; but it remains true

that in different periods ofhistory one or other ofthem tends tobecome the dominant factor for a certain time. The questionofwhich will predominate is governed by the degree ofsoliditywhich tonality has acquired during that period. If a tonal

system is securely established, as the diatonic system was duringthe major part ofthe i8th and igth centuries, it is able to build

up a solid structure of chords with which to surround and

accompany its main themes. In fact the idea ofa tune and its

accompaniment is only possible within the framework of sucha system, and we can see that this procedure was employed byevery composer from C. P. E, Bach to Wagner. Counterpointthere can be as well, of course, but it will normally be strictly

governed by the harmonic scheme; i.e. in general -die counter-

point arises out of the harmonies rather than vice versa. (Onehas only got to compare the fugues ofMendelssohn, Schumannor Klengd with those ofBach in order to appreciate this). Onthe other hand in a contrapuntal period, such as that fromPalestrina to Bach, and also today, the harmonies will generallyarise out of the movement ofindependent parts.

1

I ayn. aware that I am generalizing considerably in m^Irmgthis statement one can of course find tunes with accompani-ments in Purcell, and even Handel and Bach, and there is

plenty of contrapuntal writing in Mozart, Beethoven andBrahms* but I merely maintain that the outlook of the 'first.

period was mainly contrapuntal, and that of the second mainlyharmonic, and I think that our present period is also a contra-

puntal one. In contrapuntal periods there is a far greater degreeofharmonic experimentation, as the interweaving ofa numberof independent parts may often produce surprising results,

like this (by now, I think, fairly well-known) example fromGesuakb's "Moro lasso", published in 1611:

*Ct "Apollonian Evaluation ofaDwnyrian Epoch", Chap. XII ofSchoolboys"Structural Functions of Harmony" (London, 1954).


Ex. i

Here the sequence of chords anticipates the "Kiss" motive in

Die Walkiire, (as Philip Heseltine pointed out in his study of

Gesualdo 1); yet each part moves quite simply and naturally,

mostly by step, and there is only one diminished interval, of a

type allowed in every counterpoint treatise. Yet an eighteenth

or early igth century composer would not have dared to write

such a passage, as he would have envisaged it purely from the

harmonic point of view. Similarly the extraordinary "false

relation" clashes in the Elizabethans and Purcell arise from the

logical contrapuntal movement of the parts. Here is a typical

example from PurcelTs "My heart is inditing".

Ex. a

Chorus

String

The fact that such progressions could be written meant that

there was no clearly established harmonic system based on adefinite scale and tonality at that time. (The actual process of

the dissolution of the church modes into the major and minorscales is far too complex for me to describe here, and in any case

is not part of my subject; but it is sufficient to say that modalelements are found even in Bach and later composers) . Now we

KUarlo Gesualdo, by Cecil Gray and Philip Heseltine. London 19126.

INTRODUCTION 5

are in exactly the same position today; the diatonic system has

been broken up by the chromaticism of Liszt and Wagner, andwe are left with fragments of it, tossed like flotsam on a sea of

new and strange sounds.

The process by which the diatonic system was underminedfrom within is by now fairly familiar to most readers, and there

is no need for me to recapitulate it in detail1. IJLJS^Jif&dient to

say that by 1910 composers so different from each other as

Bartok, Busoni, Schoenberg and Stravinsky .were all making a

completely, free M&e, of all the twelve notes of the chromatic

scale, andjSchoenberg had even gone so far as to throw tonalityoverboard altogether, at any rate in theory. The whole changemay be summed up by saying, as I mentioned earlier, that

instead of regarding the seven notes of the diatonic scale as

superior to the five accidentals, we can now regard all twelve as

equals. This does not necessarily mean that all modern

composers do regard the twelve notes as equals, nor that there

is no tonality in modern music. In fact all composers useelements which are directly derived from the diatonic system,and, as I hope to show, a form of tonality is present in all

music ofthe present day, even including that ofSchoenberg andhis followers; but the fact remains, whether we like it or not,that we have nowfgot a twelve-note scale instead ofa seven-note

one. We can use this twelve-note scale as diatonically or as

chromatically as we wish that is according to our taste butwe cannot escape its implications. In this book I hope to

show the different uses made of it by various modern composers,and to draw some general conclusions from these.

This brings me again to the question of tonality in modernmusic. The diatonic system was firmly based on the major andminor triads, as we all know; but these are now replaced by far

more complex chord formations. Nevertheless these new chords

developed naturally from the old ones, usually by adding or

altering notes in them, and there are very few (e.g. the chordbuilt up ofa series ofperfect fourths) which appear to be entirelynew. The new chords are in fact distant cousins of the old ones;and though they may look different and do not usually behavehi the same way as their predecessors I have suggested that

XA concise account will be found in Mosco Garner's A Study of Twentieth-

Century Harmony (London 1942).B


in any case a good many of them arise as the result of contra-

puntal movement they can still be related to a tonal centre

corresponding to the old keynote. Even Schoenberg called his

system "Composition with twelve notes related only to each

other", meaning that for him there are twelve "tonalities" of

equal importance which require to be balanced equally againstone another.* In fact behind all the complications, variations,

compressions and ellipses of modern music one still finds the

conception ofa tonal centre, not ofcourse identical with the old

tonic, and now related to a twelve-note instead of a seven-notescale. In fact the diatonic system has now been replaced by whatI might call expanded tonality a conception -which I hope to

discuss in more detail in the next few chapters.To sum up, then, we are living ha a transitional and pre-

dominantly contrapuntal period, in some ways parallel to the

age between Palestrina and Bach; the diatonic system of the18th and igth centuries has ceased to exist in its old form, butthere is no complete break with the past; elements of the oldmusic have continued to survive in the new, and we have adifferent conception oftonality, based on the twelve-note scale.

We shall later consider these points in detail by exarnining thework of various composers who have brought about this

revolution. But let us first trace briefly the steps which led upto it.

*Cf. p. n6n.

CHAPTER II

THE DEVELOPMENT OFCHROMATIC COUNTERPOINT

As we have already seen, the steps which led to the eventual

breakdown of the diatonic system in its old form were already

present in the music of much earlier ages. The Gesualdo

example quoted above shows an advanced use ofchromaticism,and we can find similar examples in Bach and others. Here is a

passage from the Fugue in B minor (Book I of the Well-

Tempered Clavier) :

Ex.3

J&m.

The subject is in the bass, and it will be seen that its twentynotes contain all the twelve of the chromatic scale. Nevertheless

it is not harmonized chromatically, but is treated as a series of

passing modulations, as indicated above. This is typical of

Bach's harmonic procedure; however chromatic his themes

may be, he never loses sight of the basic principles of tonality.

(Compare also the Chromatic Fantasy and Fugue, which

7


contains some astounding harmonic progressions, and alsoBach's harmonisation of the chorale "Es ist genug'VThe factthat the twelve-tone composer Alban Berg was able to introducethe latter in its original harmonisation into his violin cbncertowithout any sense of incongruity shows how "advanced" wasBach's use of chromatic harmony).From the example quoted above it is clearly only a step to

this passage from Liszt's Fantasy and Fugue on BACH :

Ex.4

This shows the entry ofthe third and fourth voices, hi the topand bottom parts respectively. The theme itself is similar to theBach subject quoted in Ex. 3; but here is accompanied bychromatic counterpoint, and the result is modulation soconstant that it almost amounts to suspension of tonality.(Liszt himself evidently felt this, for he found it necessary tofollow this passage with a long dominant pedal on D beforeintroducing a later entry of the subject in G minor). This kindof chromatic writing, consisting mainly of side-slips and basedto a considerable extent on the chord of the diminished seventh,can be found in many works of Liszt's middle period, notablythis Fantasy and Fugue, and also the Variations on the basso

DEVELOPMENT OF CHROMATIC COUNTERPOINT Q

ostinato from Bach's Cantata "Weinen, Klagen, Sorgen,

Zagen" itself an entirely chromatic theme. It was in fact

Liszt, more than any other composer of the igth century, whoseized on the chromatic experiments of Bach and developedthem for his own purposes.

1

In this he was followed by several later composers, ofwhomthe most important was Max Reger (1873-1916). Reger was

pre-eminently a contrapuntal composer, and his style was con-

siderably influenced by that ofBach in fact a good deal of his

work is almost a pastiche of the older master. But he had also

learnt the lessons ofthe chromaticism of Liszt and Wagner, andthis extract from his Variations and Fugue on an OriginalTheme for Organ, Op. 73, is typical of his chromatic methodof writing :

Ex.5

r i r* r

This shows the final entry of the fugue subject (in the pedals).

It is noticeable that the first four bars show a constantly

fluctuating sense of tonality, while the last two gradually

approach a quite conventional cadence. It is this combination

XA considerable use of chromatic harmony, chiefly for purposes of modulation

and "side-slip" can also be found in the works of Spohr.

IO TWENTIETH CENTURY COUNTERPOINT

of chromatic and diatonic elements which makes Reger's style

illogical and often irritating; there appears to be no particular

purpose in his passing modulations, and the chromaticism often

only seems to be there for its own sake, without any real

structural function.

An even more typical example of Reger's methods may beseen in one of the variations from the same work :

Ex.6

Here each part moves quite logically, and each chord is

consonant according to the rules of diatonic harmony; but thetotal effect is of uncontrolled and unnecessary modulation.Compare this with the Gesualdo example (Ex. i), which also

produces chromatic modulations through the logical movementof the individual parts; but there the total effect has a dramaticand emotional purpose, which is lacking in Reger. Nevertheless

Reger is of importance as one of those who contributed to thebreakdown of tonality; his chromatic treatment of consonanceswas followed by other composers who used dissonances in thesame way, as we shall see later on (p. 71).

DEVELOPMENT OF CHROMATIC COUNTERPOINT II

Another composer of the same period who also made anadvanced use ofchromaticism was Richard Strauss. Strauss was

primarily a tonal and even a diatonic composer, but as acontrast to his normal diatonicism he often used discords of a

violent and chromatic nature, chiefly for dramatic effect.

Though he certainly made use ofpolyphonic writing to a great

extent, his counterpoint is primarily harmonic, and one wouldnot regard him as a contrapuntalist in the normal sense of the

term; i.e. with him the harmonic background came first,

however many themes might be superimposed on it. A typical

example is this passage from Ein Heldenleben, from the section

where Strauss introduces themes from some ofhis earlier works.

Ex.7

TL- j; ^-=F=^=>^.i-i


Though a number of different themes are most ingeniouslycombined here (no marks for guessing from which works theycome!), the passage does not go beyond the normal rules ofdiatonic counterpoint, except for the occasional sounding of

appoggiaturas simultaneously with their resolutions. With veryfew exceptions, Strauss generally kept within the limits of this

kind of contrapuntal writing. A more ambitious attempt,however, may be seen in the "Von der Wissenschaft" section ofAlso sprach Zjarathustra :

Ex.8

This passage begins fiigally, with successive entries in G, G,D and A; this example shows the final entry. The celli aredivided into four parts, each being doubled an octave below bydouble basses. The four-bar fugal theme (in Cello i) consists

DEVELOPMENT OF CHROMATIC COUNTERPOINT 13

of 14 notes, which include all the twelve of the chromatic

scale; nevertheless it is not in the least atonal, being constructed

out of a series of triads, and further is tonally harmonised

throughout; there is in fact a certain parallel with the Regerexample previously quoted (Ex. 6) in that the counterpoint is

predominantly harmonic, and that the chordal scheme does

not seem to fulfil any very logical purpose, except that of

accompanying the main theme; i.e. the subsidiary parts have

very little real life oftheir own. This is exemplified by the some-what automatic sequential treatment of the second and third

'cello parts in the first two bars quoted.It is certainly unfair to dismiss Strauss* contrapuntal writing

on the strength of a couple of examples, and no doubt a very

good case could be made out for him as a contrapuntalist; all I

am trying to suggest is that Strauss, in common with most

composers of his period, still thought primarily in terms of

harmony, and however complicated the surface texture of his

music may become, there is usually a fairly simple under-lyingharmonic scheme. (Cf., for instance, the prelude to Act III of

Der Rosenkavalier1, which presents the appearance of a com-

plicated fugato in six or more parts; but there is no real tension

between the different parts, of the type that we find in Bach or

Bartok) . It was not until the early years of this century that the

supremacy of harmony began to be disputed by the

individuality ofthe different parts that composed it. There were,

however, some late nineteenth century composers who were

striving in this direction, and perhaps the most important ofthese was Gustav Mahler (1860-1911).

Mahler's contribution to music is of course too far-reachingto be summarised in a few words; as a conductor of genius, his

unrivalled knowledge of orchestral effect led him more andmore to explore the possibilities of soloistic treatment of instru-

ments or groups of instruments, and to turn his back on the

Wagnerian web of sound in which practically every instrument

is doubled by another. Mahler, in fact, brought back clarity

into orchestral writing; in spite ofthe enormous forces he used,each individual part can be heard without effort. His style

tended to become more polyphonic with the years; whereas

*A typical quotation from this will be found in Eric Blom, The Rose Cavalier

(Musical Pilgrim series, London 1930).


the earlier symphonies are constructed mainly in terms of a

theme surrounded by subsidiary parts, in the later ones each

individual part tends to greater equality with the others. This

passage from the first movement ofthe 8th Symphony is typical

of his later methods.

This is a real piece of 8-part writing, with several ofthe voice

parts doubled by instruments. Though the music is entirely

diatonic, the individual parts are driven against each other

with a complete disregard for passing clashes a method in

some ways very parallel to that later used by Stravinsky. But in

the case of Mahler the main harmonies remain comparativelystraightforward.


The example above makes some use of imitation between the

parts; but a later passage from the same movement, a sort of

instrumental stretto y uses all the classical devices of augment-ation, diminution and inversion, combined with modulation.

Ex. 10

Many other passages in Mahler show the same kind oftreatment

(see for instance the quotation from "Das Lied von der Erde" in

Mosco Garner, op. cit. p. 51), and it would be easy to multiply

examples. But I think it is clear from the above that Mahler did

reintroduce into the Romantic tradition of purely harmonic

writing the tendency to value individual parts for their ownsake; i.e. with him the horizontal aspect of' music was as

important, if not more so, than the vertical. In this sense he is

the forerunner of the whole modern contrapuntal school.

A survey of this transitional period would not be complete

i6 TWENTIETH CENTURY COUNTERPOINT

without some discussion of the early works of Schoenberg. Hismusic from 1908 onwards (the date when he abandoned

tonality), is discussed in Chapter VII, but his earlier composi-tions, while remaining within a tonal framework, carry still

further the tendencies observed in Mahler. Schoenberg came to

composition by way of chamber music he was an amateurviolinist and 'cellist, but had little knowledge of piano playingin his younger days and as a result his approach is pre-

dominantly contrapuntal. Though in these early works hedoes not go beyond the post-Wagnerian harmonic scheme, his

chords are nearly always arrived at through the movement of

independent parts. The following example of the simultaneoususe of a theme and its inversion, from the string sextet Verkldrte

Nacht (1899), though complex and chromatic, remains funda-

mentally tonal.

An even clearer example of this "Mahlerian" use of counter-point may be seen in an extractfrom Pelleas andMelisande (1902) .

DEVELOPMENT OF CHROMATIC COUNTERPOINT I*J

The music represents the meeting of Pelleas and Melisande at

the castle tower; the Melisande theme appears in fourfold

imitation on the flutes and clarinets, and simultaneously

augmented in octaves on two solo violins; against it is played a

secondary theme, associated with Melisande, on ist clarinet

and bass clarinet, and also the Pelleas theme on solo 'cello.

Ex. 12

l8 TWENTIETH CENTURY COUNTERPOINT

In his following works, the first two string quartets and the

first Chamber Symphony, the chromatic element increases,

and the music is often in a perpetual state of modulation; yetthe tonal framework is still observed, and each part moves

naturally and logically in its own way. Here is an example fromthe first string quartet (1905) :

DEVELOPMENT OF CHROMATIC COUNTERPOINT IQ

Ex. 13

A more homophonic, but still fundamentally contrapuntal

passage from the First Chamber Symphony (1906), shows an

advanced use of chromatic harmony, altered and substitute

notes being used freely. The music modulates rapidly without

ever altogether losing its tonal feeling.

Ex. 14

i.vi.

sehr auadrucksvoU

Chromatic harmony could hardly go further than this

without overstepping the bounds of tonality altogether, and

2O TWENTIETH CENTURY COUNTERPOINT

in the finale of his next work, the 2nd/ String Quartet, Schoen-

berg wrote some passages which are almost impossible to explainfrom a tonal point of view. A typical passage is quoted here;for the present it must suffice to say that this represents the

logical conclusion towards which Schoenberg's ever-increasinguse of chromatic elements was leading him.

Ex. 15

Ylni

This chapter has dealt exclusively with composers of theGerman school, because it is here that the use of chromaticismis seen in its most acute form. Some French and Russian

composers, however, notably Debussy, Ravel and Scriabine,were also working on similar lines, chiefly in the free use ofaltered and whole-tone chords. Though partly used for impres-sionistic effect, these chords tended to remove the feeling of

tonality. As Schoenberg remarks 1, "Debussy's harmonies,

without constructive meaning, often served the coloristic

purpose of expressing moods and pictures. Moods and pictures,though extra-musical, thus became constructive elements,incorporated in the musical functions; they produced a sort ofemotional comprehensibility. In this way tonality was alreadydethroned in practice, if not in theory". It is, I think,unnecessary to illustrate this point by quoting examples,particularly as neither Debussy, Ravel nor Scriabine werefundamentally contrapuntal composers; but the student canfind many passages in their works where tonality is either

ambiguous or suspended altogether.1Arnold Schoenberg. Style and Idea. (London 1951) p. 104.


We can now proceed to a more detailed study of various

composers who have profoundly influenced contemporarycontrapuntal writing, each in their own way. To begin with, I

shall attempt to discuss five important figures Stravinsky,

Milhaud, Bartok, Hindemith and Schoenberg each repre-senting a different musical tendency.

CHAPTER III

STRAVINSKY ANDEXPANDED DIATONIGISM

STRAVINSKY, as we have seen, is a firm believer in the diatonic

system, and throughout his life his work has been based on this

system, no matter how many alien elements he has introducedinto it at one time or another. It is usual to think of Stravinskyas a predominantly contrapuntal composer; but though hecertainly thinks in terms of lines rather than chords on the

whole, his counterpoint is in fact rather rudimentary, beingextensively based on the use of ostinato figures a use whichwas no doubt suggested by the idioms of Russian folk music.It is important to remember, with Stravinsky as with manymodern composers, that a single part may in fact take the formof chords moving hi parallel, as in the following example fromPetrouchka:

Ex. 16

STRAVINSKY AND EXPANDED DIATONICISM 3

This is, in effect, merely two-part writing, with each partthickened out in common chords; it is also based on an ostinato

effect. A more complicated example of the same type of thingmay be found in Le Sacre du Printemps:

Ex. 17

Here the thought is fundamentally diatonic, in spite of the

chromatically descending middle part; and again we have anostinato. The famous opening section of Le Sacrea again, is

not truly contrapuntal; it really consists of one main themewith a chromatic accompaniment and a certain number of

decorations, cleverly written so as to suggest contrapuntal

development. The nearest it gets to true counterpoint is in

passages like Ex. 18 [p. 24] again based on an ostinato.

The fact that this is not contrapuntal in the true sense is

shown by the immediate repetition of these two bars, unaltered

except for the elaboration of one part; i.e. here Stravinskythinks rhythmically and dramatically, rather than contra-

puntally."Les Noces

"(1917) deliberately attempts to paint a picture of

Russian peasant life, and therefore there is naturally an almost

continuous use of ostinato. There are however occasional

imitative passages such as Ex. 19 [p. 24].

Here again the counterpoint is extremely simple, and the

ostinato provides a solid background*


Ex. 18

Ex. 19

3.

S

nr

en

"F" T I

r* T '

i

fThe chorales in "L'Histoire du Soldat" (1918) do provide

some genuine four-part writing; but as they are intended moreor less as parodies, Stravinsky is careful to avoid what wouldbe the normal diatonic harmonisation of the theme.

STRAVINSKY AND EXPANDED DIATONIGISM

Ex. 20

Largo

Here each part is quite simple and almost entirely diatonic;but the writing is carefully arranged so that the parts do not

"fit" together in the accepted classical sense. This is the so-

called "wrong note technique" ofwhich Stravinsky is an adeptmaster. It consists in substituting for what the ear expects

something different which sounds more "interesting" but hasno real logical function.

A more serious attempt at contrapuntal writing may befound in the second movement of the Symphony of Psalms

(1930), which is in the form of a double fugue though of a

fairly free sort. All the usual contrapuntal devices are found

here, and the movement certainly gives the effect of counter*

point, though it hardly has the architectural solidity of Bach.For'example take the beginning of the exposition of the second

subject (in the sopranos): [Ex. 21, p. 26].

The first subject (hi the bass) has previously been exposed bythe orchestra; it is typical ofStravinsky in that it goes round andround a few notes and never seems to progress anywhere.Note also the tendency of the orchestral alto and tenor partsto do the same thing; it is this that gives Stravinsky's counter-

point its curiously static character. It goes through all the formal

motions of being contrapuntal, but the essence of counterpoint,the interweaving of independent parts which will also create

harmonic tension and progression, is almost entirely absent.

The harmonic style, it will be seen, is fundamentally diatonic,

with a few clashes of passing-notes and some false relations.

The whole movement is well worth studying as a compendiumof Stravinsky's contrapuntal devices.

Two passages from a later work of Stravinsky's, the Mass

(1947) show how little his contrapuntal style has changed with


Ex.21

Soprani

Orch.

the passage of time. The first is a simple imitative passage,diatonic throughout with an ostinato-like accompaniment.

Ex. 22

Wind

STRAVINSKY AND EXPANDED DIATONIGISM 27

The second passage again introduces the voices imitatively

against a chorale-like figure on the brass.

Ex.23

S.A.

T.B.


As a final example we may take this passage from the Interlude

before the Bacchantes dance in "Orpheus" (1947).

Ex. 24

Moier&to

This again is very typical of Stravinsky's methods, andevokes a comparison with Ex. 21; there is no actual ostinato,but the bass descends by step throughout (a feature of thewhole interlude). Against this the upper parts move withina mainly diatonic framework, but with a certain number offalse-relation clashes arising out of the movement of individual

parts.This in fact is Stravinsky's main contribution to contrapuntal

writing; his parts move freely against each other within the


diatonic scale, without any regard for the older ideas ofaccented

passing notes or dissonances that have to be resolved. It is

true that concords tend to appear at the more important pointsin the phrase, but in the intervening chords Stravinsky has a

predilection for unresolved sevenths and ninths, which he treats

as normal concords. This tendency can be seen as early as

P&rouchka (Ex. 16); our example merely consists of two lines

of chords clashing against each other. In Exs. 20, 21, 23 and 24we have four or more single lines moving against each other in thesame way, with the added complication of a number of false

relations. These false relations normally arise out of the natural

movement of the parts, and do not constitute any threat to

tonality; they are in fact usually of the type which one finds in

Elizabethan music, arising out of the remnants ofthe medievalmodes (flattened and sharpened third, sixth or seventh, perfectand augmented fourth heard simultaneously, etc.). As stated

before, Stravinsky is essentially a diatonic composer, and anychromatic elements are definitely regarded as foreign to themain key.

