Zarlino, the Senario, and Tonality

Robert W. Wienpahl

Journal of the American Musicological Society, Vol. 12, No. 1. (Spring, 1959), pp. 27-41.

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Zarlino, the Senario, and Tonality BY ROBERT W . WIENPAHL

HE MOST IMPORTANT advances in TI 6th-century harmonic theory were made rimarily by one man, Gioseff o Zar I' ino (15 17-90), and it is safe to say that probabl no theorist since Boethius was as indiuential upon the course of the development of music theor Y. He was a man of tre- mendous ta ents, well versed in the Greek and Hebrew languages, phi- losophy, mathematics, astronomy, and chemistry, to say nothing of music. While he was a composer and maestro di cappella at St. Mark's, his chief claims to fame are his three ex- cellent treatises: L'istitutioni hm-nzoniche (first ~ublished in Venice in 1558, A d thkn followed by nu-merous reprints, 1562, 1573, etc.) ; Dimostrationi hannonicbe (Venice, I 57 1, etc.) ;and Sopplimenti msicali (Venice, 1588). The complete set was republished then in 1589, en- titled De tutte ropere del R.M. Gio-sefio Zarlino da Chi0ggia.l I t is the complete edition that we have con- sulted for this study.

It is well to begin the discussion by setting forth Zarlino's dichotomi- zation of the modal system in his treatment of consonance and the common triad.

Thus, Zarlino has the following to say concerning the use of conso-nance in composition:

. . . La varieta dell Harmonia in simili ac- compagnamenti non consiste solamente nella varieta delle Consonanze che si fa tra due parti ma nella varieta anco dell' Har-

1 D e tutte Popere del R. M. Gioseffo Zar- lino da Chioggia (Venetia: F. de Senese, I 589),:

2 L lstitzctioizi harmorziclze, Cap. 3 1 , p. 222.

monie la quale consiste nella positione della chorda che fh la terza, ouer la Decima sopra la pane graue del la cantilena. Ande, ouer che sono minore et l'Harmonia che nasce e ordinata o s'assimiglia alla propor- tionalita o mediatione Arithmetica, ouer sono maggiori et tale Harmonia 2. ordinata ouer s'assimiglia alla mediocrita Harmon- " ica. E t da questa varieta dipende tuna la diversita e t la perfettione dell'Hannonie; conciosiache 2. necessario (come dirb al- troue) che nella compositione perfetta si ritrouino sempre in atto la quinta et la T e n a ouer le sue Replicate, essendo che oltra queste due consonanze l'Udito non pub desiderar suono che caschi nel mezo ouer fuori de i loro estremi che sia in ~ t t o differente et variato da quelli . . .

. . .The variety of harmony in such com- binations does not consist solely in the variety of Consonances which are made between two parts but also in the variety of the Harmony which consists of the types of intervals which make up the third, or the Tenth above the lowest part of the song. Either it is minor and the Harmony which arises is established by or corresponds to the Arithmetic proportion, or it is major and such Harmony is estab- lished by or corresponds t o the ordinary Harmonic, and on this variety depends all the diversity and perfection of Harmony. For it is necessary (as I have said else- where) that in the perfect composition there always be found in effect the Fifth and Third or their compounds [i.e., the 10th and ~ z t h l there being nothing beyond these two consonances which the ear de-sires, no sound within or beyond their limit which may be in any way different from them. . . .

I t can be seen from this that the common triad is considered by Zar-

2 8 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY

lino as the most important of all con- sonant combinations. This attitude is reflected in the increasing inclusion of the third in the final chord. W e examined some 5,179 pieces of music from the period 1500 to 1700 and found that the period of greatest use of the final third was from 1580 to 1620; some 93.8% of all final chords included the third, and it is safe to say that actual practice exceeded written practice. Certainly theory and practice are hand in hand.

Zarlino continues:

Ma perche gli estremi della Quinta sono invariabili et sempre si pongono contenuti sott' una istessa proportione (lasciando certi cosi ne i quali si pone imperfetta), pero gli estremi della Terze si pongono differenti tra essa Quinta. Non dico pero differenti di proportione ma dico differenti di luogo; percioche (come ho detto al-troue) quando si pone la Terza maggiore nella pane graue l'Harmonia si fh allegra; et quando si pone nell'acuto si fa mesta. Di mod0 che dalla positione diversa delle Terze, che si pongono nel Contrapunto tra gli estremi della Quinta ouer si pongono sopra I'Ottava, nasce la varieth dell'Har-monia. . . .

But because the limits of the Fifth are in- variable and always are included under the same proportion (allowing certain types to be classed as imperfect) yet the limits of the Thirds are different within the Fifth. I do not say different in position, for (as I have said elsewhere) when the major Third is placed in the lower part of the Harmony it is happy and when placed in the upper part it is sad. So that from the different positions of the Third, which is placed in counterpoint between the extremes of the Fifth or placed above the Octave, is born the variety of the Har- mony. . . .

This is one of the earliest discus- sions of the effect produced by the major and minor chord and is com-

s Loc. cit.

pletely in keeping with our own feeling today. It should be pointed out, however, that Zarlino does not speak of the combination as an entity but rather as a positioning of two types of thirds. It is evident that he appreciates the value of happiness or sadness as one belonging to the third itself, since he states that it may be found between the limits of the fifth or placed above the octave. In clari- fication of this idea he states:

Se adunque noi uorremo uariar I'Hannonia, & osseruare pih che si pub la Regola posta di sopra nel Cap. 29. (ancora che nelle compositioni di pih voci non sia tanto necessaria, quanto P in quelle di due) P di bisogna, che noi poniamo le Terze dif-ferenti in questa maniera; c'hauendo prima posto la Terza maggiore, che faccia la mediatione Harmonica,. poniamo dapoi la minore, che farh la divisione Arithmetica.

If then we want to vary the harmony, and observe as far as possible the rule set forth above in Cap. 29 (although this may not be as necessary in compositions for several voices as in those for two) it is merely a matter of placing the different Thirds in this fashion; having first employed the major Third, which constitutes the Har- monic division, we then use the minor, which arises from the Arithmetic division.

Since he is speaking primarily about composition in two parts, as he states in parenthesis, it is clear that he fully appreciates the shading value of juxtaposed thirds.

It should be noted in what ways Zarlino refers to the positioning of intervals, both in these passages and those which follow, because there is a definite change taking place in the consideration of vertical combina-tions.

Up to the time of Zarlino the tenor was held to be the most im- portant voice, the determiner of the

4 Ibid., p. 221.

29 ZARLINO, T H E SENAE IIO, AND TONALITY

mode, and all intervals were figured in relation to it, both above and be- low. With Zarlino, however, we can find many statements which show directly or indirectly that this is no longer the case. W e consider the above quotations as indications of his desire to construct composite inter- vals above a bass tone, especially in the second quotation beginning "Ma perche. . . ." I t is unfortunate that Riemann miscopied this particular k ass age,^ after the parenthesis, where it continues, ". . . per0 gli estremi delle Terze. . . ." Instead of the plural "delle Terze" he used the sin- gular "della Terza." From this mis- take he drew the erroneous deduc- tion that Zarlino was speaking of only one kind of third and its posi- tion above and below the keytone, from whence he decided that Zarlino was the earliest representative of the dualistic theorists like Hauptrnann, dttingen, and himself, who consider the minor key as an inversion of the major. W e need not go into this theory here, but it is well to point out that the third quotation, begin- ning "Se adun ue . . . ,"continues to refer to the di Iferent thirds, proving that Zarlino did not merit the du- bious honor conferred upon him by Riemann.

Further proof of this may be had in the following statement by Zar- lino, in which he now carries his de- ductions in harmony into the larger fields of the modes:

La cagione 8, che nelle prime, spesso si odono le Maggiori consonanze imperfette sopra le chorde estremi finali, b mezani de i Modi, b Tuoni, che sono il Primo, il Secondo, il Settimo, I'Ottauo, il Nono, & il Decimo; come uederemo altroue; i quali Modi sono molto allegri & uiui; conciosia che in essi udimo spesse fiate le Conson-