In this appraisal of Stravinsky as a contrapuntalist, I mustmake it clear that I am not discussing his place in modern musicas a whole. Clearly his influence on the music oftoday has been

enormous, and rightly so; but this is due to the dramatic and

rhythmical elements in his music and to his command of

orchestral effect rather than to his contrapuntal technique.As Constant Lambert rightly said in "Music Ho!" 1

,"his

melodic style has always been marked by extreme short-

windedness and a curious inability to get away from the prin-

cipal note of the tune .... The essence of a classical melody is

continuity of line, contrast and balance of phrases, and the

ability to depart from the nodal point in order that the ultimate

return to it should have significance and finality/' Judged bythis standard, Stravinsky is a singularly poor melodist, and as

Ex. 21 shows, his counterpoint only too often falls into a

pastiche of eighteenth-century passage work spiced up by afew harmonic clashes. It is by endless, primitive repetition of

1London, 1934. (at present available in Pelican Books). The whole of Part Two,"Post-War Pasticheurs", is an excellent account of Stravinsky's aims and methods,and though Lambert only dealt with Stravinsky's music up to 1930, Stravinskyhas written nothing since which contradicts his judgments.


short phrases that Stravinsky makes his effect, not by the flowing

polyphony of classical composers, and therefore I feel justifiedin my claim that Stravinsky is not a contrapuntalist in the true

sense of the word.

Nevertheless he is a composer whose methods can be studiedwith advantage. Rhythm is a very important part of counter-

point, and no one can deny that Stravinsky is a master of

rhythmic effect. (Note for instance the placing of the stresses

in Ex. 25 below) . The student, therefore, who feels so inclined

may undertake the following exercises hi this style. (Followingthe example of Schoenberg in his Harmonielenre, I feel it is

better not to give the student examples to be "worked", but tolet him start from the beginning composing his own exercises

in the style given).

1. Write some 4-part chorales, of 4 or more phrases, in the

style of Ex. 20. (N.B. The student should write his ownmelody, rather than attempt to harmonise an existingchorale in this style).

2. Is it possible to analyse Ex. 20 according to the rules ofclassical harmony?

Alternatively, how few alterations are necessary in order toharmonise it in the orthodox manner? (e.g. supposing thesecond and third notes in the bass part were B[? and Ainstead of B and Bb, etc.). The student is recommended to

study the Grand and Petit Choral from L'Hfistoire du Soldat

(published by Chester).

3. Write some pieces of 4-part imitative counterpoint in the

style of the vocal parts of Ex. 22 (i.e. purely diatonic,without false relations), but at greater length. Write alsosome 4-part vocal counterpoint with a 2-part accom-paniment (not in the form of an ostinato!).

4. Analyse the second movement of the Symphony of Psalms(published by Boosey and Hawkes).

5. Write some 4-part fugal expositions in the style of the

opening of this movement (i.e. including both diatonicclashes and false relations).


Here are the first three entries :

Ex. 25

nil i

fo. f1

eU.

CHAPTER IV

MILHAUD AND POLYTONALITY

POLYTONAUTY, or the use of several keys simultaneously, is nota new device; in fact in all essentials it is as old as music itself.

Edwin Evans once -wrote that "in spirit every canonic conies

at an interval other than the octave and every fugal answerconstituted tentatives towards bitonality"

1; and in a sense the

struggle between tonic and dominant or other related keys in

every classical work partakes of a bitonal nature, in that therule of the one key is disputed by the other. It was clearly onlya matter of time before the rival disputants were presentedsimultaneously, and there are a number of examples from the

early years of this century onwards which show this happeningin a fairly radical manner; e.g. the ending of Strauss' Also

sprach ^arathiistra (B major chords in the upper wood-windalternating with C's in the basses); the famous passage fromStravinsky's Petrouchka:

Ex. 26

and the almost equally well-known one from one of Bart6k's

early Esquisses (1908).

1Cf. Mosco Garner, op. cil. pp. ^ff, for a fuller account of the historical back-ground of bitonality and polytonality.

MILHAUD AND POLYTONALITY 33

Ex. 27

But other composers treated this problem more radically.

In the often-quoted Scherzo of Szymanowski's First String

Quartet (191?) the first violin part is written in the key signature

ofA major, the second in F#, the viola in Eb and the cello in

C in fact adding up to a diminished seventh. However, if wetake a typical passage from it and write all the parts out in

G major with accidentals, the fourfold tonality does not seem

so apparent, especially if we regard Eb as enharmonic for

D$ major.

TUT T T


One does not really hear the simultaneous use of four keys;instead one gets the impression of constant enharmonic modu-lation what Schoenberg called "schwebende Tonalitat" or

fluctuating tonality. This is because the ear will always tryto relate the sum total of the sounds it hears to a definite tonal

basis; it is only really possible to listen to and distinguish

between two separate tonalities at once.

Nevertheless the use of complex polytonal schemes of this

kind can produce some interesting results, and Milhaud

exploited this idea in many of his earlier works. The finale of

the fourth of his "Cinq Symphonies" (1921) is a good exampleof this. Written for ten solo strings, it is entitled "fitude" andis built on the followingfplan:

Instrument Key 147Violin i FViolin 2 CViolin 3 GViolin 4 DViola i AViola 2 A'Cello i D'Cello 2 GD. Bass i CD. Bass 2 F

Bar

13 16 19 22 252nd subject

and subject.2nd subject

2nd subject2nd subjectist subject

ist subjectist subject

ist subjectist subject

Bar

44Instrument Key 28 30 32 34 36 37 38 39 40Violin i F ist subjectViolin 2 C ist subjectViolin 3 G ist subjectViolin 4 D ist subjectViola i A ist subjectViola 2 A 2nd subject'Cello i D 2nd subject'Cello 2 G 2nd subjectD. Bass i C 2nd subjectD. Bass 2 F and subject

It is a strict canon in ten parts on two subjects; each subjectis exposed successively in five different keys, the second subjectentering in the same key as the final entry of the first subjectand reversing the order of keys in its exposition. This process


is carried out twice, once starting from the bottom of the

orchestra, and once from the top with closer entries; then acoda oftwo bars rounds off the movement. Though this scheme

may appear a purely mathematical one, musically this move-ment is a most effective piece. Here are the final three entries

towards the end of the movement (bars 38-40). Note that the

canon here is at two bars' interval in the upper five parts, at

one bar's interval in the lower five.

Ex. 29

(Incidentally a similar scheme was adopted by Bartok in the

first movement of his Music for Strings, Celesta and Percussion

(1936) see p. 48).


In this example again one cannot really hear the five different

keys, except perhaps at the moment of entry of each voice;the general effect is of diatonic music -with a number of "false

relation" clashes, and the movement (which is well worth

studying in totoj ends quite consonantly in F. The first movementofthe same symphony makes a fairly consistent use of bitonaliry,the pairs of keys being varied throughout the movement. This

is the opening!

Here it is quite possible to hear both keys at once; and a similarscheme is carried on throughout the movement. This is a roughanalysis of the key-changes:

Bars 1-14

TopMiddle

Bottom

15-22 23-4 25-7 28-9 3-i 32-5 3^-7 38-43 44-S 49-51 52

Exposition Middle Section Reprise

There are of course more variations of detail than it is

possible to indicate in the above table; but it will be seen thatthe keys of G and

[7 are in general associated with the first

group of themes, and C and F# with the second. The studentis recommended to make a detailed analysis of the movementfor himself (Publishers, Universal Edition). The slow movementof this symphony is mainly based on a tritonal scheme; the topand bottom parts begin on block chords of F minor and Eb


minor respectively, and move outwards chromatically, while

the middle parts hold a chord which wavers between E minorand the dominant ninth of C.

These methods are typical of Milhaud's processes at that

period, and they are carried even further in other works, such

as the opera "Les Eumenides" (1922). Here Milhaud makes use

of several overlapping ostinatos in the orchestra, against whichthe voice part pursues its own independent course, as in this

extract from Orestes' aria hi Act II -.

Ex. 32

O.

je ne le niti-xi pa.s? En vengeance dt mon pc^e

Here we have four chromatic orchestral parts, three thickcJned

out with double fourths and one with fifths; the voice part

partly coincides with the top line.


The finale of the same opera provides an even more startling

example of polytonal writing. Conceived on a gigantic scale,

it is a kind of perpetually-moving ostinato. This extract is

typical of the texture:

Ex.33

Reading from top to bottom, we have first the triple voice of

the statue of Athena (three parts in B major); then a chorus

in four parts which are respectively in B, A, E b and D b (the fact

that the alto part is really in A is apparent from the two bars

before those quoted here). The first orchestral stave has a two-

bar repeated pattern of chords in Eb; the second also has a

a two-bar pattern, but in Db, while the third has a three-bar

pattern in B. The upper part on the fourth stave has a three-note


pattern in B of seven crotchets' duration; the lower partsimilarly repeats itself every seven crotchets. The fifth stave

contains a D-flattish rhythmical figure which is repeated everysix crotchets, while the bottom part, in A, comes round everyfourteen crotchets. Note the separate accentuation ofeach part,which provides a constantly changing rhythmical effect, similar

to the perpetual variation of the contrapuntal complex.It can be argued that to construct such patterns needs no more

than a knowledge of mathematics, and certainly passages like

this sound forced and ugly when taken out of their context andplayed coldly on the piano. Nevertheless when performed bysingers, chorus and orchestra as part of an operatic scene, there

is no denying their immense dramatic effect my strictures on

Stravinsky's use of ostinato in the previous chapter do not

imply that his music is thereby devoid of all interest. Milhaudwas using this kind of style for a particular purpose, in this

case to give the feeling of an immense popular gathering, and

personally I feel he was entirely justified in doing so.

This period of Milhaud's activity certainly shows his styleat its most complex, and in later years he simplified it con-

siderably. Nevertheless he continued to write polytonally for

some time, and in his huge opera Christopher Columbus (1928)

Ex.34

L!A ppa.fitear Quetza.lcc*ti

pentdu b*.-tra.- AinirA, \\ y * un


there are many passages of considerable complexity. Ex. 34,

p. 39 is an extract from the scene where the ancient gods ofMexico stir up the sea in order to wreck Columbus' fleet

(Tableau 17).

The whole passage (Vol. I p. 220-239 of the vocal score,

published by Universal Edition) is a 6-part canon which is

exposed and then played backwards in toto (from bar 1370onwards. This refers only to the orchestral parts, the voices

being independent) . The extract quoted here comes just after

the entry of the sixth part and shortly before the turning point.It will be seen that the writing here is far more flexible thanin the extracts from Les Eumenides: again the effect is of con-

stantly changing tonality rather than of true polytonality.This passage is followed by a chorus (pp. 240-251) accom-

panied by the figure in the second orchestral stave of Ex. 34,but with a varying number of crotchets between the demi-

semiquaver group in each part. Against this the first six barsof the theme of the canon appear as a two-part double palin-drome. Here is the central turning-point (bars 1420-1):

u-pe dessus I mords (est tr&v&iUe leur l'e

J J. J>J .


It will be seen that, of the four parts which have the ostinato

figure, the top part has five crotchets between each demisemi-

quaver group, the second four, the third three and the bottompart two. The part on the lowest stave is another statement ofthecanon theme, which has come in two bars previously. For thesake of completeness, here is the theme in extenso (here quotedfrom the earlier passage, p. 221):

Ex. 36

It is played twice forwards and twice backwards in each of the

top two parts, while the bass, entering ten bars later, plays it

once each forwards and backwards; meanwhile the ostinato

scheme is strictly carried out in the other parts. Here again themathematical rigidity of the plan is justified by the enormousdramatic tension which is built up, and the final resolution onto a "B-majorish" chord sounds perfectly logical. The whole

passage (pp. 220-251) is well worth studying in detail. Notethat each entry ofthe canon (in the earlier part ofthe passage)is six bars after the previous one, and a major seventh higher;


note also that the ostinato figure (cf. Ex. 35) actually forms partof the canonic theme, which repeats it five times and then

continues on its own course. It is one of Milhaud's most

ingenious and successful constructions.

In view of the fact that in most of his recent works Milhaudhas more or less given up polytonal writing, the questionremains whether this type of composition is still worthy of

study today. Personally I believe that it is; almost every modern

composer has made some use of the simultaneous combination

of different keys, though naturally the method of approachvaries considerably between them; I have chosen to analyseMilhaud's methods in some detail, as his approach seems the

most radical and logical, and therefore provides the best basis

of study. Most composers of course do not use polytonalitywith such consistency; often they only combine elements

belonging to two different keys for a few bars at a time, and theydo not usually have two parts continuing remorselessly in twodifferent keys for any length of time without modulating or at

any rate introducing chromatic elements. In fact polytonality,like the whole-tone scale, has now been absorbed into the

general language of music, and there is no need to practise it

rigidly any more in actual composition, unless a special effect

is needed for some particular purpose. Nevertheless, in order

that the student may have a good grasp of what can be donewithin this style, I have included at the end ofthis chapter some

suggestions for exercises to be worked; later the student will

be able to select for himselfsuch polytonal elements as he needs

and incorporate them into his normal writing.The other question, a much more fundamental one, still

remains; does polytonality really exist at all, or, is it merely a

"paper tiger"? We have already seen from our examples that

it is very difficult, if not impossible, to hear more than two

keys at once with any kind of continuity, though of course

occasional new entries or elements may impose themselves for

a brief time as alien to the general fabric. But in general, as wesaw, the ear tends to try and resolve the total effect of what it

hears into one main tonality plus a number of incidental notes,however complex the fabric may be, and therefore Ex. 33, for

instance, cannot be regarded as a four-cornered contest betweenfour different tonalities, all equally important; one of them is


bound to predominate, and in this case it is B major, which hasthe upper hand both in the vocal and instrumental parts.

Bitonality is the only form of this procedure which can really

represent a see-saw between two different keys, and even this

becomes wearisome after a short time; in fact the ear prefersto regard the music as constantly modulating in toto rather than

being pulled simultaneously in different directions. (We shall

come back to this in the discussion of twelve-note music, wherethe problem occurs in a more acute form). Therefore, poly-tonality is chiefly useful to the composer in helping him to create

an elaborate and complex texture; but it is in itself too rigid a

concept. When the musical fabric as a whole is so chromaticand "dissonant" (in the old-fashioned sense) as most polytonalworks are, there is really no reason why one part should stick

firmly to the diatonic scale of one particular key; it would lose

nothing (and in fact would probably gain something) by beingallowed to move freely and chromatically. This is what most

composers have realized in recent years, and that is why poly-

tonality of the orthodox Milhaud type, as exemplified in this

chapter, is hardly ever practised nowadays. Nevertheless it hashad an important influence on the development of con-

temporary music, and therefore I would advise the student to

undertake the following exercises, noting carefully that it is not

enough merely to write one key against another without anythought for the total musical effect; the total result of all the

parts must also be satisfactory as music.

1. Write bitonal movements on schemes similar to that of the

first movement of Milhaud's Symphonic No. 4 (cf. p. 35).

(N.B. Each key can be represented either by single lines or

by chords).

2. Write polytonal movements on schemes similar to the finale

of the same symphony (cf. p. 34).

3. Write polytonal passages on the lines ofEx. 33 (i.e. includingchorda! parts as well as single lines if desired), but not

necessarily using repetitive ostinatos.

4. Write canonic passages in several parts on chromatic themes

similar to Ex. 36 (but not necessarily including an ostinato

figure) ,and following a similarscheme regarding the distance

between entries and their key relationships.

CHAPTER V

BARTOK AND THEFREE USE OF DISSONANCE

BELA BART6K represents a unique phenomenon, in contempor-ary musical history. /He has remained throughout an entirely

solitary and individual figure; and though he has influenced

others, and though it is possible to find external influences inhis own works Liszt, Debussy, Hungarian folk music, etc.

he has always stood completely apart from the rest of themusical world. This is chiefly due to his own dynamicpersonality, which has enabled him to digest ideas and recreatethem in an entirely new and personal way.

Onejcouldnot describe Bart6k as primarily either a contra-

puntal or a hafmorile composer;" Ke ^\v^7A7^^ster"oCbioilLiâethods of writing, andûsed either^ pxJbothJn combmation,according to

,Jâee&^.p^^j^TO^.TT^Ttf.^,A good* deal of his

music makes use of violent percussive or rhythmic effects,which are not our concern here; but side by side with thesethere has always been a strong contrapuntal element. The first

movement ofhis first string quartet (1907) for instance is a four-

part fugato which has been compared to the first movementof Beethoven's late G sharp minor quartet; in Ex. 37,[P- 45] are me third and fourth entries (in cello and viola) .

It will be seen that, for its period, this is much more far-reachingthan anything we have so far come across, except perhaps thelast Schoenberg example in Chapter II (Ex. 15). Though onecould hardly call the writing atonal, it is yet so chromatic thatthere is little definite sense of key it could best be describedas "fluctuating tonality", in Schoenberg's phrase. It is in fact

fBart6k*s unusual handling of tonal relationships that gives hismusic a good deal of its individuality, and this is particularlyapparent in his earlier works, where familiar chords andphrases are given a new twist by Bart6k's unexpected handlingofthem. The early piano works, such as the Esquisses, Bagatelles

44

BARTOK. AND FREE USE OF DISSONANCE 45

p motto e$f>ves$im . pp

Elegies, Dirges, etc., though not always primarily contrapuntal,

exemplify this tendency to a marked degree, and are well worth

studying, as they provide the key to Bartok's later development.

A simpler example of Bartok's chromatic counterpoint maybe seen in this passage from the first Elegy for piano ( 1908) :

Ex.38

Also typical of Bartok at this period are the bars from^

the

last of the 7 Esquisses (1910); they show a characteristic

"false-relation" (major-minor) harmonic effect. [Ex. 39, p. 46.]

Perhaps the best way of describing Bart6k*s approach at

this time would be to say that he had made tonality morei

fluid: that is to say, that while still upholding the supremacy


Ex.39

8 1*1 I

of a tonal centre, he would combine this with the free use ofall

the twelve notes ofthe chromatic scale. It is true that in a goodmany works of this and later periods he made use of unusual ,

scales derived from Hungarian folk music; but this element is,

I think, not so important as his free use of chromaticism. Onecan best sum this up by saying that his music invariably

expresses tonality, but avoids normal diatonic elements. This

can be seen clearly in this extract from a work of his middle

period, the Cantata Profana (1934). This passage begins in Dand ends on the dominant of Bfr; but the parts move freely and

chromatically throughout.

BARTOK AND FREE USE OF DISSONANCE 47

In another work of the late middle period, the Sonata for

2 pianos and percussion (1932), we find this four-part fugato,of which the final entry is quoted here (in Pf. i, R.H.):

Here each entry is a fifth above the previous one, and the

passage is written as a strict four-part canon. The whole section

(Boosey and Hawkes miniature score p. 40 onwards) is well

worth studying in detail. The music cannot be described as

strictly polytonal in the sense that Milhaud's often is; but each

part is constantly moving from one key to another, and there

is certainly the feeling of the opposition to each other of four

parts in different keys. This is chiefly achieved by means of the

clarity and economy of writing. From bar 360 onwards there

are various entries of the main theme (Pf.i R.H.) and its

countersubject (Pf.i L.H.) in inversion, and finally (bar 368)the theme is split up into its two component parts (a & b),

which are played simultaneously against their own inversions.

In the Fifth String Quartet (1934) (Finale, bar 202 onwards)


occurs a passage which starts as a two-part canon, first at the

fourth and later at the third. On the entry of the two lower

parts, also in canon, the two upper ones move more freely but

still canonically.

Ex. 42

si

This passage, which also is worth studying in detail, becomesmore and more simple as it proceeds, and eventually ends upin unison a good example of Bartok's use of classical devicesfor dramatic effect.

The first movement of the "Music for Strings, Percussionand Celesta" is a very instructive example of Bart6k's later

contrapuntal methods. It is built up on a series of entries

arranged in the following pattern :

Upperpart:

B *

D

Lower part:

BEb Ab

The notes given above are the first notes of the theme on eachentry. From the central climax (Eb) onwards, the themeappears in inversion; and afterA has again been reached, thereis a short coda in which the original and inversion are heardtogether.'JBut the movement is not just worked out in terms of

BART OK AND FREE USE OF DISSONANCE 49

pure mathematics; there is much variation in the treatment of

the theme, (some entries only state a fragment of it), there are

many subsidiary parts and short connecting episodes, and the

build-up to the central climax is much longer than the descent

from it to the coda. It is in fact a very fine and moving piece of

music, and one of Bart6k's greatest inspirations. This short

extract -will give some idea of the texture.

Ex.43

Vkl.

content


Here again the music is purely chromatic; but in Bartok

we always know that tonality will ultimately be asserted, and

the movement ends with a very definite cadence on to A.

In the slow movement of the Violin Concerto (1937) wefind another of Bart6k's favourite devices a canon at close

distance. In this case it is a four-part canon for pizzicato strings

with a counter-melody for the soloist; curiously enough, the

four string parts enter in the same tonalities as in the

Szymanowski example above (Ex. 28) F#, D #, G and A.

Ex. 44

ttcx.

The whole variation (bars 105-117) is worth studying as an

example of Bartdk's ingenuity in this respect.An even closer canonic passage may be found in the finale

of the same work; here we have a canon not only at a crotchet's

distance, but with each entry a semitone apart; the purposebeing, of course, to build up a violent dramatic plimax.

Ex.45

OUCH,

A simpler type of three-part canon occurs in the finale of the

Divertimento for strings (1939); here the tonality is modal F(with flattened seventh), and the three parts simply repeateach other ha a perpetual round.

BARTOK AND FREE USE OF DISSONANCE 5 1

Ex, 46

Vt*.

All that is intended, of course, is a cheerful, pastoral effect,

gradually building up to a climax.

The last movement of the sixth string quartet (1939) maywell be compared with the first movement of the first quartet

(c Ex. 37); these two examples show the development ofBart6k's lyrical writing over a period of thirty years. The later

work is ofcourse tenser, more concentrated, and shows the handof a master as opposed to that of a young innovator; but the

same lyrical impulse is there, in a sparer frame-work whicheschews all inessentials.