6 H. Riernann, Geschichte d m Mzcsiktheorie (Berlin, 19201, pp. 393ff.

6 L'istitzctioni, Part 111, Cap. 10, p. 192.

anze collocate secondo la natura del Nu- mero sonoro; ci&, la Quinta uamezata, b diuisa harmonicarnente in una Terza mag- giore, & in una minore; il che molto diletta all'udito. Dico le Consonanze esser poste in essi secondo la natura del Numero sonoro, percioche allora le Consonanze sono poste ne i lor luoghi naturali; ...Ne gli altri Modi poi, che sono il Terzo, il Quarto, il Quinto, il Sesto, l'undecimo, & il Duodecimo, la Quinta si pone a1 contra- rio; cio8, mediata arithmeticarnente da una chorda mezana; di mod0 che molte uolte udimo le Consonanze poste contra la nat- ura del norninato Numero. Per ilche, si come ne i prirni la Terza maggiore si sot- topone spesse uolte alla minore; cosi ne i secondi si ode spesse fiate il contrario; & si ode un non sb che di mesto b languido, che rende tutta la cantilena molle; . . .

The reason is that in the first [case] the Major imperfect consonances frequently appear above the final note, as in the case of the Modes, or Tones, such as the First, Second, Seventh, Eighth, Ninth, and the Tenth; [do not forget that these are Zar- lino's new numberings71 as we saw else- where; such Modes are very cheerful and lively; because in them we often find the Consonarlces placed according t o the na-ture of the Sonorous Number; that is, the Fifth is divided harmonically into a major Third and a minor [4:5:61; which is very delightful to the ears. I say that the Con- sonances are arranged according to the nature of the Sonorous Number, for then the Consonances are put in their natural places; .. . In the other Modes, which are the Third, Fourth, Fifth, Sixth, Eleventh,

7 De tutte I'opere, Lib. IV, Cap. X, p. 399. Authentic Modes

I Ionian. Final C I11 Dorian. Final D

V Phrygian. Final E V I I Lydian. Final F I X Mixolydian. Final G X I Aeolian. Final A

Plagal Modes I1 Hypoionian. Final C

I V Hypodorian. Final D V I Hypophrygian. Final E

V I I I Hypolydian. Final F X Hypornixolydian. Final G

XI1 Hypoaeolian. Final A

3 O JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY

and the Twelfth, the fifth is placed con-trariwise; that is, divided arithmetically by the middle tone; so that many times we hear the Consonances arranged contrary to the nature of the Number in question. In the first [the Modes first referred to], the major Third is frequently placed be- low the minor; while in the second it is frequently heard otherwise [i.e., the minor Third below the major]; and there is heard a sad or languid effect, which makes the whole melody soft; . . .

This is the first recognition of the fact that there were actually only two types of modes, those which had a tonic major third and were cheer- ful, and those which had a minor third and were sad. H e then affirms the identity of each group of modes with the major and minor triad re- spectively, although they are identi- fied by the placement of the thirds rather than by the term "chord." It is remarkable that Zarlino did not go one step further and call them major and minor modes, but i t was more than one hundred years before these labels were applied.

We like to attention'before proceeding, to the use of the terms "harmonic" and "arithmetic."

"Harmonic" applies t o the division of the monochord according to the various string length ratios, expressed by the series: 1, '/z, %, 1/4, 5,%, which produces the first six partials; thus, fundamental, octave, fifth, dou- ble octave, major third, and minor third (i.e., C, c, g, c ' , e ' , g ' ) . The major harmony, therefore, corre-sponds to this series, due to the posi- tion of the major third below the minor.

"Arithmetic" refers to the arith- metical division: thus, I :2 :3 :4: 5 :6, in which the denominator, 6, remains

i'e'>6/6, 5/6, 4/6, 3/6, 2/6, 1/6. This produces respectively the

fundamental, minor third, fifth, oc-tave, fifth, fifth (ice., C, Eb, G,c, g,

hi^ is, of course, the minor bar-mOny.

Thus, the example (omitted above) in the first quotation, which he labels Harmonica and Arithmetica, is de- rived from these two series. Below, he places the superparticular ratios,s Sesquiquarta (5/4 or major third) and Sesquiquinta (6/5 or minor third).

Zarlino's whole theory of conso-nance, then, is related to a series of six numbers, from one t o six, or the arithmetical series I :2 :3 :4: 5 :6. This is not used, however, as was de-scribed above with the constant de- nominator of six. But rather, i t is the source for all possible ratios involv- ing these six numbers. This is really an extension of the Pythagorean sys- tem, which stated that all the perfect consonances were derived f rom the first four numbers; thus, I : t is the octave, 2 : 3 the fifth, and 3:4 the fourth. Zarlino calls his series the Senario. T h e r e f ~ r e , ~

Delle propried del numero Senario er delle sue pani et come tra loro si ritroua la fo,, dsogni consonanze musicale.

TRANSLATION From the propositions of the number Six and from its pans and the relation be-tween them is found the form of every consonance.

The perfection of consonances, as derived from the Senayio, is related to the simplicity of the numbers making up the ratio: l o

Et k in tal maniera semplice la Diapason, che se ben 2 contenuta da sue Suoni di- versi per il sito, dirb cosi; paiono nondi-

yuperpart icular l refers to a ratio in which the antecedent exceeds the consequent

b y Q ~ ~ ~ t i t q , L t i o l ? i ,Cap, r 5 , Chapter heading l o Ibid., Cap. 3, p. 184

ZARLINO, THE SENA.RIO, AND TONALITY 3 '

meno a1 senso un solo, percioche sono molto simili; & cib aviene per la viciniti del Binario all'Unita. . . .

TRANSLATION And it is in such a simple fashion that the Octave derives its sound from its position, thus let me say, however, that it seems to be a single sound; for they [the two tones of the octave] are much alike and are a result of the proximity of Two to One.

The octave, therefore, is the most perfect because of the proximity of two to one.

By carrying out the various ratios the following consonances are ob-tained: 2: I equals the octave, 3 :2 the perfect fifth, 4: 3 the fourth, 5:4 the major third, and 6: 5 the minor third. I t will be noted that these are super- particular ratios and that they form the basic consonances because of this close relationship; i.e., their com-ponent numbers do not differ by greater than unity (Unitd), for, as he says: l1

. . . Ma la Vniti, benche non sia Numero, tuttauia i. principio del Numero; & da essa ogni cosa, b semplice, b composta, b cor-porale, b spirituale che sia, uien detta Vna.

TRANSLATION . . . But Unity, although not itself a Number, nevertheless is the source of Numbers; & everything, whether it be simple, compound, corporal, or spiritual, comes from this Unity. . . .

From this i t can be seen that the major and minor sixth are not con- sidered by Zarlino to be basic con-sonances, since their ratios are re-spectively 5: 3 and 8: 5.

Of the major sixth he speaks as follows: l2

L'hexachordo maggiore i. Consonanza composta, percioche i minimi termini della

11 Ibid., Part I , Cap. 12, p. 29. 12 Ibid., Cap. 16, p. 34.

sua proportione, che sono 5 & 3, sono capaci d'un mezano termine, che 6 il 4.

The major sixth is a composite Conso-nance, for the minimum limits of its pro- portions, which are 5 & 3 , have a middle term which is 4.

I t is unfortunate, perhaps, that Zar- lino, as well as others both ancient and modern, became enamored of t he Senario system, because i t blinded him to certain fundamental principles of inversion which other- wise might have been obvious. The minute that he considered sixths as composite intervals, he banished the idea that they were also inversions of thirds. A t any rate, he continues: l3

Vedsi oltra di questo I'hexachordo mag- giore, contenuto in tale ordine tra questi termini 5 & 3, il quale dico esser Con-sonanza composta della Diatessaron & del Ditono: percioche 6 contenuto tra termini, che sono mediati dal 4.

There may be seen in this major sixth contained within its limits 5 & 3, what I call a Consonance composed of the Fourth and the Major Third: for it is contained between its boundaries by means of the number 4.

Thus, the perfect fourth equals 3:4 and the major third 4:s. I t has a neatness which could easily appeal to the orderly mind.

Figure 114 shows one of the nu-merous graphic demonstrations of ratios; in this case, for the Senario. A comparison of this with a figure of similar function by Salinas, which follows shortly, will show why the latter made a clearer statement of in- terval compliments.