Ex.47

Our final example, from the finale of the Concerto for

Orchestra (1943), provides an interesting contrast with the

fugato from the Sonata for 2 pianos and percussion (Ex. 41)*

Here again there is the same scheme ofentries, each a fifth above

the previous one; but the passage is not strictly carried out as

a canon, and the music is far less chromatic and is more

52 TWENTIETH CENTURY COUNTERPOINT ^

definite tonally a tendency observed in many works of

Bartok's last years. These are the third to fifth entries:

Ex.48

The examples given above (apart perhaps from Ex. 44)do not show Bartok's use of dissonance at its most violent.

There are long passages in many of the middle period works

composed of chords consisting of a number of adjacent semi-tones sounded percussively together and sometimes endlessly

repeated. But these are not primarily of contrapuntal interest;their purpose is dramatic, and for this an ostmato effect is

eminently suitable. In contrapuntal writing, however, as wehave seen in the case ofStravinsky, ostinatos are rarely effective,and Bartok wisely avoids them for the most part. What he doesoften do, however, is to combine a number of parts with little

regard for the vertical result, as in Ex. 41, where he deliberatelywishes to create a feeling of tension between the parts; but

though he often appears to allow the individual parts to gotheir own way without much thought for their combined

BARTOK AND FREE USE OF DISSONANCE 53

effect, in fact his sensitive ear saw to it that the total musical

result was always satisfactory. We can see this both in his

early works (e.g. Ex. 37) and in his later ones (e.g. Ex, 47);

and in the first movement of the Music for Strings, Percussion

and Celesta (cf. Ex. 43) we find him varying the counter-

subjects with each entry of the main subject in order to obtain

the maximum flexibility and freedom. It is this flexibility of

mind which sets Bart6k apart from the mechanical proceduresof Stravinsky or the mathematical methods of Milhaud, and

gives him a claim to true genius.This having been said, it is obvious that I cannot recommend

the student to attempt to write exercises in the style of Bartok,

when Bart6k himself used new methods for each piece. True,Bartok has certain mannerisms which can be imitated (and

only too often are), particularly in his use of rhythmic and

percussive effects. But I have hoped to show that these represent

only one side of Bart6k's genius, and that the other, the more

contrapuntal and often more lyrical side, is ofequal importance,if not greater in the end. I will therefore merely suggest that

the student makes a thorough study of the following passages

from Bart6k's works :

String Quartet No. i First movement (Zenomukiado)Cantata Profana, bars 1-58, 132 if, (ist movement); 1-25

(3rd movement) (Universal).Sonata for 2 pianos and percussion, bars 332385 (ist

movement) (Boosey)

String Quartet No. 5, Finale, bars 202-350. (Boosey)Music for Strings, Percussion and Celesta, First movement

(Boosey)Violin Concerto. First movement, bars 56-68.Violin Concerto. Second movement, bars 105-117.Violin Concerto. Finale, bars 297-319. (Boosey)

Divertimento. Finale, bars 192-247. (Boosey)

String Quartet No. 6 Finale (Boosey)Mikrokosmos for piano Books 4, 5 & 6. (Boosey)

There are, of course, many other passages which are also

worthy of study; but the above should give a fairly representa-

tive conspectus of Bart6k's contrapuntal methods. "Mikro-

kosmos", a collection of over 150 short piano pieces, is also an


excellent introduction to Bartok's compositional methods;written towards the end ofhis life (1926-37), the pieces providea kind of modern Gradus ad Parnassum, both for pianists andcomposers. Each piece illustrates a particular idea or methodof writing, sometimes of pianistic, sometimes of compositionalinterest, and in them Bartok gives a kind of "break-down" ofhis technique. His use of modal and other unusual scales maybe studied in them; there are also pieces based on particular

intervals, such as fifths, sixths, sevenths or seconds, and others

demonstrating some particular pianistic effect, e.g. harmonics,or some unusual rhythm, like the Bulgarian dances which endthe collection. The first three books, though extremelyinteresting as examples of Bart6k's methods of writing, are

mainly elementary in character; the last three venture into

more experimental directions. Not all the pieces are primarilyof contrapuntal interest, of course; but the collection providesas it were the raw stufffrom which Bartok's major works spring.The 44 Duos for 2 violins are also interesting as showingBart6k*s contrapuntal methods in their most direct form.

CHAPTKR VI

HINDEMITH ANDDIATONIGISED CHROMATICISM

WITH Hindemith we arrive, for the first time in this survey,

at the case of a composer who has actually worked out and

published a theoretical book on composition,1 This important

work, which should be digested by all students, is a brave

attempt to give a logical and consistent explanation of all types

of modern compositional procedure, and even if, as we shall

see later, the attempt cannot be said to be entirely successful,

it was certainly worth making. The problem which Hindemith

attempts to solve, as will be clear to all who have followed meso far, is that of the free use of all the twelve notes of the chro-

matic scale within a tonal framework. We have seen how this

problem arises in the case of Bart6k, and how difficult it is to

give any real theoretical explanation of his procedures; but

Hindemith felt that some explanation of this type of chromatic

writing must be possible, and he set himself to find one. Hestarted, naturally enough, from the harmonic series, and

attempted to find the order and degree of relationships of each

note in the chromatic scale to a central keynote (hi this case, let

us say C). He takes the first six overtones ofthe harmonic scale:

Ex.49320

-e- 2 3 4 5*(The overtone numbers are given below the notes, the vibration

numbers above). By means of a somewhat mathematical, but

quite logical process of dividing the vibration numbers by the

overtone numbers of the preceding notes in the series, he

arrives at the following table:

i Hindemith. The Craft of Musical Composition. Schott, London, 1942.

55


Ex. 50

(The whole passage (op. cit. pp. 32-43) is worth studying in.

detail as an example of Hindemith's analytical method; see

also his table opposite p. 48). It will be seen that this series

(which Hindemith calk "Series i") contains all the twelve

notes of the chromatic scale; the further a note is to the right

of this series the less strong is its relationship to the keynote G.

It should be made clear at once that this is neither a scale nor a

Schoenbergian note-series (see next chapter); it is simply atable of the relative order of relationships between a keynoteand the remaining notes in the chromatic scale, and it does

not show the relationship of these notes to each other.

This latter relationship is shown in Hindemith's Series 2,

which is also derived by him in a somewhat complicated way,in this case from the differential notes. These notes (whichHindemith, by the way, calls "Combination tones

55

) I have

throughout used the English "note" rather than the Americanor German "tone" in quotations, except in the case of "twelve-

tone composition" 3 which has now become a recognisedformula are produced, as "Grove" says, "when any twoloud and sustained musical sounds are heard at the same time.

The differential note is so called because its number of

vibrations is equal to the difference between those of the

generating sounds". (See article, "Resultant Tones", in

Grove's Dictionary, where the matter is more fully discussed).A further differential note is also produced between the

original differential note and one of the directly sounded

notes; Hindemith calls these "combination tones of the second

order". (See op. cit. pp. 5?ff). By using these two series of

differential notes he is able to evolve a second table whichshows the relative harmonic value of the various intervals;

he calls this "Series 2".

HINDEMITH AND DIATONICISED CHROMATICISM 57

The intervals in this table become "less pure", as Hindemith

puts it, as we move from left to right. Hindemith shows that

these intervals are invertible (still by using the differential

notes), and is also able to determine the root of each interval

(shown by arrows in the table above) from them. But in the

cases of the minor third and major and minor seconds (andtheir inversions) he admits that his decision as to which note is

to be regarded as the root is based more on past compositional

practice than on any theoretical justification derived from the

differential notes. The tritone, he says, has no theoretical

root; but for practical purposes he regards the note in it which

proceeds by the shortest step to the root of the chord on whichit resolves as the "root representative**. It should be noted in

the whole discussion of the table above that Hindemith does

not refer to "consonant" or "dissonant" intervals; he is in fact

following the practice of most modern composers in regardingthis distinction as no longer valid, in view of the collapse of the

diatonic system in its old form.

The above discussion may appear to be primarily of

harmonic, rather than contrapuntal interest; but as harmonyand counterpoint even today remain the two sides of the same

medal, it will be necessary to consider Hindemith's remarks

on harmony a little further before we can discuss his approachto contrapuntal writing. He first discusses his Series 2 from both

the harmonic and the melodic point ofview; "harmonic force",

he says, "is strongest in the intervals at the beginning of the

series, and diminishes towards the end, while melodic force is

distributed in just the opposite order (pp. 88-9) .... Thetritone has no definite significance, either harmonic or

melodic"; it needs a third note added in order to determine its

position, Hindemith next attacks the traditional theory of

harmony, on four grounds :

(i) The old theory that chords are constructed by the super-

imposition of thirds cannot explain many chords, e.g. those

based entirely on fourths,

(ii) Chords cannot now be considered invertible, as this wouldoften completely alter their character,

(iii) The conception of "altered chords" is out of date now that

harmony is chromatic and no longer related to a diatonic

system.


(iv) The same chord could bear various interpretations in the

old system according to the key it was related to; it is

illogical to continue this practice.

As we shall see, it is by no means certain that Hindemith is

right in all these strictures, particularly as regards point (ii);

but they do give him a working basis on which to build up a

new system of chords which includes all possible formations.

The question then arises of estimating the relative harmonicvalue of these chords; and as a chord may contain several

different intervals, Hindemith states that the harmonic value

is determined by the 'best' interval in it, i.e. the one furthest to

the left in Series 2. In the same way the root can be found.

Ex.52

In the first chord the 'best' interval is the perfect fifth A-E, andits root A is therefore the root of the whole chord. Similarly,

says Hindemith, in the second chord the 'best* interval is the

perfect fifth C-G, and its root G is therefore the root of the

whole chord. Traditional harmony would probably agree with

Hindemith in his analysis of the first chord, regarding it as anA major chord with major seventh + an A minor chord

(first inversion) with added sixth. (An alternative, though not

so satisfactory explanation, would be to regard it as a 4/3 chordwith F as the root, with added sixth (Db for C#) and minorthird (Ab for G#) as well as major third; but the doubling of

the 7th (E) is against this) . But on the second chord traditional

harmony would undoubtedly disagree with Hindemith, andI think rightly; it is surely more logical to take the other perfectfifth A E as tie fundamental interval, and to regard the wholeas an A major-minor chord with flattened seventh and addedsixth. (The student may try these chords for himself, puttingunder them in turn the alternative roots suggested, and makehis own decision). This illustrates the danger of adopting a

purely mathematical system of harmonic analysis; Hindemithattacks the "Procrustean bed" of the traditional inversion

system, but his own system can be equally Procrustean.


I have devoted some space to this discussion of Hindemith's

harmonic theories, as it is essential to understand them before

approaching his method of contrapuntal analysis. He beginsthis with his theory of the "two-voice framework, constructed

by the bass voice and the most important of the upper voices'*.

He regards the bass part as the most decisive for the develop-ment of the harmony; the next most important line may beentrusted to any one of the upper parts, or may move aboutfrom part to part. Ifeither ofthe outside parts has a long holdingnote or pedal point, then the next part below or above it

becomes the upper or lower member of the framework. Hinde-mith next tackles the question of chord progressions in some

detail, observing (c Series 2, p. 56) that as the harmonictension of chords increases, their harmonic value decreases;this "up-and-down change of values and tensions" he calls

"harmonic fluctuation". By means ofthe methods set out abovehe is able to determine the relative degree of harmonic value

and harmonic tension of all chords in any given progression.For this purpose he divides all chords into two groups, those

without and those containing a tritone; each group is againsubdivided into three (see table at the end of Hindemith's

book).

The (condensed) groupings are as follows;

A. Without Tritone

I Without seconds or sevenths

1 . Root & bass note identical

2. Root lies above bass note.

(i.e. major & minor triads & their

inversions)

HI With seconds or sevenths orboth


2. Root lies above bass note

V Indeterminate

(Chords built of major srds or 4thsonly)

II

B. Containing Tritone

Without minor 2nds or majoryths.

Minor yth only; root & bassnote identical

(i.e. "dominant sevenths")With major ands or minor yths

or both

Root & bass note identical

Root lies above bass note

With more than one tritone

IV With minor ands or major 7thsor both


2. Root lies above bass note

VI Indetenninate

(Chords built ofminor 3rds only)


Hindemith then proceeds to work out the relative value of

root-progressions in some detail, basing his method on his

Series i. From this, by taking the 'best' interval (see Series 2)in the succession of roots, he is able to determine the tonic of

any progression. Chords containing a tritone, he says, tend to

resolve on to chords which do not contain one; and the root ofthe chord of resolution is the tonic in this case. In progressionswhere all chords contain a tritone, (and therefore none are

resolved) the tonal centre of the progression is to be regardedas the dominant ofa tonic lying below it. (op. cit. p. 136, Ex. 97).Hindemith next gives rules for these successions of roots, or

"degree-progressions" as he calls them; he regards as detri-

mental to them "the absence over a long period ofthe strongestintervals, the fourth and fifth; the melodic interval of the

tritone; broken chords of any easily recognised species, exceptmajor and minor triads; chromatic progressions, i.e. too manyminor seconds close together; and explicitly melodic treatment,i.e. the use of passing notes, anticipations etc." The presence ofmodulation can also be established from these root-progressions:

(op. cit. p. 151, Ex. 116).

Further, the different tonalities through which a piece movesthemselves form a succession of roots which shows the con-struction of the piece as a whole; and the tonal centre of this

secondary root-succession is thus the tonic of the whole piece.We shall see shortly how Hindemith applies this method to the

analysis of both classical and modern works, including eventwelve-tone music.

Hindemith next delivers an attack on atonality and poly-tonality. "Tonality", he says, "is a natural force, like gravity.". . . There are but two kinds of music; good music, in which thetonal relations are handled intelligently and skilfiilly, and badmusic, which disregards them and consequently mixes themin an aimless fashion". He says, however, that there are twotypes of music,"which, although they cannot be called atonal,yet by the accumulation ofharmonic means of expression placetoo great a burden on the listening ear for it to be able to followthem completely." One of these is based on "a multitude ofdominant relations, alterations and enharmonic changes"; theother makes a continuous use of chords based on seconds andsevenths, and "produces an opaque kind of harmony which in

HINDEMITH AND DIATONICISED CHROMATICISM 6l

its avoidance ofany chord resembling a triad seems to fly in the

face of Nature. Neither of these types can be made reasonable

by the logic of its degree-progression; both are too crowdedwith material to be enjoyed." He goes on: "there are today aconsiderable number of composers who issue works that theycall atonal. To what extent the atonality of these compositionsrests upon the lack of a convincing degree-progression and to

what extent it is a more or less developed tonality concealed

by an uninterrupted succession of sharp sonorities, the reader

himself can determine by extracting the degree-progressionsof such pieces." Thus Hindemith would appear to say that,

according to his method of analysis, any music in which the

tonal implications are not clear is badly constructed; i.e. he is

not prepared to extend his system in order to cover all the

elements actually manifested in contemporary music thoughhis system in itself is certainly capable of such extension. This

strikes me as unnecessary prejudice; surely all that one wantsto do is to examine all contemporary phenomena and ifpossiblefind an explanation for them, rather than exclude or dismiss

them if they do not happen to fit well into a preconceivedscheme. It is quite probable, as we shall see in due course, that

twelve-tone music does often exhibit a "developed tonality",as Hindemith calls it in fact, Hindemith himself finds con-

siderable elements of tonality in Schoenberg's Piano Piece,

Op. 33a (cf. p. 67). I do not therefore feel that Hindemith is

justified in saying "the existence of this style seems to me onlyto lend final confirmation to the fact, everywhere to be observed,of the disappearance of understanding judgment and critical

sense in the field ofmusic." On the other hand, in his discussion

of polytonality, he says quite rightly (as we have seen in

Chapter IV) : "the game of letting two or more tonalities run

along side by side and so achieving new harmonic effects is, to

be sure, very entertaining for the composer, but the listener

cannot follow the separate tonalities, for he relates everysimultaneous combination of sounds to a root and thus wesee the futility of the game Since organic work, growingout ofnatural roots, will always stand on a firmer basis than the

arbitrary combination of different elements, polytonality is not

a practical principle of composition."Hindemith now takes a practical example in order to show


the method of working of his system. Though this concerns a

purely chordal progression, it will be useful to follow it in

detail, as it exemplifies Hindemith's contrapuntal as well as

his harmonic approach. He takes the following progression:

Ex.53

(I have somewhat simplified Huidemith's analytical table fromthe original, omitting certain points of purely harmonic

interest). Hindemith says that this progression "sounds

horrible", and sets out to offer criticisms and improvements.He finds the linear construction poor, except for the top partbut one; he says there is no plan in the two-part framework,and that "the weak fourth G-C in the fifth chord flatly contra-

dicts the intention to make this the harmonic climax". Heregards the harmonic fluctuation as an "aimless zigzag"; hearrives at this conclusion from his own method of grouping ofchords, (cf. p. 59). As regards the succession of roots, he says"the combination of chords from the fourth to the eighthchord does not allow any harmonic life to unfold, while afurther brake is provided by the repeated Eb of the sixth andseventh chords." Personally I should be inclined to disagreewith some of his diagnoses of the roots of these chords, and in

Chapter IX (p. isGff.) some alternative suggestions will befound; these would appear to fit better with the principles oftraditional harmony, which (as I suggest there) can still be ex-

tended to cover more recent developments. The tonality he

regards as G$ (Ab), which appears twice, and is confirmed by the

repeated fifth E|? and the leading note G, as well as the minor


third B; but a case could be made out for the first four chords

being in A, he says.

After some discussion (pp. 160-3) Hindemith produces an

"improved" version of this progression, as follows:

Ex.54

Personally I cannot see that this is any improvement; admit-

tedly the chords increase in harmonic tension towards the

middle according to HindemitKs chord-table (p. 59) and then

decrease again; but do they do so in actual sound? Here againHindemith's root-diagnosis is open to question: surely the roots

of chords 7 and 8 are E and F# respectively. And I cannot see

any objection to the original chord 5 (without tritone) comingafter a series of chords containing tritones; to my mind it

provides a welcome contrast and does actually produce the

harmonic climax which the composer intended. It would appearthat Hindemith, having worked out a methodical scheme for

grouping chords, insists that music can only be good if it

complies with this scheme; i.e. he is working a priori instead of

a posteriori. Surely if any such scheme is to have universal

validity it must take into account all possibilities of expression;

we are in fact back again at the old idea of the Procrustean

bed.

However, it is clear that Hindemith's methods of analysis

contain the elements of something which might well be

developed into a universally applicable scheme, and it is worth

pursuing his exposition ofthem to its conclusion. After a short

chapter on inessential notes (changing notes, passing notes,

suspensions, anticipations, etc.) in which Hindemith more or

less agrees with the classical method of treatment of these, he

proceeds to discuss melody. In listening to a melody, he says,

the ear always seeks triad formations; hence it is always


possible to establish the "degree-progression" (root-succession)of any given melody (p. 185, Ex. I56)

1.

The root-succession of a melody follows the same rules as the

root-successions of chorda! progressions: but is of course, quite

independent of the main root-succession upon which the joint

harmony of the several voices of a piece rests. In a piece madeup of several simultaneous melodic parts, as many root-

successions are possible as there are parts, and these may all

be independent of one another. On the other hand the root-

succession of the melody may fully coincide with that of the

general harmony.Hindemith then discusses in detail (pp. 187-193) the inter-

relation of the various major and minor seconds within the

compass of a fifth an important passage which I have not

space to give in detail here, but which the student should readfor himself. He calls seconds "the real building units ofmelody";they act as the measuring units and content of the briefest

melodic sections, and also as regulators of the larger melodicconnections. "A rising interval creates tension and a fallinginterval resolves it", he goes on. But if a rising or falling interval

takes place between two members of the same chord, there is

no feeling of either rising or falling tension. Hindemith then

analyses the falling intervals in detail, remarking that "to knowthe effect of the rising ones, we need only change the minus

sign in our result to a plus sign". Next Hindemith discusses

"step-progression" in melody; as opposed to the roots of thechorda! groups which form the "degree-progression" of a

melody, "more important are those notes which are placed at

important positions in the two-dimensional structure of the

melody: the highest notes, the lowest notes, and notes thatstand out particularly because of their metric position or for

other reasons. The primary law of melodic construction is thata smooth and convincing melodic outline is achieved onlywhen these important points form, a progression in seconds.The line that connects one high point to the next, one low

point to the next, and one rhythmically prominent note to the

irThe page- and example-references in the remainder of this chapter apply(unless otherwise stated.) to Hindemith's book; unfortunately it has not beenpossible to obtain permission to reproduce more than the handful of examplesquoted above.


next, without taking into consideration the less important partsof the melody lying between these points, is called the step-

progression" (p. 194, Ex. 174).

In simple melodies like the above, "the step-progression consists

of a single succession of upward and downward steps of majorand minor seconds"; but in more complicated melodies there

may be many more step-progressions going on simultaneously.The notes forming a step-progression are sometimes in direct

succession and sometimes widely separated (p. 195, Ex. 176).

Further points are that sevenths and ninths can take the placeof seconds in step-progressions (cf. the methods of the twelve-

tone technique, discussed in the next chapter) : a melody maymove quickly from one register to another by means of abroken chord and not by seconds: and "the prominent notes

of a melody may not belong to either a chord or a step-pro-

gression, when the need for intense expression requires that the

attention shall be riveted by the conspicuous strangeness of

such notes" (p. 196, Ex. 179).

Clearly step-progressions may conflict with the root-progressionsof a melody or the former may be completely subservient

to the latter. But in most modern melodies it is the conflict

which is more apparent.

It is clear that Hindemith's schemes of root- or degree-

progression and step-progression do provide a useful basis for

the analysis ofmelodies ofall types. How far they can be appliedin the exact way that Hindemith uses them must be left for

discussion later; but it is at any rate something to have a pointof departure. Hindemith concludes his discussion of melodyby talking firstly of those themes in which the root-progressionis satisfying but the step-progression is faulty (and he quotes amotive from D'Albert's Tiefland) : "such melodies give no morethan a certain pleasant impression". On the other handmelodies which "strive for the most definitely linear character,

may have a well worked-out step-progression and a poor root-

progression. Such melodies make the listener restless, since hecan follow the vague harmonic connections only with

difficulty." This latter type of melody of course brings us close

to the central problem of modern composition the recon-

ciliation of its linear and harmonic aspects. We shall be able to


return to this problem in our discussion of twelve-tone musicand afterwards. Hindemith finds the perfect balance betweenthe two elements, root- and step-progression, in the maintheme of the Andante of Beethoven's Fifth Symphony. He ends

by quoting a melody of which he finds the root-progression

unsatisfactory and the step-progression insufficiently developed:(p. 199, Ex. 182).For this he produces an "improved" root-progression, andinserts further step-progressions (p. 200, Ex. 184).I think it cannot be denied that this second melody has a better

shape, and that therefore to this extent Hindemith's methodsare justified; but it remains to be seen how far they can be

applied to more chromatic themes.