Concerning the minor sixth, Zar- lino has this to say: l5

13 Ibid., Cap. 15, p. 33. 1 4 Ibid. , Cap. 15, p. 32. 15 Ibid., Cap 16, p. 34.

32 Prima pcllr ~ o p r i e i idrf nymrro Srnrrio fl dellrjiic parti ;0comc tra

loyol;ritrow laforma d'ogni [o$nan<d (aujicale, cap. X V .

N c H o a c H r moltcfianole propricti dcl,numero Scnario; nondimcno, pernon andar troppo in lungo, racconteri, folamentc qucllc chc fauno a1 pro pofito ;& la prilnafari ,che cgli 2 tra i Numcri pcrfctti il Primo ;& contic-ncin fe Parti, chcfono proportionate trzloro in tal modo ;chc pigliandonc

Due qua1 fi uagliono ,hnnno tal rclatione, chc ne danno la ragionc ,b for~na di unit deUe Proportioni dellc muficali confonanze j o femplicc ,6 compoff ;Ich' clk fia ;co-me fi pud uederc nclla fottopoita figura .

Sonoancoralc fueParti in tal no do collocatcPcordinatc, chelc Formc di cinfcuna delle Ducrnaggiori femplici confonanzc, Ic qunli da i Mufici urngon chianlntc IJcrKbt- tc ;efindo c6tcnutc tralc parti dclTcrnario,fono in ducparti diuifc in Hnr~nonicn pro jmrtionaliti,dn un tcrminc mcrmo: conciofin cllc ritroamdoliprimn la Dinparon nrl- a forma& proportionc,chc 2 trn s S( I. fcnz'alc~ln mczo, 6 tiopoi dnl Tcr~larin lioflo tl.;~ i14.&il 2 . in duc parti diuic~ ;c1o2,in duc conihnatlt.~, nclla DintcKiron pri~nn~noi- t ~ ~ c h c f i r i t r o u atra 4.& 3.hnclln I)inpc11tccollocrtatrnil3.&il 2. Q c R n poi liritro- ua tra 6.& 4, diuifa dnl 9 , in duc particonionanti; cio6,in 1111Ditono contcnuto tra 7. &4. &in unScmiditonocontcnuto tra 6. Sr j. H o dctto, chc hnodiuik in Duc parti

in Figure I

ZARLINO, THE SENARIO, AND TONALITY 3 3 Alquale aggiungeremo il minor Hexa-chordo, che nasce dalla congiuntione della Diatessaron col Semiditono, . . . Imperoche ritrouandosi tal proportione tra 8 & 5. tai termini sono capace 8 u n mezano termine h-onico, ch'b il 6; il quale la divide in questa maniera 8.6.5. in due proportioni minori; c i d , in una Sesquiterza & in una Sesquiquinta.

TRANSUTION similarly we shall figure the minor Sixrh, which is born of the union of the Fourth with the ~i~~~ Third, . .For such pro-portions are found between 8 & 5 whose limits contain a middle harmonic number which is 6; which divides it in this way 8:6:5, in two minor proportions; that is, in a Fourth & in a Minor Third.

Here he seemingly goes outside of the Senario but manages to excuse it in this way: le

Et benche la sua fonna non si troui in atto tra le parti del Senario; si troua nondimeno in potenza; conciosiache ueramente la piglia dalle parti contenute tra esso; c i d , dalla Diatessaron & dal Semiditono; perche di questa due consonanze si compone: la onde tra'l primo numero Cubo, il quale 6 8 uiene ad hauerla in atto.

And although its ratio is not found in actuality within the parts of the Senario, they are nevertheless found potentially; because indeed the elements of the parts are contained within; that is, in the Fourth & in the Minor Third: wherefore it is composed of two consonances: so that actually this 8 is a Cube of the first num- ber.

And further on: l7

. . . PerB dico .. .che nel Senario; ciob, tra le sue Parti, si ritroua in atto ogni Semplice musical consonanza, & anco le Composte in potenza. . . .

TRANSLATION . . . However I say . . . that as every

10 bid. 17 Ibid., p. 35.

Simple musical consonance is found in actuality in the Senario, so the composite are found potentially. . . .