The final section of Hindemith's book consists of a numberof analyses, carried out according to all the principlesenunciated up to now, of passages from various classical andmodern works. The student is recommended to study the

analyses of the "Dies Irae", Guillaume de Machaut, Bach,Wagner (the "Tristan" Prelude), and the opening of Stravin-

sky's Piano Sonata. All that I have space to discuss here arethe analyses of passages from Schoenberg's Piano Piece Op.33a and Hindemith's own "Mathis der Maler". (Concert of

Angels, Allegro, bars 1-16).We will take the Hindemith example first, as it presents fewer

problems. The composer remarks: "the strongly chordal designof the degree-progression is based upon the effort to organizechord-groups as closely as possible around a tonal centre, while

leaving the greatest freedom to the individual parts. The factthat the notes of the degree-progression in bars 9-13 form abroken chord ofgroup VI* results in a gentle but very noticeable

cadencing towards the B ofbars 13-16. The tonal scheme showsthe same effort. Here, too, a large group of tonal centres is

chordally related, so that great activity of details takes placeagainst a smooth and gently restful background." Of the three

pedal points in the passage, the first and last are disregarded inthe harmonic analysis; the second (bars 9-12) is reckoned in.

With the aid of the examples given earlier, the student shouldfind no difficulty in following Hindemith's analysis; he shouldnote how the degree-progression of the upper part sometimes

*Cf. table on page 59.


varies from and sometimes coincides with the degree-progressionof the passage as a whole.

With the Schoenberg example we reach more debatable

ground. Hindemith gives a purely harmonic analysis; but it is

worth discussing, as the fundamental problem of tonality is

bound up with it. By his own methods Hindemith arrives at asomewhat complicated system of root-progressions, but I fear

that I must disagree with his analysis to some extent. Onecan, I think, adopt Hindemith's rule that chords containingtritones are normally felt as dominants of tonics a fifth below

(cf. p. 60). Now the root notes of the two chords whichalternate in the bass part of bar 19 are clearly B and C; wecan therefore regard the B as an augmented fourth in F leadingon to the dominant, G; and the bar is therefore in F. Further,the passage which begins at the end of bar 19 and continues

through bar 20 has a bass part centring round D, the dominantof G, which is therefore the tonality of the passage. Bars 21-22

begin as if on the dominant of F; but the presence in the bass

part of F, Bfc] (=Cb) and Bb show that the passage is reallybased on the dominant ofBb. For the remainder ofthe passage

my analysis corresponds more closely to Hindemith's in that the

main tonalities are Db (C#) and Gb (F#), but there is also aclear movement towards the dominant of D at the end of the

quotation. I would therefore prefer to suggest the following

analysis for the whole passage:

Ex.55


It is of course obvious that Schoenberg would have objectedto both Hindemith's and my analysis, in that this piece waswritten purely according to the rules oftwelve-tone compositionand without any regard for tonality; but it is, I think, still

possible to relate a good deal of twelve-tone music to a tonal

basis, and I believe that that is what the listener's ear actuallydoes in practice; i.e. instead of "atonality" we have constantly

modulating tonality. I hope to discuss this concept (and also

the method of chordal analysis employed above) in a later

chapter (cf. p. 136 ff.).

Before proceeding to discuss twelve-tone music in detail,

let us sum up what we have learned from Hindemith's theories.

It is clear that he has been at great pains to build up a systemof both harmonic and melodic analysis which will if possible

explain all modern developments and will provide technical,

apart from artistic, standards by which a composer can judgehis own and others' works. Where it appears to go wrong is in

dealing with more advanced chromatic music; here Hinde-

mith's system of root-diagnosis leads him to conclusions which

do not correspond with reality and the fact that he finds

difficulty in analysing music of this kind tends to make himdiminish its artistic value. The fact that such music uses chords

which are low down in Hindemith's table of harmonic values

does not necessarily make it bad music. For the present then

we may in principle accept Hindemith's system of analysis as

valid for music of a more or less diatonic type (such as his own,or that of Stravinsky and the later Milhaud, for instance), but

we must make some reservations when it comes to discussing

more chromatic music, and will try in due course to see if a

better solution can be found. Nevertheless every musician

must be grateful to Hindemith for having tried to tackle these

problems at all; and he has certainly put forward some valuable

ideas which may well serve as stepping-stones for the future.

I do not propose to suggest any exercises in Hindemith's

style to the student, as Hindemith himself has published a

volume of "Exercises in Two-Part Writing" (Schott, London,

1948), which is to be followed by further exercises in three-part

writing. The exercises so far given are mainly diatonic in

character. In addition, in the German edition ofhis composition

treatise, Hindemith gives a list (for some reason not included in


the English edition) of various works of his own which particu-

larly exemplify his principles. Of these I quote the following

(all published by Schott & Go.) :

String Quartet No. 3, Op. 22 (1922)

Kleine Kammermusik, Op. 242(1922)

Concert Music for viola & chamber orchestra, Op. 48 (1930)

Concert Music for piano, brass and harps, Op. 49 (1931)

Concert Music for strings and wind, Op. 50 (1931)

Das Unaufhorliche, Oratorio (1931)

Philharmonic Concerto (1932)

String Trio No. 2 (i933)

Symphony, Mathis der Maler (1934)Mathis der Maler, Opera (1934)Der Schwanendreher, for viola and small orchestra (1935).

Since then Hindemith has of course published a number of

important works, including three more string quartets; but

perhaps the most useful for our purpose is the "Ludus Tonalis"

for piano (1943). This is sub-titled "Studies in Counterpoint,Tonal Organisation and Piano Playing" and consists of a

Praeludium, 12 Fugues in all the keys (alternating with nIntermezzi), and a Postludium, which is the Praeludium

played backwards and upside-down. Incidentally the order of

keys of the Fugues is that of Hindemith's Series i (Ex. 50).

The \vhole collection should be studied as a compendium of

Hindemith's contrapuntal technique.

CHAPTER VII

SGHOENBERG ANDTWELVE-TONE COMPOSITION

WE may now return to Schoenberg at the point where we left

him in Chapter II that is to say in 1908, the year in which he

composed his first "atonal" pieces. So much has been written

both for and against "atonal" and "twelve-tone" music noother methods of writing seem to have aroused so muchdiscussion in this century that I think it best to try to clear

the fog ofcontroversy aroused by Schoenberg's more doctrinaire

supporters and opponents by seeing what Schoenberg himself

had to say on the subject. This information is contained in a

lecture, "Composition with Twelve Tones", delivered at the

University of California on March 26, 1941, and published in

Schoenberg's collection of essays, "Style and Idea'*. Study of

this is essential for anyone who wants to understand Schoen-

berg's methods.

Schoenberg begins with a short preamble, in which he says

"Formjn ^^artSa^^and^^pecially in music, aims primarily at

coinprehe^biHtyJ': and that alone isTthe aim of compositionwifH twelve tones, surprising though this may seem in view of

the lack of understanding shown to works written in this style.

He then traces the development of chromatic harmony (cf.

Chapter II); tonality gradually developed into what he calls

"extended tonality", and simultaneously there arose the

"emancipation of the dissonance." The ear had graduallybecome acquainted with a great number of dissonances, andso had lost the fear of their "sense-interrupting effect". One no

longer expected preparations of Wagner's dissonances or

resolutions of Strauss' discords; one was not disturbed byDebussy's non-fdnctional harmonies, or by the harsh counter-

point of later composers. This state of affairs led to a freer use

of dissonances, comparable to classical composers* treatment

of diminished seventh chords, which could precede and follow

7*


any other harmony, consonant or dissonant, as if there were nodissonance at all. Schoenberg goes on to say that discords are

distinguished from concords not by beauty but by compre-

hensibility. In his Harmonielehre he suggested that the ear was less

intimately acquainted with dissonant notes than with consonantones because the former appeared later in the harmonic series;

but "this phenomenon does not justify such sharply contra-

dictory terms as concord and discord". (Cf. Hindemith's treat-

ment of the same problem, p. 57). Closer acquaintance withthe more remote consonances i.e. the dissonances graduallyeliminated the difficulty ofcomprehension, and finally admittednot only the emancipation of dominant and other sevenths,but also the emancipation of Wagner's, Strauss', Mussorgsky's,

Debussy's, Mahler's, Puccini's and Reger's more remote. dissonances. 1 This meant in fact that what were formerlyregarded as discords could now be treated as freely as the

traditional concords; and, as we have seen, that is what mostmodern composers do in practice.The other, and more difficult, side of this problem is the

question of tonality. This is what Schoenberg has to say on the

subject: "Very soon it became doubtful whether [a basic noteor root] still remained the centre to which every harmony andharmonic succession must be referred. Furthermore, it becamedoubtful whether a tonic appearing at the beginning, at the end,or at any other point really had a constructive meaning.Richard Wagner's harmony had promoted a change in the

logical and constructive power of harmony." He then goes onto discuss Debussy's impressionistic use of harmony (quotedin Chapter II, p. 20), ending, as we have seen, by saying: "inthis way, tonality was already dethroned in practice, if notin theory."

Schoenberg thus takes the opposite point of view to Hinde-mith's statement (cf. p. 60) that "tonality is a natural force, like

gravity". Which of the two is the more justified will have to bediscussed later; but meanwhile let us follow the further develop-ment of Schoenberg and his first pupils, Berg and Webern.Starting from their twin conceptions of the dethronement of

tonality and the free use ofthe former "discords", they produced

Incidentally Janacek in his treatise on harmony also held that "the historyofharmony is, in fact, the history of the gradual tolerance of dissonances".

SCHOENBERG, TWELVE-TONE COMPOSITION 73

a series of pieces of which "the foremoot oharacteriaticB ;wgre

their extreme expressiveness and their extraordinary brevity."This phase of development covered the years 1908-1923; thatis to say, up to the discover)- of the twelve-tone" technique.The principal works of this period were Schoenberg's Piano

Pieces, Op. n and 19, 5 Pieces for Orchestra, Op. 16, thedramas Erwartung and Die gliickliche Hand, and Pierrot Lawaire;

Berg's String Quartet, Op. 3, Three Pieces for Orchestra,

Op. 6 and the opera Wozzeck;\ Webern's 5 Movements and 6

Bagatelles for string quartet, Op. 5 and 9, two sets of piecesfor orchestra, Op. 6 and 10, Four Pieces for violin and piano,

Op. 7, and several collections of songs, accompanied by various

combinations of instruments. 1

Now it will be seen that nearly all these pieces are compara-tively short, except where they are settings of literary texts;

and Schoenberg gives the reasons for this. "Formerly harmonyhad served not only as a source of beauty, but, more important,as a means of distinguishing the features of the form", e.g. the

necessity ofending a work with a concord. "Harmonic variation

could be executed intelligently and logically only with dueconsideration of the fundamental meaning of the harmonies.

Fulfilment of all these functions comparable to the effect of

punctuation in the construction of sentences, of subdivision

into paragraphs, and of fusion into chapters could scarcelybe assured with chords whose constructive values had not as

yet been explored. Hence, it seemed at first impossible to

compose pieces of complicated organisation or great length."In fact the music written by Schoenberg and his followers at

this time was primarily experimental; they had rejected the

traditional methods of manipulating the elements of music,but had not yet found a new and sound method of organisingthese elements.

Schoenberg continues: "A little later I discovered how to

construct larger forms by following a^ text or poem. Thedifferences in size and shape of its parts and the change in

character and mood were mirrored in the shape and size of the

composition, in its dynamics and tempo, figuration and

accentuation, instrumentation and orchestration. Thus the

1For more detailed discussion of these works, see Ren Leibowitz, Schoenbergand his School (Hinrichsen, London, 1954).


parts were differentiated as clearly as they had formerly been

by tHe tonal and structural functions of harmony."Clearly music, if it was going to develop at "all, could not

continue to be merely subservient to a literary text, andremain unable to create larger forms of its own; but before westudy the further developments which made this expansionpossible, let us consider sonic typical passages from the musicwritten by Schoenberg and his followers during this transitional

period. These bars are taken from the first of Schoenberg'sThree Piano Pieces, Op. 1 1 his first atonal compositions.

Ex.56

Massig

Here we have a free use of chromaticism and an avoidanceof definite tonal feeling, combined with the normal classical

devices of repetition and imitation. The first three bars do in

fact contain all the twelve notes of the chromatic scale, though

SCHOENBERG, TWELVE-TONE COMPOSITION* 75

there are some repetitions of the same note. Bars 4 6 showanother characteristic of this type of music the perpetual

shifting of the rhythmic accents; this follows the principle of

"perpetual variation" which became more and more importantto Schoenberg and his followers as time went on, leading

eventually to the complete avoidance of sequential figures anddirect repetitions of any type.A similar preoccupation may be seen in the first of Webern's

Five Movements for String Quartet, Op. 5, written in 1909.

Ex.57

Vlni

Here again we have imitative figures combined with a perpetualdislocation of the rhythm, while the chromatic nature of the

phrases precludes any tonal feeling.

Ex. 58

^ ^ ^ ^i

[iJirJJlu/n'Y} f IpjqjiE

Vcl..

=**3

Piano pp


With "Pierrot Lunaire" (1912) contrapuntal problems

begin to dominate the scene. The eighth piece in it, "Nacht",is a passacaglia, based on a three-note phrase which appearsin every conceivable form throughout it.

1[Ex. 58, p. 75].

The whole piece is worth studying in detail as an example of

Schoenberg's methods at the time. Similarly the i7th piece,

"Parodie", begins with an imitative passage between the viola

and the speaking part, while the clarinet plays the same figurein inversion: later the theme is heard in imitation between

speaker and piccolo, while clarinet and viola have a separatecanon by inversion.

Ex.59

tuut Win - k*uty In form m*

The 1 8th piece "Der Mondfleck", is even more remarkable.It consists of a double mirror canon, between piccolo andclarinet on the one hand and violin and cello on the other;from the middle of the tenth bar all these parts go backwardsnote for note. To this is added a three-partfugato on the piano(which does not, however, reverse) and a free voice "part.

1Cf. Envin Stein, New Formal Principles, in "Orpheus in New Guises,"London, 1953; also Leibowitz, Introduction L la musique de 12 sons, p. 46.(Paris 1949).


In a slightly later work, Die Jakobsleiter, an oratorio which

Schoenberg left unfinished and unpublished at his death, we

get a premonition of twelve-tone composition.*

1See Ren6 Leibowitz, Introduction it la musique de 12 sons, pp. 49^, for a fuUer

discussion of this passage.

TWENTIETH CENTURY COUNTERPOINT

From bar 6 onwards we have a held chord of six notes, againstwhich the other parts play the other six notes of the chromatic

scale, in varying orders.

Act i Scene 4 of Berg's opera Woz&ck, written between

1917 and 1921, is a Passacaglia, based on the following twelve-

note theme.

The scene consists of 21 variations, in which this theme appearsin a great diversity of shapes; but apart from the theme itself,

the general texture of the music is not based on a serial tech-

nique. In addition Berg's increasing preoccupation with formal

problems is sKbwn by the construction ol the opera as a whole.TheTIrst act consists 6Fa~"set of pieces representing the variouscharacters in their relations to Wozzeck: these are a Suite, a

Rhapsody, a Military March and Cradle Song, a Passacaglia


and an Andante affettuoso, quasi Rondo. Similarly the secondact forms a Symphony in five movements a movement in

sonata form. Fantasy and Fugue, Largo, Scherzo and Rondocon introduzione. The last act consists of six Inventions on a

theme, on a note, on a rhythm, on a chord, on a tonality

(Interlude) and on a regular rhythmical figure.

More definite steps towards twelve-tone composition may be.

found in various works of Schoenberg, Berg and Webernwritten about 1923-4; these are Schoenberg's 5 Piano Pieces

Op. 23 and Serenade Op. 24, Berg's Chamber Concerto andWebern's Canons Op. iG.1 The first four pieces of Schoenberg's

Op. 23 are based in general on the exclusive use of certain

intervals, and there are some passages which use an actual

serial technique; tile-fifthpiece is Schoenberg's first twelve-tone

work. Similarly the first half of the theme of the variations in

the Serenade consists of fourteen notes, of which eleven are

different notes; and the second half consists of the same notes

played in reverse order.

Ex. 62

ThemeAndante

Cl.

The first canon of Webern's Op. 16 also shows the use of a

serial technique which is atonal but is not based on a twelve-

note series. [Ex. 63, p. 80].

As will be seen, this is a strict canon with one part an inversion,

the voices entering at ever closer intervals towards the climax.

a fuller analysis of this tendency see Josef Rufer, Composition with

Twelve Notes, London 1954.

8o TWENTIETH CENTURY COUNTERPOINT

Ex.63

# ^ \^ 9~ ' "1 -B=jSF

Alban Berg's Chamber Concerto (1923-5) also containselements which are characteristic of twelve-tone composition.It is written in a complex form, which I have no space to

analyse here in detail 1: but we may note, for instance, that the

second variation in the first movement presents the theme in1Sec Willi Reich, Alban Berg (Vienna 1937 English translation in preparation) ;

also The Gramophone, Dec. 1950, for a fuller analysis.


mirror form, the third in inversion and the fourth in retrogradeinversion. Similarly the second half of the slow movement is

the first halfin mirror form. In addition the principal themes ofboth the first two movements consist of twelve-note series:

Ex.64

<'*

while the third movementintroducesno new material but consists

of a combination of the material of the first two movements.It will be seen from the foregoing that this transitional period,

Awhile starling with a mainly harmonic revolution against older

methods of writing, became progressively more preoccupiedwith contrapuntal problems. Schoenberg thus describes the

developments which led to the evolution of twelve-tone

composition: "Formerly the use of the fundamental harmonyhad been theoretically regulated through recognition of the

efiects of root progressions. This practice had grown into a

subconsciously functioning sense of form which gave a real

composer an almost somnambulistic sense of security in

creating, with utmost precision, the most delicate distinctions

of formal elements The desire for a conscious control of

the new (italics mine, H.S.) means and forms will arise in everyartist's mind; and he will wish to know consciously the laws andrules which govern the forms which he has conceived "as in a

dream" He must find, if not laws or rules, at least waysto justify the dissonant character of these harmonies and their

successions." It should be pointed out that, as we have seen,


the works ofjSchoenberg and his followers were tending moreandlriore tcTthe equal use ofall the twelve notej^oftibie scale,

often arranged in serial form; and therefore, when Schoenbergdiscovered twelve-tone composition,

"

he was rationalisingmethods that were already in practical use rather thanlmposinga purely theoretical discipline from outside. He calls this

procedure "Method of Composing with Twelve Tones whichare related only with one another", and goes on: "Thismethod consists primarily of the constant and exclusive use ofa set of twelve different notes. This means, of course, that nonote is repeated within the series and that it uses all twelvenotes of the chromatic scale." Schoenberg pointk out that this

is not a "system" but only a method of working; "a methodcan, but need not, be one of the consequences of a system."

Twelve-tone composition, then, is founded on a i2-note

series; Schoenberg calls it a "basic set", but it is also oftenknown as a "tone-row", from the German Tonreihe; for Englishreaders "note-series" would seem to be the most convenientterm. The series below is the basis of Schoenberg's WindQuintet, Op. 26:

Ex. 65

Basic Set (O) Retror*dc Set (R)

Inversion (I) Retro^tde Inversion (RI)

Such a series should not be regarded as a scale, though it canact as a "substitute for some of the unifying and formative

advantages of scale and tonality." Like a scale, a series "is thesource of many figurations, parts of melodies and melodies

themselves, ascending and descending passages, and evenbroken chords". Further, as will be seen later, "the associationof notes into harmonies and their successions is regulated bythe order of these notes. The series functions in the manner ofa motive". Hence a new series has to be invented for each piece;and from it every note in the piece is derived, whether by using


it horizontally as a melody, or vertically as a chord-succession

or by a combination of both methods. No note in the series

should be emphasised at the expense ofthe others, as this wouldcreate false associations of tonality; for the same reason, onlyone series should be used in each piece it would also lessen the

unity to have more than one series, for obvious reasons. Theseries may be used in inversion or in its mirror forms, and anyof its four forms may be transposed so as to start on any note

ofthe chromatic scale.1 The ultimate principle, for Schoenberg,is "the absolute and unitary perception of musical space/'Much ink has been spilt on the question of whether the wholemethod is a purely "abstract and mathematical cerebration,"as some have called it; I feel that it is profitless to discuss this

until we have seen how it works in practice and what results it

can produce. All I will say now is that the method grew out of

actual compositional practice (and not vice versa) ; that it does

satisfy the principle of unity which all serious creative artists

demand; and that a number ofworks have been produced with

its aid which are generally acknowledged as masterpieces.The earliest works of Schoenberg in which this method was

used were, as we have seen, the Five Pieces for piano, Op. 23,

and the Serenade, Op. 24; it appears here, however, in a some-

what rudimentary form, and for his first examples of its use

Schoenberg quotes his Wind Quintet, Op. 26, written in 1924.

[Ex. 66, p. 84].

The series (cf. Ex. 65) is here divided into two halves of six

notes each a frequent practice with Schoenberg, as wejshall.see. The first six notes build the main theme in the upper part,

while the other six provide a chordal accompaniment; then

the position is reversed. It should be noted that pieces written

in this style normally begin with a clear and direct statement

of the series, in its original form and on its'

'basic" degreejof

*In the musical examples in this chapter the four forms are shown as Original

(O), Inversion (I), Retrograde (R) and Retrograde Inversion (RI). Their

transpositions are indicated by numbers, as follows:

1 = Basic level

2 Semitone higher, major 7th lower

3 = Whole tone , minor 7th

4 = minor 3rd , major 6th

5= major 3rd , minor 6th= Fourth , fifth

7 = tritone higher or lower8 = fifth higher, fourth lower

9 =B Minor 6th , major 3rd10 SB Major 6th , minor 3rdn= Minor 7th , whole tone

12 Major 7th , semitone

Thus RI 9 =Retrograde Inversion a minor 6th higher than the basic level.


Ex.66, 2 3 ^ s

the scale; further that the notes in the series may appearjln anyoctave (c Hindemith's methods, p. 65) ; but octave doublingsare normally" avoided, though, as we shall see", there _.are

exceptions to this rule.

The next example, taken from the last movement ofthe same

work, shows, as Schoenberg says, that the same series" of notes

"ca*n produce different themes, different characters."

Ex.67

0.1

*7_8 9 M i|

In the top part we have the original series on its basic degree;

the lower parts begin with the inversion on its basic degreeand continue with the inversion transposed a fifth down. Onother occasions the main theme of this Rondo uses the notes

of its retrograde or retrograde inversion, but by maintainingits original rhythm is still easily recognisable (see Style and

Idea, p. 121).


A more complicated procedure is shown in the following

example:

Ex/68

Ex.69

,iE^Q~1


This is based on the retrograde, transposed a tone down, and

repeated three times. The bassoon has three-note phrases, whilethe accompaniment uses groups of six notes, so that the series

overlap the phrases, giving adequate variety; yet there is adefinite plan throughout.A simple example of two-part writing comes from the

Andante of the same work: [Ex. 69, p. 85],

Here the basic series is split up between horn and bassoon in

such a way as to give a definitely contrapuntal effect.

In another example, from the Scherzo of the same work,we have a further method of using the basic series. The accom-

paniment plays the first three notes ofthe series; the main themeenters with the fourth note. The accompaniment then continues

with the notes of the series, but never at the same time as the

theme.

Ex. 70


Schoenberg's final example from this work shows inversion

and retrograde inversion played against each other.

Ex. 71

8^ 7

The transposition is a major third higher than the basic degree.

The Suite, Op. 25, for piano is based on the following series:

Ex. 72

0.71 (transposed a* diminished 5th.}

0.1-

1.7. (transposed A. diminished 5th.)


This is divided here into three four-note groups, as opposed totwo of six notes (in the previous work) . In the Praeludium wehave the basic series in the right hand combined with its

transposition a diminished fifth away:

Ex.73

In the Gavotte the third group (notes 9-12) appears before thesecond (notes 5-8).

Ex.74

Schoenberg justifies this on two grounds: (i) as the Gavotteis the second movement of the Suite, the series has becomefamiliar by now; (ii) each group is treated as an independentunit and does not change within itself and there is a resem-blance between the first and second groups in that the intervalbetween the last two notes of each is a diminished fifth. Asimilar procedure is followed in the Intermezzo, in whichgroup s and 3 overlap. The Menuet begins with the fifth note(Group 2), Group i entering later.

SGHOENBERG, TWELVE-TONE COMPOSITION 89

Ex.75

Schoenberg's final examples are taken from his Variations for

Orchestra, Op. 31, one of the finest works of his maturity. Heprefaces his remarks by saying that in orchestral writing "manycomposers can manage with a small number of parts bydoubling them in many instruments or in octaves, by breakingand doubling the harmony in many ways sometimes therebyobscuring the presence of a content, sometimes making Its

absence clear." He is against the use ofcolour purely for its ownsakea preferring

*cto be coldly convinced by ihe transparency

ofclear-cut ideas." And he recommends the avoidance ofoctave

doublings, though (as we shall see) he afterwards somewhat

changed his standpoint on this subject. In order to facilitate this,

the first six notes ofthe basic series, together with their inversion

starting a minor third below, make up the twelve notes .of the

chromatic scale.

Ex.76

J"

IA M 3^' T

jj*'^(tfansp 4, third of I)

M


The theme (basic series) is announced against chords con-structed from this transposition of the inversion.

53

It is followed by (a) retrograde inversion at this transposition(b) retrograde original (c) inversion, transposed as above,thus completing the four forms. Similarly the accompanimentto

^

each phrase is derived from a different form of theseries.

In the first variation Schoenberg uses additional trans-

positions of the original and inversion to obtain parallel thirdsand sixths.

SCHOENBERG, TWELVE-TONE COMPOSITION 9!

Ex.78

In variation 5 six independent parts are derived from, one

transposition of the inversion.

Ex.79


In Variation 6 inversion and original are set against eachother in two-part canonic imitation.

Ex. 80

IT.

3SOio

&

k+ -****

In this bar from the Finale the upper parts consist of the first

six notes of the basic series followed by the remaining six in

retrograde order; the lower parts are derived from the inversion.

Ex. 81

0.1.

Finally Schoenberg even introduces the theme BACH as acountermelody, taking the notes from the retrograde inversion.


Ex.82

These examples may give some idea of the contrapuntal andharmonic variety which is possible by the use of this method;and before going on to consider some of Schoenberg's later

works, as well as those of his pupils Berg and Webern, we mayquote his concluding words on the subject. "The main advan-

tage of composing with twelve tones is its unifying effect . . . .

Prior to Richard Wagner, operas consisted almost exclusivelyofindependent pieces, whose mutual relation did not seem to bea tnusical one. Personally, I refuse to believe that in the greatmasterworks pieces are connected only by the superficialcoherence of the dramatic proceedings ... In music there is noform without logic, there is no logic without unity, I believethat when Richard Wagner introduced his Leitmotiv for

the same purpose as that for which I introduced my BasicSeries he may have said: 'Let there be unity.*"

Before discussing Schoenberg's later works, let us considerthe rather different handling of tKe twelve-tonermethod used

by Berg and Webern, which will further exemplify the varied

possiBiEties provided by it. Berg first used the method in his

Lyric Suite for string quartet ; 1925-6^; of its six movements,two and two half movements axe written according to the

principles of twelve-tone composition, while the remainderare not. Yet I defy any listener to detect any stylistic difference

between the movements, or even to tell which use the twelve-

tone method and which do not, unless he has previously been


^om^j^J^^p^jstA. the score. (The twelve-tone move-ments' are ui fact the first, the outer sections of the third, themiddle section of the fifth, and the sixth movement). Thedesign of the work as a whole again shows Berg's predilectionfor symmetrical arrangements; the titles of the movements areas follows:

i. Allegretto gioviale 2. Andante amoroso

3. Allegro misterioso 4. Adagio appassionato

5. Presto delirando 6. Largo desolato

i.e. the fast movements became successively quicker, and theslow ones slower. In addition each movement contains somematerial from the preceding one, and the circle is closed by thelast movement containing a reminiscence of the first. In thethird movement, which is in the form of a Scherzo and Trio,the Scherzo is repeated backwards note for note after the Trio,but in a slightly shortened form. All these devices, however^are of little importance compared to the dramatic andemotional significance of the work, which is among Berg'sfinest achievements; as the title implies, the form is lyric anddramatic rather than symphonic, and the Suite has aptly beencalled a "concealed opera". It is well worth studying in detail

(score published by Universal Edition); I will not give anyactual quotations, as Berg's individual handling of twelve-tone

composition may perhaps be more clearly seen from his operaLulu and his Violin Concerto. (Berg's only other twelve-tone

work, the concert aria Der Wein, though a fine work and well

worthy of study, does not raise any technical problems whichdo not also apply to Lulu] .

Like Schoenberg in his opera Moses and Aaron (whichremained unfinished at the composer's death) Berg in Luluattacked the problem of creating a whole full-length work fromone single note-series. The dramatic structure of the work is

again built on a symmetrical basis (see Willi Reich, Alban Berg,for an analysis of this) and just as all the other charactersrevolve round the central figure of Lulu, so Berg derives fromhis original series:


Ex. 83

a.-juimber of other scries which represent the various per-

$onalities of the drama. One of Lulu's themes is arrived, at bytaking in turn the upper, middle and lower notes of the four

three-note chords into which the original series can be gro'jpeH

(Ex: 83b):

Ex.84

b)

Similarly by taking ^i\ates-aX stated intervals from the original

series, we get t&is theme of "minor" character, representingAiwa:

Ex, 85

^T"l *'

-Jx x x 5 x x x


In the same way the pentatonic music characteristic of the

Countess Geschwitz is derived:

Ex.86

Ce.

"prx

and also the theme of Dr. Schoen:

Ex.87

CO (2)

AlUgro trur^ico (J 80 )

b);

SCHOENBERG, TWELVE -TONE COMPOSITION 97

It will be seen that a good many ofthese themes have a "tonal"

character; and in the last act Berg actually introduces a

perfectly diatonic song composed by Wedekind, the author ofthe plays on which the libretto of Lulu is based. This is used as

the theme of a set of variations in an orchestral interlude:

Ex.88

This brings us back again to the question of expressing tonal

feeling within a twelve-tone framework, which, arises in aneven more acute form in Berg's last work, his Violin Concerto.

The basic series of this actually consis-s solely of major andminor triads plus a whole-tone scale:

Ex.89

Whole- tone sca\e_

Mmo-i Minor1

Major

Further, in the last movement, Berg introduces the Bach

chorale "Es ist genug" as the theme of a set of variations; the

opening four notes of this chorale are the same as notes 9-12of the basic series, and the last four notes of the chorale are

the same as the inversion of notes 8-1 1.

Ex. 90

^


The use of a "tonal" series means that a good many passages

in the work have a "classical" sound; e.g. this one from the

first movement

Ex. 91

The general tonality of the concerto wavers between B flat

and G minor, and it ends with a chord of the added sixth on

B flat; nevertheless the writing is strictly based on twelve-tone

methods, though there is some use of octave doublings.

Tonal composition is thusjclearly possible within a twelye-

tone^framewoA; TjutTis "it" desS-ableE^Schoenberg's remarks,

quoteH ea3FHer7aBbut the necessityto avoid emphasising anyone note at the expense ofthe others, would appear to be against

it, as well as his statement that by 1908 "tonality was already

dethroned in practice, if not in theory." On the other hand,

his standpoint appears to have undergone a slight modification

in later years, as may be seen from this appendix, dated 1946,

to his essay on "Composition with Twelve Tones". This

was published in the French magazine Polyphonic (4me Cahier,

Le Systeme Dodecaphonique, 1949); as for some reason, it is

not included in "Style and Idea" I reproduce it here in extenso.

"In the course of the last ten years, certain strict rules

concerning octave doublings and the use of certain funda-

mental chords of the older harmony have been relaxed to a

certain extent. In the first place, it became clear that such

isolated happenings were not in a position to transform the

"non-tonal" style into a tonal style. There still remain the

melodies, rhythms, characteristic phrases and other formal

elements which were born together with the style of the

emancipation of the dissonance.

"Also* if the complete avoidance of a tonal centre is foundniiMi.mrfmr i !/* ***>. <<'<> * "" .

w - ^"J'

to be ccmira^ctedT^oK occasions and jin a provisional way,


such a contradiction docs not necessarily destroy the stylistic

merits of a composition."I must admit that Alban Berg, who was perhaps the least

orthodox of the three of us Webern, Berg and myself in his

operas mingled pieces or fragments distinctly written in a

given tonality with other pieces or fragments which were"non-tonal". He explained this by saying that an operatic

composer, for reasons of expression and dramatic characteris-

ation, could not always renounce the contrast provided by the

change from major to minor. Though as a composer he was

right, from the point of view of theory he was wrong; I have

proved in my operas Von Heute aitf Morgen and Moses and Aaron

that every kind of expression and characterisation can be

produced in the style of the free dissonance."

This point of view explains the greater "tonal" feeling whichcan be found in many of Schoenberg's later works; but before

considering these we must first discuss the use of the twelve-tone

method made by Schoenberg's other prominent pupil, AntonWebern. Webem went in exactly the opposite directionJ.Berg; his use of this method reduces it to its simplest andconciscst terms, and is, if anything, "purer" than that^ofjus.master Schpenberg. We can see this already iifhis first twelve-

tone wor% the Sacred Songs Op. 17.

In the String Trio, Op. 20, we find this method used on a

larger scale and in a more complex manner: here Webern

IOO TWENTIETH CENTURY COUNTERPOINT

returns to the classical forms, the first movement being a rondoand the second in sonata form. But it is the Symphony, Op. ai,which perhaps gives us the best insight into Webern's methods.The first movement is a 4-part double canon in contrary motion,

except for the Coda, which is a 2-part canon. Here is the

opening:

It will be seen that the order of entry is basic series; inversion

a major third lower; inversion at original pitch; basic series a

major third higher. Further, as the interval between notes

SCHOENBERG, TWELVE-TONE COMPOSITION IOI

1 1 and 1 2 of the series is the same as that between notes i and2, Webern takes the last two notes of one series as the first twoof the next and thus forges a perpetual chain of series. Inaddition the notes of each series are always leaping from oneinstrument to another and also from one octave to another, so

that the canon cannot be heard as a continuous line. This

texture, however, is typical of most of Webern's later works;and his extraordinarily acute ear enabled him to make the

exact choice of octave and instrumental colour required for

each note, so that the effect in sound is ravishing.The second movement, in the form ofa theme and variations,

shows a slightly less fragmentary method ofwriting. The theme,which is the inversion of the series of the first movement is

announced by the clarinet, accompanied by its own retrogradeversion on harp and two horns; but as the retrograde consists

of the same intervals as the original, one can say that the themeis in fact accompanied by itself another example ofWebern's

economy of means.

Ex. 94

The variations which follow show the same contrapuntalcontrol; the first is a 4-part reversible double canon in contrary

motion, the second is also a canon in contrary motion, while

the fifth variation, based on repeated chords, treats the series

from the harmonic point of view. (For a fuller analysis see


Leibowitz, Introduction pp. 232-8 and Schoenberg and his School*

Webern remained faithful to the principles exposed here for

the rest of his compositions; though in his choral works, like

Das Augenlicht and the First and Second Cantatas, Op. 29 and31, the style is often less rarefied and there is considerable use

of dramatic and emotional effect, there is the same quest for

absolute purity and transparence. Here is the first entry of thechorus in Das Augenlicht:

Ex- 95

Sopr.

SCHOENBERG, TWELVE-TONE COMPOSITION IO3

The vocal parts form a mirror canon between sopranos andtenors; and there is another mirror canon in the orchestra

(up to the middle of bar 13). Each of the four parts uses oneof the four different forms of the series.

Lest it be thought that Webern's later works consist of

nothing but academic contrapuntal devices, let me quote this

passage from one ofhis last works, the Variations for Orchestra,

Op. 30; it is the beginning of the final variation.

Ex. 96

The four-part harmony is made up of three statements of the

basic series and one of the inversion, the latter starting in the

tenor part. Such expressive passages are often to be found in

the works of Webern's final period; and the remarkable

quality of these works is their combination of extraordinaryaural beauty of sound with strict formal control. The key to

Webern's approach may perhaps be found in a letter1 to

Willi Reich dated 23rd February, 1944 the year before

Webern's tragic and untimely death: "To quote freely from

Holderlin: To live that is to defend a form. . . . Imaginewhat an impression it made on me, when this passage occurred

in the notes to Holderlin's Oedipus translation: 'Also, other

works of art lack reliability, as compared with those of the

Greeks. They have, at least up to now, been judged more bythe impression they convey than by the artistic considerations

and otter methods through which their beauty is created.9 "

Webern was ruled throughout his life by a strong sense of

natural law; he felt that by exploring the nature of these laws

he was also aiming at the creation of beauty; i.e. beauty can

only come through the fulfilment of a natural principle.

Works which ^im solely at beauty without _any regard for

1Quoted*5i "Tempo", London, March 1946.

IO4 TWENTIETH CENTURY COUNTERPOINT

the_means by which_ this beauty is produced tend to "lack

reliability" one only has to think of, say, Tchaikovsky to see

what he means. As a result Weberh devoted' his life to tEe

e3cpI6fafion of the"

cdndTensedr" and""concentrated "fornrj-neverynote in his music has its own meaning, and it would be impos-siblejto omit or alter a single one without damage. He eschewedworks of long^duration his longest atonal work, "tEe Secpn5Cantata, Op. 31, is in six moyements and lasts for 15 minutes,.

Nevertheless Webern can say more in two minutes than mostother composers in ten; his method of approach is entirelydifferent to theirs. No wonder then that his music has either

met with complete incomprehension or has been wildlyacclaimed by those who have ears to hear it; by his ultra-

sensR^?Hai^uIaHon oTpe^ct^normal elements of sonorityWebern has created music quite unlike any written before.

It is interesting too that many young composers are now seekingto adopt his methods rather than the more "normal" ones of

Schoenberg or the expressive technique of Berg; but withoutWebern's aural acuteness his technique is not easy to master

successfully, and I feel personally that history will regardWebern. as an isolated figure of extoordmary^ importancerather than as the direct ancestor of a new technique of com-

position. (For a fuller discussion ofWebern's work, which I Have

only been able to treat here in a very superficial manner, the

student is referred to the two books of Leibowitz previously

mentioned, especially Schoenberg and his School, which contains an

important section on Webern; I have also contributed a short

analysis ofWebern's last three works (which are not discussed in

Leibowitz' books) to the Monthly MusicalRecordforDec. 1946).In 1933 Schoenberg left Berlin and settled in the United

States. Thereafter he produced a number of works, of whichthe majority use twelve-tone methods, though some are

tonal in character. These latter include a Suite for strings,

written in 1934 for high school performance; a setting of the

traditional Jewish theme Kol Nidrei for reciter, chorus andorchestra; Variations on a Recitative for organ, based on atwelve-note theme, but treating it tonally for the .most part;a Second Chamber Symphony, which in fact merely representsthe completion of a work begun thirty years earlier; and a set

of Variations for military band. Schoenberg explained his

SCHOENBERG, TWELVE-TONE COMPOSITION I(>5

reasons for his occasional returns to a tonal style in a short

essay, On Rsment Toujours, published in "Style and Idea".

He felt that just as the classical composers from Haydn to

Wagner often felt the need to interpolate strict counterpointinto their own essentially homophonic style, perhaps because

they considered the art of their predecessors superior to their

own, so he himself sometimes felt the longing once again to

try to achieve, in the older style, what he was sure ofbeing able

to produce in his own style. There is thus no question of

Schoenberg definitely "returning to tonality" in these works;

they were written because as he says, "a longing to return to

the older style was always vigorous in me; and from time to

time I had to yield to that urge." But all the other works

written in this period are strictly dodecaphonic, including his

last composition, the Fantasy for violin and piano (1949)

apart from one exceptional work, which deserves special

consideration, the Ode to Napoleon, for speaker, string quartet

(or string orchestra) and piano.This work is very freely derived from a note-series but its

effect is entirely "atonal", apart from its final E flat majorchord. It is based on a logical and consistent use ofcertain inter-

vals contained in its opening chord (F G sharp C sharp E) ;

i.e. minor second or major seventh (F-E); major third or minor

sixth (F-C#, E-G#); minor third or major sixth (F-G#,

C#-E); and fifth or fourth (C^GJ).The following extract

shows the use of these two latter intervals:

Ex.97 I* V

I06 TWENTIETH CENTURY COUNTERPOINT

Here we have fifths in the first violin and cello; parallel sixths

leaping a fourth hi the second violin and viola; and both

elements in the piano. The passage also contains all the twelve

notes of the chromatic scale. Elsewhere, in view of the fact that

the opening chord contains the constituent notes of both a

major and a minor triad, Schoenberg makes some use of

superimposed common chords, but not in a "polytonal"

manner. The whole work, which is worth studying in score1

and is more fully discussed in Rufer, Composition with Twelve

Notes, appears to show a new kind of compositional tech-

nique which may well prove to be of historical importance;

but Schoenberg himself did not attempt to use this method

again in any other work.

Of the strictly twelve-tone works composed during this

period, the most important are the Violin Concerto, the Fourth

String Quartet, the Piano Concerto, the String Trio and the

Fantasy for violin and piano2

. All these follow the same basic

principles that we have discussed in connection with the

Variations for Orchestra, but there are certain new elements

which are worth noting. The Violin Concerto, one of Schoen-

berg's masterpieces, uses a method which Schoenberg in-

creasingly adopted in his later years the first six notes of

the original series, together with their inversion a fifth lower,

make up the twelve notes ofthe chromatic scale.

Ex. 98

*M mJA recording is also available (Esquire and French "Classic").*The scores of his very late choral works [Op. 50] were not available when this

book went to press.

SCHOENBERG, TWELVE-TONE COMPOSITION IO7

The opening of the work exposes these two series in succession:

Ex.99

r p^^i* HVWy*** |^

^"T^ uX^> L^ |I |IM^ ,^1

fk *,

The bars which follow consist of the basic series in the violin

accompanied by chords derived from the inversion; then the

violin plays the inversion and the accompaniment is derived

from the basic series.

The end of the whole work introduces another point.

Ex. ioo

In spite of the "polytonal" appearance of this passage, it will

be seen that it is in fact strictly based on the inversion (Ex. 98b),

starting from both ends at once, and with a slight variation

in the order of the notes (Bb before E in the retrograde form).

The opening of the Fourth String Quartet, Op. 37, shows

io8 TWENTIETH CENTURY COUNTERPOINT

us another method of exposing the basic material. The series

is played by the first violin; it falls into four three-note groups(a, b, c, d), which are simultaneously used as accompanyingchords.

Ex. 101

Note that the relation of the melody to its accompanimentis logically arranged in the following manner:

Melody a b c dAccompaniment bed cda dab abcA similar procedure is carried on for the rest of the theme forfuller discussion see Leibowitz, Schoenberg and his School:, also

Josef Rufer, Composition with Twelve Notes.

The Piano Concerto introduces a still more interestingelement, in that although it strictly based on twelve-tone

methods, it contain passages which have a definitely "tonal"effect. An instance is the opening of the final Rondo. [Ex. 102,p. 109].^This is in fact derived from two transpositions of the originalseries and two of the inversion. The right hand first plays thefirst six notes ofthe inversion (I6

1) ; the left hand plays the whole

of the same series. Meanwhile the right hand plays the lastsix notes of the original (Oi) in retrograde form. But the first

six notes of 16 are the same as the last six of Oi, in a slightlydifferent order (similarly the first six of Oi are the same as the

1This number refers to the degree of transposition of the series; cf. p. 83.

SCHOENBERG, TWELVE-TONE COMPOSITION

Ex. 102

-*o^

last six of 16), so that Schoenberg does not use the remainingnotes of the retrograde of Oi these notes are already in the

left hand part. Instead the right hand begins 04, which is

completed by the left hand, while the left hand begins Ig,

which later crosses to the right hand. Though the whole passageshows how a "tonal" effect (including the middle pedal on

F#) can be obtained by strictly twelve-tone means, it does not

really imply a "return to the older methods" for -here all the

twelve notes ofthe scale are strictly and logically used. One can

therefore conclude that while twelve-tone music need not

necessarily avoid a feeling of tonality, its principal aim is the

equilateral exposition of the twelve notes ofthe chromatic scale.

The same approach applies to the use of octave doublings,

which are also occasionally present in this work; cf.

Schoenberg's remarks on this subject quoted above (p. 98).

If the Piano Concerto and the Prelude to a "Genesis" Suite

(J945) inay ke sa^ to COIltain certain tonal reminiscences, this

is certainly not true of the String Trio (1948), which adopts a

more "radical" style. Here Schoenberg uses the same method

as in many of his later works, of dividing the series into two

halves, each of which, together with the corresponding half

no TWENTIETH CENTURY COUNTERPOINT

of the inversion transposed a fifth lower, makes up the twelve

notes of the chromatic scale. But he carries this process even

further by making frequent alterations in the order of the notes

within each six-note group; that is to say, that as long as all

twelve notes ofthe scale are exposed in close sequence (six from

the original series and six from the inversion) their actual order

is not considered so important. (For a detailed analysis see

"Music Review", Vol. XI, No. 3 August 1950).

This method again opens up new possibilities which are clearly

capable of further exploration. In "A Survivor from Warsaw"

(*947) we again have the use of a series plus its inversion a

fifth below, in this case coupled with the use within the series

of an augmented triad which can act as a "pivot chord"

between three transpositions of the series and three of the

inversion.