And elsewhere, he seals the union which Cut him off from the invertibility of sixths and thirds.ls

. . . L'hexachordo mapeiore, . & anco il mi-"" nore, nascono dalla congiuntione della Dia- tesaron col Ditono, b Semiditono; come diligentemente habbiamo dimostrato nel second0 Ragionamento delle Dimostrazioni harmoniche'

TRANSLATION . . . The major sixth, and also the minor, are a product of the union of the Fourth with the Major Third, or Minor Third; as we have carefully demonstrated in the second Rule of the Dimostrazioni har-moniche.

However, in spite of this statement and his reference to the Dimostra-zioni hamzonichse, it is in the latter work that he gives some hint that he may have understood the inverti- bility of intervals; for, in the Ra-gionmento Terzo, he gives the fol- lowing rules: l9

Delle Consonanza e ordinate in cotal guisa, dal fine del Semiditono A quello del Ditono ui b la dxerenza del Semituono minore; & dal fine del Ditono A quello della Diates- saron ui B quella del Semituono maggiore. I1 fine della Diatessaron da quello della Diapente si troua differente per il Tuono maggiore; & il fine della Diapente da quello dell'Hexachordo minore i: differ-ente per il Semituono maggiore. Dal fine di questo Hexachordo al fine del maggiore ui cade la differenza del minor Semituono. Et dal fine della Diapente A quello dell'- Hexachordo maggiore ui b la differenza del Tuono minore. Dal fine dell'Hexa-chordo minore a1 fine della Diapason si troua la differenza del Ditona. E t dal fine dell'Hexachordo maggiore A quello dell istessa Diapason ui b quella del Semiditono.

1s Ibid., Cap. 16,p. 30. 19 Dimostrazioni harmoniche, Proposta 40,

p. 184.

34 JOURNAL OF THE AMERICAN MCTSICOLOGICAL SOCIETY

Simigliantemente il fine della Diapason da quella della Diapason diatessaron c5 dif-ferente per la Diatessaron, & da quell0 della Diapason diatessaron 1 quello della Diapason diapente casca la differenza del Tuono maggiore. Vltimamente dal fine dalla Diapason diapente vi 1: la differenza della Diapente; & da quello della Diapason diapente a1 fine della Disdiapason si troua la differenza della Diatessaron.

TRAMLATION Concerning consonances and how they are arranged. From the end of the minor third to that of the major third there is a dif- ference of a minor half step; and from the end of the major third to that of the fourth it is a major half step. From the end of the fourth t o that of the fifth is found a major whole step; and from the end of the fifth to that of the minor sixth there is a difference of a major half step. From the end of this sixth to that of the major sixth there is a difference of a minor half step. And from the end of the fifth to that of the major sixth there is a difference of a minor whole step. From the end of the minor sixth to that of the octave there is a difference of a major third. And from the end of the major sixth to that of the same octave is a minor third. Similarly from the end of the octave to that of the octave and a fourth there is a difference of a fourth, and from that of the octave and a fourth to that of the octave and a fifth there is a difference of a major whole step. And finally from the end of the octave to that of the octave and a fifth there is a difference of a fifth, and from that of the octave and a fifth to the end of the double octave there is a difference of a fourth.

This is as close as Zarlino comes to the realization of invertibility. Rie- mann thought that he clearly un-derstood the principle, in justifica- tion of which Riemann points to the word "Replicate" (which will be found in the first quotation shortly after the parenthesis). This he trans- lates as "Oktavversetzungen" or "in- version."20 However, we believe that

20 Riemann, lor. cit., p. 3 7I.

the following statement by Zarlino clearly shows that by "replicate" he meant compound intervals in contra- distinction to simple intervalS.21

La onde dico, che gli Elementi del Con- trapunto sono di due soni; Semplici & Replicati. I Semplici sono tutti quelli In- tervalli che sono minori della Diapason; com'1: l'Vnisono, la Seconda, la Terza, la Quana, la Quinta, la Sesta, la Settima, & l'ottaua; ciok, essa Diapason. Et li Repli- cati sono tutti quelli che sono maggior di lei; come sono la Nona, la Decima, la Vndecima, la Duodecima, & gli altri per ordine.