Ex. 103

This work (which is fully analysed in Leibowitz, Introduction

p. 322ff) is one of Schoenberg's most moving and dramatic

pieces; apart from the chorale at the end, it is chiefly built upfrom small "athematic" fragments, the only motive of im-

portance being the four-note theme with which it opens.

Finally, in the Fantasy for violin and piano (1949), Schoenbergreturns to an almost classical simplicity while exploring every

possible method of variation technique. Its basic series is

mainly founded on major and minor seconds (B[j, A, C#, B,

F, G, Eb, Etl, C, D, Ab, Gb), and there is a considerable use

of sevenths and ninths. It is essentially a work for violin and

piano and not vice versa; the piano part is largely accompani-mental.

SCHOENBERG, TWELVE-TONE COMPOSITION III

This survey of twelve-tone writing would not be completewithout some discussion of the first handbook to be publishedin English on the subject. This is a short treatise called "Studies

in Counterpoint based on the Twelve-Tone Technique" byErnst Kfenek (published in 1940 by Schirmer, New York).Kfenek says in his introduction: "The idea of tonality emanates

from a basically harmonic conception of music. The essentials

of tonality such as the key, the dominant-tonic function, the

tonal cadence are harmonic phenomena. In so far as atonality

depends for its organisation on motif-relationships, it apparently

brings melodic phenomena to the fore. Thus, the new idiom is

based on an essentially polyphonic conception of music, verymuch related to the angle from which music was viewed in

the Middle Ages, before tonality (in our sense of the term) had

developed. Therefore it seems sound to approach atonality andtwelve-tone technique by way of counterpoint. Harmonicfacts in atonality have but a secondary significance, at least in

the present stage of atonal development." Explaining that his

book "does not pretend to sum up or codify the practice of

the twelve-note technique as it appears in the works of Schoen-

berg, his disciples Alban Berg and Anton Webern, and several

other composers", but merely "to set forth the elementary

principles of the twelve-tone technique as the author has

applied it in a number of his own works", Kfenek ends bysaying "the knowledge of strict (Palestrina) counterpoint is

recommended as prerequisite, though not indispensable.*'

Two points should be noted from this: (i) that the views

expressed in this book are Kfenek's own, and not necessarily

those of Schoenberg or any other members of his school (ii) that

Kfenek tends to discount the importance ofharmony in twelve-

tone writing, though (as we shall see) he does give some rules

regarding harmonic relations. These points should be borne in

mind by any student who wishes to use this book for the purposeof technical exercises; unfortunately Kfenek's somewhat

mathematical method of analysing twelve-tone writing tends

to give the impression that this style can be approacheda priori, without any previous knowledge of music, whereas

every pupil of Schoenberg, Berg and Webern will know that

these composers insisted on a thorough knowledge of classical

harmony and counterpoint (including both Bach's and Pales-


trina's styles) as an essential prerequisite before embarking on

twelve-tone writing. Even twelve-tone music still has its roots

in the past; and one cannot completely disregard the

importance of harmonic laws which are based on the nature

of music itself. If any note could equally well be played against

any other note, music would cease to have any meaning at all.

If the student will bear these provisos in mind, he may find

Kfenek's book useful as an exposition of twelve-tone methods.

He begins with hints on the construction of a series, recom-

mending the avoidance in it of more than two major or minortriads formed by consecutive notes, as "incompatible with the

principles of atonality" though, as we have seen. Berg has

made use of such a series, and so have other composers. Hethen gives some rules for melodic construction, remarkingquite rightly that "the protracted use of unaltered rhythmic

patterns results in a monotony less admissible in this style thanin any other idiom . . . Symmetric periods are not consistent

with the contrapuntal character of this music." The student

may profitably study this section, and decide for himselfwhetheror not he agrees with Kfenek's methods of melodic analysis.The next chapter, Two-Part Writing, of course brings in

the question of harmony, and here Kfenek gives the followingrules:

1. Octaves and parallel unisons are not allowed (cf. Schoen-

berg's remarks on this, p. 89).

2. The following are consonances: Unison, minor and majorthird, fifth, minor and major sixth.

3. "Mild" dissonances are major second and minor seventh.

"Sharp" dissonances are minor second and major seventh.

4. The fourth may be either consonant or dissonant, dependingon the context.

5. The tritone is neutral, as it divides the octave into two equalparts (cf. Hindemith on this, p. 57).

"Culmination-points", he says, should be introduced "byaccelerated motion and increasing sharpness of dissonances.

Where the composition, however, tends to decrease in intensity,a slowing-down of the motion^ milder dissonances and con-


sonances will be adequate." Personally I do not feel that it is

still necessary to divide chords into consonances and dissonances

Hindemith's table of harmonic tensions seems a moresatisfactory method of analysis (cf. p. 56) nor does Kfenek

attempt to give any explanation of harmonic progressions.The student is, momentarily at any rate, left completely in the

air, with only the sentence quoted above to help him. Andwhy such coyness in the treatment of the perfect fourth?

After a discussion of two-part writing, including imitation,which the student may find useful, Kfenek introduces the

derivative forms of the series (inversion, retrograde and

retrograde inversion), and shows various methods of handlingthem; this again is worthy of study. Next comes a chapter on

three-part writing, which explores the harmonic problemfurther. "Atonality", Kfenek says, "has neither rules for a

special treatment of dissonances (as in Palestrina counterpoint)nor does it formulate a harmonic theory comparable with that

of tonality. The only characteristic of a chord that has to betaken into consideration is the degree of tension that the chordshows by virtue of its constituent intervals." He does notconsider it possible to form as definite a harmonic system in this

style as the rules ofeither strict counterpoint or tonal harmony,"Music written in the twelve-tone technique as well as music

organized by any other principle rests, in the final analysis,

upon imagination and inspiration." But let us first follow

Krenek a little further in his harmonic analysis.

He divides three-part chords into six groups, consisting of:

1. Three consonances (e.g. perfect or augmented triad),

2. Two consonances and one mild dissonance.

3. One consonance and two mild dissonances.

4. Two consonances and one sharp dissonance.

5. One consonance, one mild and one sharp dissonance.

6. One mild and two sharp dissonances.

(In the above the intervals between all and each of the three

notes are of course reckoned in).

Chords containing perfect fourths or tritones may be

consonances or mild or sharp dissonances, depending on the

third note in the chord apart from the fourth or tritone.


E.g. a second inversion ofa triad is consonant; so is a diminished

triad:

Q> Q aba '* n^ * "*" rtfl"^B S8=

J >-ea J^ " 4- -a- -^ ^^ ^- nS1 ^ H^sh. m. cons. m. sh. sh. m. cons. m. sh.

The above classification may be useful as an indication of

relative harmonic tension just as Hindemith's table is; butKfenek quite rightly points out that different inversions of

chords in his Group 6:

Ex. 105

may produce different effects of sharpness or mildness. Similarlythe same chord in the same position may make quite different

effects through variations of dynamics and orchestration. Oneonly has to think ofthe first chord of Ex. 105 played successively

by violins, clarinets and trumpets (and, ifyou like, successively

increasing in loudness) to realise this.

The point about dynamics is one that has been with musicsince the beginning of time; and though dynamics of course

vary the surface colour of a musical progression, they do not in

fact alter the harmonic structure. The other point, regardinginversions, is ofcourse more important; Hindemith, as we haveseen (p. 57) tries to disregard them altogether, but, I think,

mistakenly. It is true that in complicated chords it is not

always easy to recognise inversions as such, or even to see whatthe root is the chord discussed here (Ex. iO5a) consists ofthree equal intervals, and therefore it is impossible to determineits root without the context. But I still think that it is possibleto adhere to the inversion principle in analysing at any rate

SGHOENBERG, TWELVE-TONE COMPOSITION 115

the vast majority of chords, and I hope later to give a practical

demonstration of this.

Having thus presented us with a method of chordal analysis,

Kfenek leaves us to get on with it, making only the sameremark as before (cf. p. 112) regarding the use of sharperdissonances towards culmination, points; he does add however

that consonances "should be used with great caution, for the

same reason that excludes the use of the octave interval. It is,

however, admissible to use such consonant chords occasionallyif the context does not obtrude their latent tonal implications"

(cf. Schoenberg's remarks, p. 98). Kfenek now gives some

practical examples of three-part writing, which the student

should study for himself. He then deals with the grouping of

notes of the series so as to form chords, on the lines discussed

above (p. 1 13). He follows this with a note on the repetition of

chords; this, as we have seen, is permissible if the other parts

sound the remaining notes of the series at the same time.

Ex. 106

Next comes the question of the transpositions of the basic

series and its other forms; Kfenek recommends that these

should not be used haphazardly, but rather according to a

certain plan that emerges from definite musical purposes

(cf. the methods of Schoenberg and Webern quoted above,

pp. 89, 100, 1 06). It is obvious that endless variety is possible

from these means; and Kfenek gives further hints in his final

chapter, "Disposition of Larger Forms," though the pattern

quoted for his use of transpositions of the series in his Piano

Variations, Op. 79, would appear on the surface, at any rate,

to be mathematical rather than musicaL An Appendix deals

with symmetrical series (frequently used by Webern), all-

interval series and symmetrical all-interval series.

Il6 TWENTIETH CENTURY COUNTERPOINT

Though Kfenek's book does little more than scratch the

surface of the subject, it does provide some useful hints for

students, and I would certainly recommend its use as a text-

book for those who will approach twelve-tone writing from a

musical rather than a mathematical point of view. For this

reason I do not propose to include any exercises of my own;but I do repeat that it is useless for a student to handle this

book unless he has a thorough grounding in classical andromantic harmony. That is to say, he should approach twelve-

tone writing from the point ofview that Schoenberg approachedit, from the development of chromatic harmony. (Schoenberg's

Theory ofHarmony1is the best book for analysing this particular

development; but the student should also examine and analysethe works of Liszt, Wagner and Strauss from this point ofview).He will see that a great number of chords used in twelve-tone

music are not very different from those used in chromatic

harmony, but they are used with more freedom that is to

say, with less feeling of attachment to a root. Nevertheless the

feeling of attachment still persists to a great extent, and the

listener cannot help hearing it. Instead of twelve-tone music

floating in a completely non-tonal world, it is rather modulatingrapidly from one point to another (one can hardly talk anymore of "key" in the old-fashioned sense), and the student,with his knowledge ofthe tonal past, should be able to recognisethe points through which it is floating. I hope to discuss this

in a more detailed manner in a later chapter; meanwhile I

would suggest that the student should analyse for himself as

many twelve-tone works by Schoenberg, Berg and Webernas possible, particularly those mentioned earlier in this chapter,

1 The subject is also discussed in considerable detail in Schoenberg's "StructuralFunctions of Harmony" (London, 1954). In the final chapter Schoenberg makessome illuminating remarks about tonality and harmonic analysis in twelve-tone music. The following are significant extracts : "My school does not aim atthe establishment of a tonality, yet does not exclude it entirely. . . . Evaluationof (quasi-) harmonic progressions in such music is obviously a necessity. . . . Butas such progressions do not derive from roots, harmony is not under discussion. . . .

(These progressions) are vertical projections of the basic set, or parts of it, andtheir combination is justified by its logic. . . . There exists no definition of the

concepts of melody and melodic which is better than mere pseudo-aesthetics. . . .

One day the structural evaluation of these sounds will again be based upon theirfunctional potentialities. But it is improbable that the quality of sharpness ormildness of the dissonances which in fact is nothing more than a gradationaccording to lesser or greater beauty is the appropriate foundation for atheory. . . . From such gradations one cannot deduce principles ofconstruction."

SCHOENBERG, TWELVE-TONE COMPOSITION

and thereby gain a practical knowledge of the methods of these

great masters. It is only by studying the methods of the presentin relation to those of the past that one can acquire the

"musicality, taste and imagination" which Kfenek demandsof composers.

1

How can one then sum up the achievement of twelve-tone

music? It is clear that the "emancipation of the dissonance"

has conferred complete harmonic freedom on music, and that

it is now possible to make a free and equal use of all the twelve

notes of the chromatic scale; on the other hand the use of a

serial technique has imposed a control which prevents freedom

from becoming chaos. Further, as we have seen, this methodof control did arise out of compositional practice, and was not

imposed a priori; and it does fulfil a genuine compositionalneed. On the other hand, the fact that composers have recentlyfelt the need to relax some of its provisions shows that it maynot remain as a permanent ideal; all revolutions begin with

rigid precepts which are later relaxed. In particular, the doubt

whether it can really be said to have abolished tonality has led

composers to experiment more and more with the introduction

of tonal elements within its framework; and further, it has not

yet produced a harmonic system to replace the one which it has

dethroned. We are back again then at the crucial question of

tonality, with the problem still unsolved; but we have travelled

a good deal further along the road, for we have found a method

of handling the chromatic scale not only systematically but

realistically in fact a method which has not yet realised its

full possibilities, and may even be only in its infancy, for all

we know. Here at least we have fertile soil; for we have a

completely new and self-contained method of writing with

unlimited capabilities, and yet containing a possibility of

ultimate reconciliation with the past. That reconciliation it is

our task to try and find./JBut before making such an attemptwe may profitably examine the contributions made by some

composers who have worked on more or less independent lines,

and have on the whole not been greatly affected by the various

methods so far discussed.

further valuable information on Schoenberg*s methods and aims will be found

in Josef Rufer's Composition with Twelve Notes (London, 1954)? &** k00^

appeared too late to be discussed in this chapter. It contains some suggestions

for exercises to be worked. .

I

CHAPTER VIII

SOME INDEPENDENTS

FERRUCGIO BUSONI (1866-1924) might alraost be regarded as

the prototype of an independent composer. Of mixed Italian

and Austrian parentage, he spent a good deal of his life touringthe world as a concert pianist; a man of restless and enquiringmind, he absorbed influences from many directions Bach,Liszt and the Italian operatic tradition being prominent amongthese and synthesised them in a number of compositions of

great originality. In his "Sketch of a New Esthetic of Music",

published in 1907, he clearly pointed out the shortcomings ofthe traditional diatonic system; what is the point of

transpositions, he asked, when a piece sounds exactly the samewhen transposed into another key "when a well-known face

looks out ofa window, it matters not whether it gazes down fromthe first storey or the third". And how can one divide con-sonances from dissonances, when we have an octave composedof twelve equal intervals? He worked out 113 different seven-note scales within the compass ofan octave, and also examinedthe possibilities of using thirds and sixths ofa tone. (The wholeof this little book, though it does not claim to lay down anyformal principles, is full of stimulating remarks, and is wellworth reading) .

In his compositions Busoni, though using the background ofthe diatonic system, made within it a free use of chromaticelements. His thought was essentially linear, and most of his

works are not "abstract" music, but aim essentially to conveya mood, picture or idea. Hence his most important work is tobe found in his operas; and these quotations from his last opera,Doktor Faust, may give some idea of his individual methods.

[Ex. 107 and 108, p. 119].

The first is an agitated dramatic passage; the second comesfrom a symphonic interlude (Prologue II). It will be seen thatin the latter, though the thought is certainly linear, the back-

118

SOME INDEPENDENTS

Ex. 107

hJ""n r 173 jsjajE

Ji

t> ~M ri

H I'

Ex. 108

ground is harmonic; but the progressions are of an uncon-

ventional type. The student is also recommended to examine

Busoni's Second Sonatina and Fantasia Contrappuntistica for

piano, which will give a further idea of his tendencies. A full

account of the career of this extraordinary man may be found

in Edward J. Dent's usom9 (London 1933), and there is also

a long essay on Busoni in Bernard van Dieren's Down Amongthe Dead Men (London 1935)-

Van Dieren himself (1887-1936) was an interesting composerwhose tendencies were mainly contrapuntal. Just as Busonfs

Second Sonatina showed him to be going in much the same

direction as Schoenberg's Piano Heces Op. ri (Busoni actually

made a "concert arrangement'* of Schoenberg's Op. n No. 2),

so van Dieren in his early Sketches for piano adopted a more

or less atonal style. Later he somewhat modified this, and his

maturer work, though based almost entirely on chromatic

I2O TWENTIETH CENTURY COUNTERPOINT

harmony, shows much more tonal attachment. Though each

part moves freely and contrapuntally, and often the texture

is extremely complex, as in the "Chinese Symphony", the

actual harmony produced by the movement of the parts is

normally of the Wagnerian "altered chord" type. This is clear

from this extract from van Dieren's setting of Sonetto VII of

Spenser's Amoretti (1921):

Ex. 109

n

SOME INDEPENDENTS 121

Van Dieren was a most cultured and sensitive musician, and nota little of the originality of his music rests in the handling ofindividual instrumental colours. This may be clearly seen fromthe extract above; merely to play it on the piano gives no idea

of the continuous crossing and changing of the parts. Thismethod is in itself an integral part of modern counterpoint;

though, as we have observed, it is not fundamental to the

harmonic or contrapuntal structure, it can make a considerable

difference to the final effect ofa piece. Both Busoni and Schoen-

berg realised this at an early stage, and their methods have hada profound effect on modern music. A more radical use of

this method of splitting up the parts between individual

instruments may be seen in the extract from Webern's

Symphony quoted above (Ex. 93, p. 100). An early exampleof this type of orchestration is of course Schoenberg's First

Chamber Symphony (1906); the student should also examine

Webern's remarkable orchestration of the six-part Ricercar

from Bach's Musical Offering, in which the instrumentation

is continually changing in a kaleidoscopic manner.

Another composer of this period, Karol Szyinanowski

(1883-1937), though not primarily a contrapuntalist, is

interesting in combining the influence of Debussyan impres-sionism with a modern contrapuntal technique. That is to say,

that though his orchestral writing is brilliant and complex, it

often contains a good deal of decoration and accompanimentwhich is not of strictly contrapuntal interest. The passage on

p. 122, the (climax of the slow movement of his SymphonicGoncertante, Op. 60) illustrates this point. [Ex. no].

Here the piano and wind parts decorate the mam theme and

support the harmonies, while a solid bass pedal holds the

structure together. This kind of writing is typical of manymodern works which appear complex in sound, but in fact

rest on a very simple and firmly tonal basis. It would be easy

to multiply examples, as it is a favourite method of manymodern composers, some of whom write even more compli-

cated-looking arrangements of chords but there is nearly

always a firm underpinning, by means of a sustaining note of

some kind, which makes the whole complex easily assimilable.

(For Szymanowski's use of "polytonality" see Ex, 28, p. 33).


Ex. no

Another Slav composer, Leos Janacek, used an almost

exactly opposite method to Szymanowski; primarily a dramatic

composer, he based his style chiefly on continuous repetition

SOME INDEPENDENTS

of short, simple phrases, coupled with striking and unusualeffects. The texture is usually entirely transparent, and thevoice parts follow the natural rhythm of speech against a con-tinuous orchestral background; this passage from his last opera,"The House of the Dead" is typical.

Ex. in

SK. n \nw I'nmEffo-ci vy-pl.ie-M. Ho-din-k, u* Tfo-ci vy-pi.ie-W. Ho-din-k, tj^VV/ 5M *rM -je

-5W..(.. Ei* f*,-fi.fi* ii^-*-d<:

Vic.

Occasionally, however, Jandcek did make use of normal

contrapuntal devices, but always in his own unusual way.The third movement ofhis First String Quartet ("The Kreutzer

Sonata") begins with what looks like a double canon:

Ex. 112

Con tnbto[J

* 5


However, instead of "developing" this in the normal way wesimply have the opening phrase (ist violin and cello) and its

successor (2nd violin and viola) repeated one after the otherseveral times, still in double canon, but in slightly varied forms.

Just before the end of the opening section all four parts take upthe "successor"; but thereafter completely new material

appears, and it is only at the end of the movement that the

opening phrase returns, this time without the canon, thoughits successor remains in canon as before. Yet, though Janacekis certainly not a normal contrapuntal composer, the freshness

and originality of his approach and his directness of musical

speech make him deserving of much more consideration thanhe has so far achieved outside his own country.

Janacek, as we have seen, remained faithful to the tonal,and even in a certain way to the diatonic system, but the

remaining three composers who will be discussed in this

chapter have all in different ways experimented with atonality.None of these however have studied with Schoenberg or anyof his disciples, and they may all well claim to be completelyindependent figures. The oldest of the three was Charles Ives,

(1874-1954), of Connecticut. Working without any knowledgeof Schoenberg's experiments, he produced, chiefly between

1895 ^cl 1916, a number of extremely original works in a

highly complex chromatic idiom which borders on atonality.The following example, from an orchestral suite called "ThreePlaces in New England" written between 1903 and 1914, givesa fair idea of his style.

SOME INDEPENDENTS 1*5

Ex. 113

Ow.tel

It \vill be seen that the texture is consistently polyphonic; the

harmonic style is developed from late igth century chromatic

harmony, but used in a far bolder manner. There is no use of


a serial technique; and in general Ives' music corresponds to,without resembling, the works produced by Schoenberg andhis followers between 1908 and 1923. Another interestingparallel is that though Ives* music is not fundamentallypictorial in character, nearly every work of his is based on a"programme" of some kind, whether it be the description ofa place or person or the evocation of some past or presenthappening; this in some way corresponds to the necessity felt

by Schoenberg during the same period to have the shape of his

works controlled by a literary text. 1 As might be expected,Ives, though regarded with considerable respect in the U.S.A.,did not found a school or system of composition, and remainedan isolated figure.An even more extraordinary personality is Edgar Varese

( 1 885) . He was born hi Paris and underwent a normal academiceducation (Schola Cantorum with d'Indy and Roussel,Conservatoire with Widor) and developed an early interest inold polyphonic music. However, after some years in Berlin andPrague, he went to the U.S.A. in 1916 and has since madethat country his home. He has become known through a series

of intricately written compositions which have made newexperiments in harmony, rhythm and timbre and it is not

surprising that he has devoted a considerable part of his timein recent years to the study of acoustics and of new electronicinstruments. He has always been interested in the nature ofsound for its own sake, and has never let himself be bound byany academic formulae. He has thus created an entirely newtype of music, which is without parallel in our time. Theextract from his Octandre for wind, brass and contrabass is

typical of his methods. [Ex. 114, p. 127],

It will be seen that this is based on (a) the use of extremediscords (groups ofadjacent semitones) constantly and violentlyrepeated (b) instruments constantly changing in compass andoften playing in unusual parts of their compass (c) phrasesconsisting of constant repetition of the same few notes (d) asubtle use ofrhythm. A more complex example may be seen inhis Integrales (1931) for chamber orchestra and percussion.[Ex. 1 15, p. 128].

1Ives also made considerable use in some of his works of hymn tunes and folksongs, often treated in the chromatic style exemplified above.


Ex. 114

C.B.

Here each instrument has constant repetitions of the same

phrase at varying times; the percussion adds further contra-

puntal parts, and the whole is firmly founded on a discordant

pedal for bass and double bass trombone. It must be admitted

that this method of writing is extremely static, and allows

little possibility of development and perhaps for that reason,

most of Varese's pieces are comparatively short. The complexof sound is, moreover, an extremely violent assault on the ears

it can hardly be called "music" in the normal sense of the

word. On the other hand there is no doubt that as a noise it is

extremely powerful and exciting, and it has a kind of "abstract"

quality at the same time which is something quite new in

music. (Stravinsky's "abstraction" usually means meaningless

padding, whereas with Var&se one's attention is riveted

throughout, and every note is there for a purpose) . "lonisation",

for instance, a work for 41 percussion instruments, is an

extremely remarkable study in purely rhythmic counterpoint,

128

Ex. 115

TWENTIETH CENTURY COUNTERPOINT

and holds the attention by its fascinating use of sonorities.What Varese's ultimate contribution to music may be is aquestion that must remain in abeyance for the presentespecially as his more recent works do not seem to be generallyavailable but there is no doubt that in him we have a pioneerwho has added new elements to the musical language.The last of these three independent atonalists1 is Fartein

work of the Czech composer, Alois Haba, lies rather outside the scope ofthis book, as he has mainly devoted himself to writing music in f and 1 tones Hehas however, also composed some works which show an individual handling oftwelve-tone methods, such as the Fantasia quasi Toccata, Op. 38. He has alsobeen an exponent of athematic" writing, and had at one time a considerableinfluence among the younger Czech composers.


Valen [1887-1952], a Norwegian pupil of Max Reger. Forthe last thirty years of his life he composed works based ona serial technique of his own. Though his series normallycontain all the twelve notes of the chromatic scale, he did not

stick to strict twelve-note series repeated round and round;each piece is based on a number of different serial themes

which recur sometimes complete, sometimes in fragments,

Ex. 116


and usually without transposition. That is to say, his use ofseries was at once freer and more "thematic" than Schoenberg's,and he did not normally derive his harmonies from his series*

in fact his methods were predominantly linear, and it is onlyin certain works, notably those for piano and organ, that heused chords as such at all. He made an occasional use ofinversions and mirror forms; here is an example of the formerfrom his Second String Quartet, Op. 13 (published by NorskMusikforlag, Oslo). This movement (which is worth studyingas a whole, for it gives a good idea of Valen's contrapuntalmethods) is written in the form of a fugue; after the fourth

entry of the theme, on the cello, the inversion is heard on thefirst violin, while the accompanying figures are mainly derivedfrom fragments of the theme & typical process with Valen.[Ex. 116, p. 129].

Mirror forms are rarer on the whole, but here is an examplefrom the Kano Variations, Op. 123; the theme consists of atwelve-note series followed by its retrograde form.

However, in the variations which follow the theme is variedand decorated in the usual classical manner, and the accom-panying harmony is not derived from the series.

Valen thus developed a free atonal style of his own, inwhich serial technique provided a constructive element. Butthe effect of his music on the whole is rather static, partlyperhaps because the texture is so continuously contrapuntalwithout any very strong rhythmic impetus, and partly becausethere is a good deal of continuous repetition of themes orthematic fragments without transposition as if all parts movedin an unending ostinato. Nevertheless Valen's sensitive handlingof this linear technique did produce some very successful results,particularly in his orchestral works, where he had the aid of

SOME INDEPENDENTS 13!

instrumental colour. The student is recommended to examinethe scores of "Sonetto di Michelangelo" (Norsk Musikforlag),"La Isla de las Calmas" and the Violin Concerto 'both pub-lished by Lyche, Oslo the latter is also available on NorwegianH.M.V. records). The Violin Concerto in particular makes aclearer use of its thematic material than many of Valen'sother compositions, and is a very powerful and moving work.

Nearly the whole ofthe material is derived from the two openingphrases:

Ex. 118

CHAPTER IX

CONCLUSION A NEW HYPOTHESISBEFORE trying to sum up the lessons which may be learnt fromour survey, I must point out again that I have not attemptedto give an account of what all contemporary composers in all

countries are doing in the field of counterpoint. Such a task,

apart from needing a book several times this size, is not mypurpose; all I have attempted to do is to analyse certain

significant tendencies which have had varying effects on almost

all modern composers, and I do not imply that the composersmentioned in this book are better as composers than those whoare not. The former are discussed here because they exhibit

certain tendencies in an easily appreciable form; many of the

latter also exhibit the same tendencies, but hi most cases theyhave inherited these from the original pioneers in the field and

adopted them to suit their own personalities and methods of

expression. The music of Vaughan Williams, for instance,

becomes easy to analyse when we realise that it is mainly based

on the use of (a) modal scales derived from mediaeval andfolk music (b) block chords moving in parallel (cf. the quotationfrom Petrouchka, Ex. 16) and (c) polytonality (Flos Campi,Pastoral Symphony; cf. Chapter IV). But though VaughanWilliams has invented no specifically new technique, that does

not affect his stature as a composer; Mozart was a greater

composer than C. P. E. Bach, but C. P. E. Bach was a pioneerof the style in which Mozart wrote. This survey, then, is

solely concerned with the assessment of new techniques as such,and with the evaluation of general tendencies; and the student

should be able, by comparing the examples given here with the

works of other composers, to see what use the latter have madeof the principles here enunciated, how far they have followed

them and how far deviated from them. I have no wish to

labour this point; I feel there is no need for me to make a

catalogue of composers by schools and influences the student

may (ifhe feels inclined) undertake this task himself.

132

CONCLUSION A NEW HYPOTHESIS 133

This having been said, we may now see what conclusions,if any, can be drawn regarding the present and future develop-ment of music, and whether it is possible to outline a system ofharmonic and contrapuntal rules for it. At first sight this mightseem impossible in view of the chaotic complex of opposingtendencies which contemporary music appears to present.As we have seen, this is mainly due to the disintegration of theold rules of harmony through the breakdown of the diatonic

system; but further factors have entered in through the in-

creased complication of musical texture. This was partly dueto the greater virtuosity in orchestral playing which becamepossible during the nineteenth century; just as Paganinirevolutionised the technique of the violin and Liszt that of the

piano, so Berlioz5

orchestral writing introduced new effects ofsound which could only make their mark if played by theinstruments for which they were intended, and became mean-ingless if transcribed for another medium. (One has only tothink of the flute and pedal trombone chords in Berlioz'

Requiem to see the point of this). This tendency was carried

successively further by Liszt, Wagner, Strauss and Mahler,until we reach examples of the complexity of the Szymanowskiand Ives quotations above (Ex. 1 10, p. 122 and Ex. 1 13, p. 125).It tends increasingly towards the use ofsound purely for its ownsake, without any harmonic and contrapuntal control of theolder sort. (Gf. also Debussy's impressionistic effects in La Merand the orchestral Images, for instance).We are thus confronted simultaneously with a breakdown of

harmony and an ever-increasing complication of surface

texture. And an even more serious consequence of the break-

down of harmony is that it undermines the foundations of the

musical structures which were based on the diatonic scale

the sonata form, rondo, fugue etc. All these were based on the

contrast between a main tonality and its nearer or remoter

neighbours; if tonality is removed, how can one continue to

use the form? The Schoenbergian transpositions of the note-

series do not help in this matter, for they axe not really felt as

"modulations", in spite of the efforts of Schoenberg, Webern,and others to create a new sort of tome-dominant relation

Schoenberg by his use of the original series combined with its

inversion a fifth lower, and Webern by his employment of theK


tritone as a kind of dominant. Nevertheless, composers havecontinued to use the old contrapuntal forms as representingsome method of imposing order on chaos but the canons of

Webern, for instance, are more noticeable to the eye than the

ear, however exquisite their musical result may be. What would

appear to have been the logical solution to the problem, the

Lisztian system of transformation of themes in the symphonicpoem, has fallen into disrepute; perhaps because Liszt wasrated more highly by his contemporaries and successors for his

pictorial imagination than for his symphonic construction

(which admittedly could often be weak), the form he devised

degenerated1 into the pure impressionism ofDebussy and others

and the "Fantasies" of the older generation of English

composers.This system of"thematic transformation" is ofcourse very akin

to the methods of Schoenberg and his followers and in EnglandAlan Bush uses a similar system, though not based on twelve-

note series. The difference between Liszt's and Schoenberg'smethods (apart from the question of tonality) is that Liszt's

themes are recognisable as such in their various transformations,whereas Schoenberg's note-series are not necessarily so. In fact

the tendency of a good deal of modern music is towardsathematism and the avoidance of repetition of any kind; whichcan of course be combined with the use of a note-series whichis there as a unifying background, but is not consciously heardas a theme.

Theme, no theme or transformations of theme? That is oneofthe problems ofmodern music; and another is the question ofmovement from one musical region, to another. This is the wholebasis of the diatonic system one has only to think of the

wonderful effect of Schubert's modulations to see that. Busoni

may have been logically right to say that a face seen at onewindow does not differ from the same face seen at another;but he would not be right to say that dress makes no difference

to a woman's appearance and the position with the diatonic

system is more like that. On the other hand chromatic musicwhich is modulating so constantly that it gives us little or nosense of position has little or no feeling of movement either;it can indeed be dramatic, lyrical, expressive and moving,

1I am speaking here of form, not of music per se.

CONCLUSION A NEW HYPOTHESIS 135and often is but does it always give a sense of direction? Indramatic works, such as Berg's Lulu, the alliance of words andmusic does help to create a directional feeling; but this cannotbe done by transpositions of the note-series alone.As we have seen, Schoenberg latterly admitted the pos-

sibility of "tonal references" in twelve-tone music, providedthat they are "not in a position to transform the non-tonalstyle into a tonal style." This rather careful point ofview wouldseem to date back to the early days of atonality, when, in orderto complete the break-up ofthe diatonic system, tonal referenceswere deliberately avoided. But now that the diatonic system hasdefinitely been dethroned in favour of the chromatic system(by which I mean not atonality, but the free use of all thenotes of the chromatic scale in relation to a tonal centre), is

such caution still necessary? And is it really always necessaryto play every note-series complete and always in the same order?The fact that twelve transpositions of each of the four forms ofthe series are always available means that it is easy'to introduce

any notes one wants at any given moment by using one orother of these forms; but one may not want thereafter to usethe whole of the rest of the series thus introduced, and in that

particular order ofnotes. The experiments made by Schoenbergin some of his later works (consistent use of certain intervals

loosely based on a series in the Ode to JfcpoLox, variation ofthe order of notes within six-note groups in the String Trio)seem to foreshadow new possibilities which other composersmay exploit further.

I hesitate to add yet another to the numerous systems andmethods employed by present-day composers; but I would like

to suggest a possible method ofanalysis which may be applicableto most types of modern music. It is clear that what is neededis some system of classifying harmonic relations; admittedlythis book is intended primarily as a study of counterpoint, butto study contemporary music purely from the horizontal

point of view would merely give the impression that no holdsare barred and that any part can do anything it likes against

any other part. It is clearly only possible to see what is in fact

happening by using some method of harmonic analysis, i.e. bystudying the vertical complex produced by the movement ofthe various parts.


What we need then is (i) a means of analysing chord-

structures (ii) a method of determining the relative value of

root-progressions. For neither of these do I suggest anything

spectacular; in fact I think it is best to depart from a traditional

viewpoint, and to analyse chords as far as possible according

to the traditions of classical harmony. After all, music still

remains based on the harmonic series, which is a fundamental

law; we are merely making more use of notes higher up in the

series at the expense of those nearer the fundamental. If weturn back to Hindemith's chordal progression (Ex. 53, p. 62)

we can perhaps see a method of applying this. The first chord

can be analysed in two ways: (i) as a first inversion ofA sharpminor (B flat minor) with two added notes (flattened fifth,

Efcj, and flattened seventh (G#), or (ii), as Hindemith prefers,

root position of C sharp, with both major and minor thirds

(Etj and E#) and added sixth (A#). The latter explanation

certainly puts the chord on a more solid basis, as being a root

position, but historical tradition would probably favour the

former, regarding the so-called "added sixth" as one of the

inversions ofa seventh chord (6/5) . Here then, at the very outset,

we are confronted with a chord capable ofbearing two different

interpretations, which shows us that our task will not be an

easy one; but there is no need of great alarm, as many such

chords with double meanings can be found throughout classical

and romantic harmony. Then- meaning may be decided by- the

general tonality of the passage, sometimes by the theme they

accompany, or by the root progressions many hi fact are

deliberately treated as "pivot chords", being introduced as

bearing one meaning and left with the meaning changed

(e.g. the use of the so-called French, German and Neapolitansixths in igth century modulations). In this case, however, there

is no change of tonal region, A sharp being the relative minorof C sharp.We must then consider if the root-progression will help us.

In his Harmonielehre (German ed, p. I4off) (English ed, p. 6gff )

Schoenberg gives some rules on this subject for diatonic

harmony which may well be expanded to suit chromatic

harmony. The following are "rising" or strong steps: fourth

upwards, third downwards; "falling" or weak steps are fourth

downwards, third upwards. Seconds upwards or downwards

CONCLUSION A NEW HYPOTHESIS

are "super-strong" steps, for they consist in essence of two

strong steps (see loc. cit. for a fuller explanation of the

theoretical basis of this). The step which has the most powerfuleffect ofall is the rising fourth (or falling fifth) ,

for it correspondsmost closely to the harmonic series; next after it in power is

the falling third (or rising sixth). The step of the second, though

superstrong by nature, has not in fact such a powerful effect,

simply because it is too strong for everyday use: "Allzu Scharf

macht schartig" (Too sharp makes notches), as the German

proverb goes.If we adapt these principles to chromatic harmony, we get

the following results:

Ex. 1 19

Strong

:II .P^TTT^ i. u~ =z===^==^-JiK>-4^ "

. . U vII

-" bii OC iir i*J I

"'Z^Zfl

-<or

-Q-

Neutr*.l

-*m

(The step ofa tritone remains neutral, as we have seen before;

it divides the octave into two equal parts, and therefore

neither rises nor falls). Schoenberg recommends a judicious

mixture of strong and weak progressions; not too many strong

ones in succession (and especially not too many superstrong

ones) , and weak ones to be used sparingly, chiefly in conjunction

with strong progressions (see loc. cit. for further details). All

of this still applies in chromatic music to a considerable extent;

so let us return to the Hindemith progression (Ex. 53) and

see if it helps us.

We are still doubtful if the root of the first chord is A sharp

or C sharp; the root of the second is certainly B, as Hindemith

states (B minor chord with both flattened and sharpened

seventh, A and Bb) so the root-progression does not help us

here, being a super-strong step in either case. Let us then leave


this question for the moment the general tonality of the

passage will probably help us to decide this in due course andcontinue with the analysis of the remaining chords.

The root of the third chord is given by Hindemith as Gsharp, on the strength of the fifth G#-D# in the middle of it.

This does not strike me as possible, as the remaining notes all

contradict this interpretation the bass note is Bb (A sharp)which is the "supertonic" in old-fashioned parlance, and the

others are the augmented fourth (D) and the minor sixth

(E). Two alternatives are preferable E or Bb; the latter has

the advantage of being the bass note, which always tends to

preponderate, and in that case we should have a B flat chord

containing major third, perfect fourth (D#), diminished fifth

(E) and flattened seventh (G#). Ifwe take the root as E, whichwould probably be the "classical" method ofanalysis, we should

have major third, diminished fifth (Bb), and both major andminor sevenths (D# and D); in favour of this is the movementof the root a fourth upwards from the previous chord (B E) .

This chord too, then, is doubtful; it is based on two pairs of

major thirds a tritone apart (Bb-D, E-G#), and therefore wecan only decide its root from the remaining note in the chord

(Dfl) and the root-progression in general; let us therefore notethe alternatives (Bb and E) and return to it later.

The root of the fourth chord is given by Hindemith as A,and this is probably correct; in this case it would contain both

major and minor second, perfect fifth, and minor sixth. Theonly alternative is B flat the third inversion ofa major seventh

with B flat as its root but the Bfc] and Etj are against this

interpretation. (It should be remembered, however, that if

arranged for orchestra this chord could be scored in such a

way that the Bb would predominate and thus alter its whole

efiect).

The root of the fifth chord is certainly G, as Hindemithstates; in the old days it would have been known as an eleventh.

I feel, however, that Hindemith is wrong in calling the root ofthe sixth chord Eb; it is surely an Ab chord with Bb as appog-giatura for Ab and Etq for Eb. The seventh chord he correcdybases on Eb, with augmented fourth, perfect fifth, majorseventh and minor ninth (or minor second, if you prefer) ;

Chord 8 is merely another position of Chord 5 and is of course


based on G; and Chord 9 is a triad ofA flat minor. Our analysisthus gives us the following root-progression:

Ex. 120 12345

The general tonality is Ab; and therefore it would appear more

logical to regard Chord i as based on C sharp (Dj>), especiallyas this makes it a triad in root position. As regards Chord 3,

obviously it is better from the point of view of root-progressionto regard the root as E, which gives us the best type of strong

progression (root moving upwards a fourth) between Chords

2, 3 and 4; if we take Bb as the root we have nothing but

superstrong steps from Chords i to 6. A further factor is that

the major seventh E-D# acts as a better limiting or definingelement than the perfect fourth Bb-D#, which tends to suggestthe tonality of Eb-

I am aware that the above method of analysis is open to

criticism, but I think it better to advance slowly and cautiously,

recognising our difficulties as we go, rather than to impose a

preconceived scheme which may not be in accordance with the

facts of the case. The progression analysed above is of course

not a very "good" one musically, as Hindemith justifiably

remarks, but it will serve as a starting point.

Let us now examine a simple example from twelve-tone

music, the main theme of Schoenberg's Wind Quintet (Ex.

66, p. 84). I would analyse the root-progressions as follows:

Ex. 121

The first chord ofbar i is clearly based on E; the movement of

the bass to F# on the fourth beat, together with the D and Ahi the upper parts, clearly indicate D as the next root. The

root on the fourth beat of bar 4 is more debatable; the C has

entered on the third beat as a minor seventh above the root

D, and the appearance ofEb and G under it could be construed

I4O TWENTIETH CENTURY COUNTERPOINT

as Implying a classical 6/4 chord; but this is soon negatived

by the entry of the lower parts on A and C#, building up the

neutral chord consisting of two major thirds a tritone apart,

which has two possible roots, A and Eb- It is only in the middle

of bar 5 that C emerges as the root of this chord, confirmed bythe Bb and D in the top part. (Incidentally in the "neutral"

chord above, Eb is clearly preferable to A as the root, both

through the context and as giving a stronger root-progression.)The passage is not of course long enough for us to be able to

place it in a definite tonality.

The next quotation for the same work (Ex. 67) gives aneven clearer example of tonal implications within a twelve-tone

framework. I would suggest the following analysis of the root-

progressions:

Ex. 122

It will be seen that this gives a succession of descending thirds,

all strong steps, and very much in the classical tradition.

In the following example (Ex. 68) the harmonic basis is also

perfectly clear, as follows:

Bar Root

1-2 Eb3-4 Db5-6 B(7 D)89 Ab

Again we have a series of superstrong and strong steps, if wedisregard the preparatory D in bar 7. The student may nowattempt the analysis of some of the other Schoenberg examplesgiven in this chapter, and see what he makes of them. He mayfor instance, study the theme of Schoenberg's Variations for

Orchestra (Ex. 77, p. 90) ; here he will find constantly changingroots, e.g. Bars 34-5, G-C; bars 36-37, E-Bb; bars 39-40, Camounting to a kind of 6/4 chord; bars 41-42, A~D; bars

43~45> Bb, etc. In fact, instead of regarding this type of writing

CONCLUSION A NEW HYPOTHESIS 14!

as having no tonality at all, it is truer to say that it is constantly

moving from one point to another within the twelve-note scale.

Whether such a passage as a whole can be said to have a general

tonality will of course depend on the root-successions; this

theme has a definite ending rooted on B (bars 56 -7), but one

certainly could not say that the whole theme is "in" B; B is

merely the final point of rest. (Of. also the analysis of a passagefrom Schoenberg's Op. 33a, p. 67 above).We are thus approaching a new conception of tonality in

which root-progressions move freely within the twelve-note

scale, not following the classical laws of preparation andresolution (in most cases the resolution of what would be a

discord in traditional parlance is simply taken for granted and

omitted) but still governed by the old principles of strong,

superstrong and weak progressions. Note for instance, as a

further example, the series of root-progressions hi the firat half

ofEx. 77 G, G, E, Bb, G, A, D, Bb respectively strong, weak,neutral (altering the significance of a held chord), superstrong,

and three successive strong progressions. What could be nearer

to classical procedure? We may then lay down then as a

provisional method of analysis for predominantly harmonic

passages (i) find the root note of each chord, which will

normally be the same as in the traditional method of analysis,

and (ii) set out and analyse the root-progressions. From these

it will be possible to discover the general tonality of a passage

or a piece if any; for a composer, whether he uses twelve-

tone methods or not, may engender a general feeling oftonality

by emphasising one particular root note, or he may avoid it

as far as he can by using as many different roots as possible.

I am certain that it is by this means that tonality is suggested

or avoided, and not by the mere use of note-series, which of

themselves neither engender nor suppress tonal feeling.

Let us now see if this method can be applied to predominantly

contrapuntal passages. We will take a simple example first,

the quotation from Bart6k's ist Quartet (Ex. 37, p. 45>- Here

we have music moving chromatically in four parts; the roots

are as follows:

Bar i

Roots F Ab E (Ab) Bb F3 4

B G (Bb) I (E) etc,


The roots in brackets in bars 2 and 3 are used only in passing.It will be seen that a good many of the progressions are weakones, which may account for the slightly indeterminate effect

of this passage, as well as the fact that the music is constantly

moving from one point to another.

A more complex example may be seen in Ex. 80 (from

Schoenberg's Variations for Orchestra). In the first half barthe successive E, Bb and Gff suggest E as the root of a"dominant" chord of A; but this is immediately contradicted

by the Gfc] which is clearly the root of the first half of the next

bar; C and D are the roots of the third and fourth quaversrespectively, though on the last semiquaver the bass has

already moved to B.

Ex. 8 1 also presents some complications. We may take theroots of the first two semiquavers as C# and B, and of the third

and fourth as F; but the second group is not so easy. Though the

main tonal centre is E, the roots of the individual semiquaverswould appear to be E, G, B and G; so that we are back at the

old classical concept of *

'inessential" or "passing" notes, but in

a different form.

Our next examples are taken from Webern (Ex. 93 and 94,

pp. 100-1). Here tonality is so attenuated that it is very difficult

to give any analysis of root-progressions, especially in Ex. 93.A style which is based to a large extent on the use of adjacentsemi-tones and which also contains so few actual notes marksthe nearest approach to atonality that we have yet met. At thebest one can say that the roots are constantly changing a

possible scheme might be as follows:

Bar 2 3 4 56 7 8 9 10 n 12 13 14 15

Roots F# G Ab B Bb C Bb G D F D G EBut I admit that such an analysis is by no means satisfactory.

Ex. 94 is not quite so complex. Bars 1-2 are rooted on B,which acts as a kind of "dominant" to the E of bars 3-4.Bars 5-7 alternate between Bb and E the "neutral" tritone

again ending on E; in bars 8-9 we have successively C, F#(tritone again) and D, acting as "dominant" of the G which is

the root of bars 10-1 1; so here the root-progression tQQa symmetrical shape.


As a final example let us take the passage from Valen'sSecond Quartet quoted above (Ex. 116). Here there is a use ofa various ostinato-like figures which somewhat confuse thepicture; but one can say that the main root of bar i is

E and bar 2 B; in bars 3-4 we move from A[> (G#) viaG and D to Bfr. Admittedly this sort of music is difficult to

analyse from a tonal point of view, as there is a considerableuse of what one might call "inessential" notes; but if one cankeep the main lines of the harmony clear, it is not difficult todiscover the root-progressions.

I do not think it is necessary to continue to give further

examples, as I hope the method of analysis will be clear bynow, and the student may amuse himself by applying it toother examples in this book. The chief principle is of course todiscover the main harmonic complex, strip it of its inessentials,and discover its root. The root may not necessarily be in the

bass, though it very often is; the presence of a fifth or fourth inthe chord may be a help to its discovery, but this cannot be

applied as an automatic rule in the manner of Hindemith,as we have seen. It is a question mostly of common sense andexperience, but I think it can produce useful results if properlyapplied. In very complex combinations, such as the Milhaudexamples above (Ex. 33-35) it may be necessary to find the

predominant chord or note, and derive the root from that

e.g. B in Ex. 33, C# in Ex. 34, E in Ex* 35. 1 fear that I cannotbe more precise than this; the subject is an enormous one, andhas not yet been folly explored by any means.

It should be emphasised that the root notes in themselves donot always add up to a general tonality; as we have seen, it

is up to the individual composer to decide how much or howlittle tonal feeling he wishes to present, and he does this by his

handling of the root progressions. If, as in Webern, his roots are

constantly changing, and are accompanied by other notes which

sharply contradict them, he will approach very close to true

atonality. We can certainly accept a table of the type of

Hindemith*s Series 2 (Ex. 51, p. 56) as showing the relative

degree of tension (or "dissonance" in traditional parlance) in

various intervals, and the more intervals contained in achord or harmonic complex which appear towards the left-

hand side of this table, the easier it will be for us to analyse it


by traditional methods. We must however extend our theoryof traditional harmony by admitting the emancipation ofthe dissonance and removing the traditional distinction betweenconcords and discords; intervals in a chord which are further

to the right of our table may be less consonant or less essential,but they are not dissonant or inessential. Nor does this implythat the major triad is the "best'* chord musically; it is certainlythe nearest to the harmonic series, but we may not want to

stick to the harmonic series. It is purely an aesthetic matterwhether we use more concordant or less concordant material;all one asks is that each piece of music shall be consistent withitself. One cannot lay down any formulae for artistic values;one can merely analyse technical processes and try to see howthey work.

Similarly, though we cannot speak any longer of dominants,subdominants, mediants, etc., we do have a number of roots

in each piece which may revolve round a main tonal centre

or may move freely from one point to another; or one can of

course combine both methods, i.e. having a main tonal centre

which is only stressed at crucial points, with the roots movingfreely in between these. These roots now move within a twelve-

note instead of a seven-note scale, but the relations of the roots

to each other still remain the same, as we saw in our discussion

of strong and weak progressions; and the strongest progressionis still that corresponding to the old dominant-tonic step

(V-I). It does not matter if both the "dominant" and "tonic"

chords contain innumerable altered or additional notes the

underlying movement is still there. So that in a sense there is

no real division between the different methods used by con-

temporary composers; some ofthem have a "main root" which

they exalt by repetition or other means of emphasis into

becoming a "tonal centre", while others do not.

Most composers do not, I imagine, consciously analyse their

roots when they are writing music; their unconscious ear,trained in the classical past, will help them to produce theresults they want. Nevertheless the study of root-analysis will

show us how to produce effects which many people complainare missing from the music of today; one can emphasise oneroot as a tonal centre, perhaps leaving it for short stretches

and then returning to it; then a decided move to and dwelling


on another root will give an effect comparable to modulationfrom one diatonic key to another no matter how chromaticthe complex above each root may be. Admittedly the morechromatic the complex is, the more it will contradict the root;but this method of procedure is at any rate possible, and weat any rate know the relative value of the different root-

progressions.Can we also retain the old forms, sonata, fugue, rondo, etc.,

which depend on modulation? It can, I think, be done, thoughmodulations of this kind will not perhaps have the incisiveness

or effect of the classical modulations, simply because they are

likely to be carried out with more complex means; but in

theory they are certainly possible. But I think also that the

freer forms engendered by the Lisztian transformation of themes

may have a good deal to offer us; ifwe can forget the pictorial

associations which they were given by nineteenth-century

composers and treat them organically, as Liszt did in his piano

sonata, for instance, we may find that new possibilities are

opened up. Personally I feel it is better to control our material

itself and enlarge the forms rather than to put into the tight

framework of the canon and fugue a type of music for which

they were never designed.Our last point concerns melody; if we have found some

glimmerings of a method of evaluating the vertical basis of

contemporary music, what about the horizontal? Here againwe have tradition to guide us; the traditional values of the

different intervals are not necessarily upset by the more

complex system ofharmony in which they partake, and we can

still hear a melody in relation to the root ofthe chord or complexin which it participates. The relations between a melody and

its accompanying harmony may have become more abstruse,

but it is a question of degree, not of a fundamental revolution.

And this brings me to my conclusion; the fundamental basis

of music is still the same. The harmonic series is still there,

however much we get away from it, and it remains a strong,

unseen power in the background. We are perhaps making

less use of its fundamental notes and more of those that come

higher in the series; but the fundamentals are still implied,

and all that we are doing is to work at a remove from them.

I believe therefore in the free use of all the twelve notes of the


chromatic scale; I also believe that every harmonic and contra-

puntal complex contains a root note which can be discovered.The root note may lie still for a long time or it may changerapidly; and the more any one root note is emphasised themore "tonal" will the music sound and vice versa. "Tonality"and "atonality" are thus questions ofdegree, not offundamentaldifference; the consistent and equal use of all the twelve notesof the scale can still produce a feeling of tonality if required.Music cannot get away from its roots, and it is through thevariation in the movement of its roots that it produces its variedeffects. If in this survey I have concentrated on the moreextreme and chromatic handling of the roots, it is becausethis is the most difficult to analyse and reconcile with thetraditional and historical past. But though music may haveits revolutions, it is also fundamentally an evolutionary art,and if I have helped to show that the same forces whichgoverned its processes in the past are still at work today, albeitin a substantially different form, I shall have achieved mypurpose.

POSTSCRIPT, 1954

THIS book has been some time in the press; and corr.scsitio:: has

naturally not stood still during this period. Schoenberg has died;and the remaining three leading figures of the old guard of

revolutionaries Stravinsky, Milhaud and Hindemith havenot shown any signs of launching out in new directions, apartfrom some use of a serial technique (of a kind) and a Webern-like texture in some recent works of Stravinsky, like the Septetand the Shakespeare Songs. Meanwhile the younger com-

posers have been consolidating the territory first explored

by their predecessors; here again there has been no specificallynew development apart from one which affects a number of

the younger twelve-tone composers, and which appears to

contradict my statement in Chapter VII that Webern is

unlikely to become "the direct ancestor of a new techniqueof composition." A group of young composers, all at presentin their twenties, and belonging to several different countries,

are experimenting with a style which clearly steins from

Webern's later technique; they are, however, attempting to

carry this further by a much more complex use of rhythm and

sonority, in some cases based on mathematical principles; that

is to say, they appear to be aiming to impose the same type of

formal control on the rhythm, tone-colour and pitch of the

music as the twelve-tone method imposes on the notes them-

selves. A typical example is taken from the "KontrapunkteNo. i

"by the young German composer Karlheinz Stockhausen

[Ex. 123, p. 148]. (The ties over the bar-lines indicate that the

notes are held on). It will be seen that this is pre-eminently

contrapuntal, and the student may be interested in seeing

how the note-series run through the different instruments.

Other composers who are tending in this direction include

Pierre Boulez (France), Luigi Nono (Italy), Giselher Klebe

(Germany) and Jacques Wildberger (Switzerland). It is

obviously too early to make generalisations about a movement

which is as yet only in its infancy, but certain points can be

47

POSTSCRIPT, 1954

VI*.

(N.B. All notes sound as written.)

noted regarding this style. Tonality is clearly avoided as

rigorously as possible, rhythm is dislocated to the utmost(Stockhausen's "Kontrapunkte" contains several passages ofeven greater rhythmical complexity than the one quoted here),

POSTSCRIPT, 1954 149

there is no question of the use of themes longer than small

motifs of the type seen above, and isolated notes provide the

main basis of the music; in addition there is a tendency to use

the extreme registers of the instruments as much as possible

(cf. Varese's methods) and also to pass rapidly from one

extreme to the other the trumpet part seen here is a good

example of this. The difficulty of this sort of music is to avoid

lack of continuity; it is hard to see any overall form or designin many of the works in this style, though each individual

passage is logically constructed within itself. That is to say,

the music gives a predominantly static effect, and one cannot

feel that it is normally aiming towards a goal or conclusion.

However, there is no doubt that it presents some new elements

from the technical point of view, and its future developmentwill be interesting to watch.

Finally, I should mention the appearance of an important

analysis of Schoenberg's methods by his pupil and assistant

Josef Rufer, Composition with Twelve Notes (Rockliff, London

1954). This may be regarded as the authorised exposition of

"classical" twelve-tone technique, and it also discusses the

innovations made by Schoenberg in his last works. Unfor-

tunately its publication came too late for it to be discussed in

the main body of this book, but its contents may be briefly

summarised here. After chapters devoted to general theoretical

discussion and to an account of the break-up of the major-

minor tonality, Rufer deals with the concept of the Grundgestalt

(literally, basic shape) : this is the musical phrase which is the

basis ofeach work and is its "first creative thought", in Schoen-

berg's words from it everything else in the work is derived,

including the series itself. This concept applies equally to

classical music, and Rufer shows how all the elements in Beetho-

ven's Sonata Op. 10, No. i are derived from the Gnmdgestati

in its first four bars. Rufer then deals in detail with Schoenberg's

"transitional" works, Op. 23 and 24, before giving a full

account of the principles of twelve-tone composition itself:

in this chapter he discusses whether it is legitimate to base a

work on more than one series, and whether twelve-tone music

should tend towards athematism, as has been suggested by some

writers. He next describes the special uses of melody, harmony

and rhythm in twelve-tone music, and gives a detailed exposi-

POSTSCRIPT, 1954

tion of Schoenberg's methods of inventing thematic material

from a twelve-tone series: the final chapter deals with problems

of form, including an analysis of Schoenberg's Fantasy for

violin and piano. Op. 47. The whole book is a most valuable

account of Schoenberg's own approach to the subject, in both

theory and practice: an appendix is contributed by a number

ofcontemporary composers, describing their individual methods

of twelve-tone composition.

SELECT BIBLIOGRAPHY

Books and articles on contemporary music are legion I

have only chosen those which are likely to be of most use to

the student. As far as possible, all are written in English,

though in certain cases, where no other equally valid sources

are available, I have mentioned books in French or German.

They are arranged in the order ofsubjects discussed in this booL

General

ABRAHAM, GERALD. This Modern Stuff. London 1939.

GARNER, Mosco. A Study ofzoth Century Harmony. London 1942.

DYSON, SIR GEORGE. The New Music. London 1924.

GRAY, CECIL. A Survey of Contemporary Music, London 1924.

LAMBERT, CONSTANT. Music Ho/ London 1934.

MELLERS, W. H. Studies in Contemporary Music. London 1947.

MYERS, ROLLO H. Music in the Modern World. London 1939.

PISTON, WALTER. Counterpoint.

SLONIMSKY, NICHOLAS. Music since igoo. New York 1949.

Stravinsky

STRAVINSKY, IGOR. Chronicles of my life. London 1936.

Poetics ofMusic9 London 1947,

WHITE, ERIC WALTER. Stravinsky. London 1947.

Milhaud

BECK, G* L'Oeuvre de Darius Milhaud. Paris 1949.

COLLAER, PAUL. Darius Milhaud. Brussels 1948.

MILHAUD, DARIUS, Notes sans musique. Paris 1949.

Bartok

HARASZTI, EMIL. Bela Bart6k. Paris 1939 (in English).

MOREUX, SERGE. Bela Bart6L London 1953.

STEVENS, HALSEY. The Life and Music of Bela BarttL London

1953-

152 SELECT BIBLIOGRAPHY

Hindemith

HINDEMTTH, PAUL. The Craft of Musical Composition.

Vol. I, Theory. London 1945.Vol. II, Exercises in Two-Part Writing. London 1948.

Twelve-Tone Music.

KRENEK, ERNST. Studies in Counterpoint. New York 1940.

LEIBOWTTZ, RENE. Introduction d la musique de 12 sons. Paris 1949Qu'est-ce que la musique de 12 sons? Li&ge 1948.

Schoenberg and his School. London 1 954.NEWLIN, DIKA. Bruckner , Mahler, Schoenberg. London 1947.

REICH, WILU. Alban Berg. Vienna 1937.*

ROGNONI, LUIGI. Espressionismo e Dodecafonia. Turin 1954.

RUFER, JOSEF. Composition with Twelve Notes. London 1954.

SCHOENBERG, ARNOLD. Harmonielehre. Vienna 1921*

Theory ofHarmony.* New York 1948.

Style and Idea. London 1951.Structural Functions of Harmony. London 1954.

STEIN, ERWIN. Orpheus in New Guises. London 1953.

WELLESZ, EGON. Arnold Schoenberg. London 1924.

Independents

BUSONI, FERRUCCIO. A New Esthetic of Music. New York 191 1.

Von der Einheit der Musik. Berlin.*

DENT, EDWARD J. Ferruccio Busoni. London 1933.VAN DIEREN, BERNARD. Down Among the Dead Men. London 1935.AP!VOR, DENIS. Bernard van Dieren. Music Survey. Vol. Ill, No. 4.

JACHIMECKI, Z. Karol Szymanowski. London (School of Slavonic

Studies).

MULLER, DANIEL. Leos jfandcek. Paris 1930.

BELLAMANN, HENRY. Charles Ives. Musical Quarterly, Jan. 1933.GoWELL, HENRY. Charles Ives. Modern Music, Nov. 1932.HELM, EVERETT. Charles Ives. Musical Times, July 1954.

COWELL, HENRY. The Music of Edgar Varise. Modern Music,Jan. 1928.

KLAREN, J. H. Edgar Varese. Boston.

1Tbis, unfortunately, is only a translation of extracts from the Harmonielehre;

most of the important theoretical discussions are omitted.

^English translation in preparation.

DISGOGRAPHYA GOOD many records ofcontemporary music are now available,especially in the United States since the advent of the long-playing record. These are useful adjuncts to the study of theworks discussed in this book, but the student is recommendedto follow them with the score where possible. The followinglist does not pretend to completeness, and should be supple-mented by enquiries at gramophone shops etc. regarding up-to-date recordings

1. (N.3B. LP = long playing, 33 r.p.nu All

other records mentioned are 78 r.p.m.)

StravinskyMost of Stravinsky's major works have been recorded, and are

readily available, both on 78 and 33 r.p.m.

MilhaudLa Creation du Monde (Columbia)Miniature operas (Columbia)Extracts from the Oresteia (including Les Eumenides) (Fr.

Columbia)Nos. i, 2, 3 and 5 ofCinq Symphonies (Concert Hall, U.S.)

Suite, Protee (Victor)

Bart6k

A good deal of Bartok has been recorded, including all 6

quartets (U.S. LP; some also available on 78 r.p.m.). Musicfor Strings, Percussion and Celesta, Violin Concerto, PianoConcerto No. 3, Concerto for Orchestra, Sonata for 2 pianos and

percussion, and a series made for U.S. LP. in collaboration

with the composer's son, including The Wonderful Mandarin,Two Portraits, Dance Suite and Viola Concerto.

*The Record Gwdc, by Edward Sackville West and Desmond Shawe-Taylor(London 1951), together with all its regular supplements, provides an up-to-dateguide to records available in Great Britain. Exhaustive information about all

types of records will be found in Clough & Cuming's The World's Encyclopaedia,

ofRecorded Music (London 1952), which is also kept up to date by regular supple-ments.

153

154 DISCOGRAPHY

Hindemith

Here too, a certain amount has been recorded, of which themost important is the Mathis der Maler Symphony (Telefunken-

Decca), and some of the chamber works.

Schoenberg

Verklarte Nacht (HMV and Capitol LP)Pelleas and Melisande (Capitol LP)Gurrelieder (HMV)Chamber Symphony No. i (French Classic)Pierrot Lunaire (U.S.)Piano Pieces, Op. n and 19 (Danish HMV)Quartets Nos. 1-4 (U.S. LP)Ode to Napoleon (Esquire-Classic)

Complete Piano Works (Esquire LP)Serenade (U.S. LP)Suite Op. 29 (Classic)Prelude to Genesis Suite (Artist, U.S.)A Survivor from Warsaw, Kol Nidrei, 2nd Chamber

Symphony (U.S. LP)

Berg

Songs, Op. 2 (Esquire-Classic)Three Fragments from Wozzeck (Columbia)Chamber Concerto (Esquire-Classic)

Lyric Suite (Polydor-Decca)Violin Concerto (Columbia LP)Seven Early Songs (U.S.)Piano Sonata (U.S.)

String Quartet Op. 3 (U.S.)Woz&ek complete opera (U.S. LP)Lulu complete opera (U.S. LP).Der Wein (Capitol LP)

Webern

Selection of Chamber Works (including 5 Movements for

string quartet, Op. 5 U.S. LP)String Trio (Decca)

Symphony (Classic)Cello pieces Op. 11 and Saxophone Quartet (U.S. LP)

DISGOORAPHY 155

Busoni

Die Ndchtlichen (Polydor)Sonatina 5 (Friends of Recorded Music, U.S.)Fantasia in memory of his father (Columbia) and several

other piano works recorded by Egon Petri.

Van Dieren

Nothing, unfortunately, seems to have been recorded.

Stymanowskiist Violin Concerto (Parfophone) otherwise seems to

be represented only by some unimportant pieces

The Fountain of Arethusa and Theme and Variations in

B flat (both Columbia): also Mazurkas, Op. 50

(HMV) and fitudes, Op.33 (U.S. Columbia)

Jandcek

Concertino for Piano and 6 Instruments (Supraphon)

String Quartet (Kreutzer Sonata) (Supraphon)

Overtures, Mafcropoulos and Katya Kabanova (Supraphon)Music from "The Cunning Vixen" (Supraphon)Taras Bulba (Supraphon)Laski Dances (Supraphon)

Capriccio for Piano (left hand) and Chamber Orch.

(Supraphon)Various smaller choral works (Supraphon)Sinfonietta (HMV)Diary of a Young Man who Disappeared (Supraphon)

Glagolithic Festival Mass (Supraphon)

Ives

Concord Sonata (U.S. Columbia)2nd Quartet (Nixa, Period)

No. 3 ofThree Places hi New England (Artist, U.S.)

Violin Sonatas 2 and 4 (Alco and NMQR, U.S.)

Holidays, Suite (NMQR)Songs (NMQR and Concert Hall, U.S.)

Varise

Octandre, Integrates, lonisation, Density. 217 (U.S. LP)

156 DISCOGRAPHY

Valen

Violin Concerto (Norwegian HMV)Le Cimetiere Marin (Norwegian HMV)Symphony No. 3 (Norwegian HMV)

Hdba

Various works in J and tones (Supraphon and Esta)

INDEX

d'Albert, Eug&ie, 65 d'Indy, 126

Ives, Charles, 124-6, 133

Bach, G. P. E., 3, 132Bach, J. S., 1-4, 6-9, 13, 25, 66, Jandcek, 7272, 122-4

III, Il8, 121

Bart6k, i, 5, 13, 21, 32, 35, 44- Klebe, Gisclher, 147

54, 55, I4 1 '2 Klengel, 3Beethoven, 3, 66 Kfenek, 111-117Berlioz, 133Berg, Alban, 8, 72-3, 78-81, 93- Lambert, Constant, 29

8, 99, 104, in, 112, 116, Leibowitz, Ren<, 73*, 77*, 102,

104, noBlorn, Eric, 13/1

Boulez, Pierre, 147Brahms, 3Busoni, 5, 118-9, IJ

Bush, Alan, 134

Liszt, 5, 8-9, 44, 116, i 18, 133-4*145

Garner, Mosco, 5/2, 15, 32^

Debussy, 20, 44, 71-2, 121,

133-4Dent, Edward J., 119Dieren, Bernard van, 119-121

Gesualdo, 3-4, 7, 10

Gray, Cecil, 4*1

Haba, Alois, 128/1

Handel, 3Haydn, 105Heseltine, Philip, 4Hindenuth, i, 21, 55-70, 72, &

Hdlderlin, 103

Machaut, Guillaume de, 66

Mahler, 13-15, 16, 72, 133Mendelssohn, 3Milhaud, i, 21, 34-43, 47, 53,

69, 143, 147Mozart, 3, 132Mussorgsky, 72

Nono, Luigi, 147

Paganini, 133Palestrina, i, 3, 6, in, 113Puccini, 72Purcell, 3-4

Ravel, 20

Reger, 9-10, 72, 130Reich, Willi, 94, 103Roussel, 126

Rufer, Josef, 7971, 106, 108,

149-150

158 INDEX

Schoenberg, i, 3/1, 5-6, 16-21, Szymanowski, 33-4, 50, 121-2,30, 34, 44, 61, 66-9,

98-9, 104-111, 115-6,

119, 121, 124, 126, 130

Schubert, 134Schumann, 3Scriabine, 20

Spohr, gnStein, Erwin, 76*2

Stockhausen, Karlheinz, 147-9Strauss, Richard, 11-13, 32

71-2, 1 1 6, 133Stravinsky, i, 5, 14, 21, 22-31,

32, 52, 53> 66, 69, 127, 132, Widor, 126

133

Valen, 129-131, 143Varese, 126-8, 149Vaughan Williams, 132

Wagner, i, 3, 5, 9, 66, 71, 72,93* !05> n6, 120, 133

Webern, 72, 73, 75, 79-80, 93,99-104, in, 115, u6, 121,i33-4 r42 5 14

Wedekind, 97

147 Wildberger, Jacques, 147

Great XZiritam by CJ. Tinling *F Co-

searl 20th century counterpoint

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