TRANSLATION Therefore I say that the Elements of Counterpoint are of two types: Simple & Compound. The Simple are all those inter- vals which are smaller than the Octave; such as the Unison, the Second, the Third, the Fourth, the Fifth, the Sixth, the Seventh, & the Octave; that is, the Diapason. And the Compound are all those which are larger than the Octave: as are the Ninth, the Tenth, the Eleventh, the Twelfth, & the others in order.

At thispoint we againlike to digress briefly in order t o discuss similar views held by Zarlino's contemporary, Francisco de Salinas (15 13-90). W e do not know whether the two men ever met, but i t seems highly probable in view of the fact

salinas came to R~~~ in 1538 and remained in Italy until I 56 I . At least, if they did not meet, the simi-larity of their basic theories indicates that Salinas was acquainted with Zar- lino's writings.

Salinas's treatment of consonance is also based upon the Senario and is clear and concise. The accompany- ing figure (Figure 2 ) is of consider- able interest since it helps to clarify the explanation. Thus, concerning the Senmio, Salinas saysz2

21 L'istitutiolti, Part 111, Cap. 3, p. 183. 22De nzusica libri V I I (Salamanticae : M.

ZARLINO, THE SENA ,RIO, AND TONALITY 3 5

Et quo clarius Senarii virtus elucescat non solum in eo omnes formae consonantiarum simplicium inveniuntur singulis ejus parti- bus ad proximas et ad quamcunque ejus partem comparata consonantiam facit sim- plicem aut compositam, ut non tantum in sex primis simplicibus sed etiam in sex primis (cum aequa) multiplicibus inven- iantur, in tripla sicut in sesquialtera, in quadrupla sicut in dupla, in quintupla sicut in sesquiquarta et in sextupla sicut in tripla et sesquialtera. Neque Jtrn sextuplam in proportione septupla consonantiam inven- iri, sicut neque in sesquisexta ultra ses-quiquintam. . . . Sciendum est, intervalla nunc secundum Arithmeticam divisionem disponi nunc secundum Harmonicam. Di-visione Arithmetica aequales esse differ-entias ac spacia, inaequales vero propor-tiones . . . talem autem divisionem in primo Senario reperiri satis et praecedenti figura liquet.

And to what extent the real value of the Six begins to shine forth not only in all forms of simple consonances t o be met with in their single parts in the closest and most immediate comparison . . . but in all parts in relation to the whole and in each part united in consonance, simple or com- posite, where it is met with not only in six simple ratios, but also six multiple ratios, in 1:3 just as in 2:3, in 1:4just as in 1:2, in I: j just as in 4: j and in 1:6 just as in I : 3 and 2:3. And neither beyond I :6 in the ratio 1:7 is a consonance to be found, just as not in 7:6 beyond 6:j . . . It is un- derstood, intervals are distributed now ac- cording to the Arithmetic division and now according to the Harmonic. Arith-metic divisions may be equal in difference and also in space, unequal indeed in pro- portion. . . . for such a division moreover right from the first the Six is found to be

Gastius, I 577), Lib. 11, Cap. 12, pp. 61-62. The Senario concept continued to be quoted in later years, as by Descartes, Compendium Mu- sices, written in 1618, published in 1650; English trans. Renatus Des-Cartes Excellent Compendium o f Musick (London : T . Harper, 1653)~ pp. 9-10. And Kircher, Musurgia uni- versalis (Romae : F. Corbelletti, 1 6 5 0 ) ~ Lib. 111, Cap. V, p. 100.

sufficient and this is evident from the fore- going figure. [See Figure z below.]

The example happens to be for the arithmetic division, but the principle would be the same for the harmonic, concerning which he states: 23

Et mirum est quanto suaviorem efficiant auribus concentum hae consonantiae, sic Harmonica medietate divisae, quam Arith- metica ut in priori chorda dispositae sunt.

T~kvsLAnox And it is wonderful how smooth these combinations are to the ear, whether di- vided in the Harmonic manner, or the Arithmetic, as the intervals are distributed above.

It scarcely seems possible that Salinas could have looked at the graphic representation without real- izing the principle of inversion, es- pecially when, in a later chapter, he continues as follows: 24

. . . Inter duo Diapason extrema ita dis- positae sunt consonantiae, ut quae ad al- terum eorum sit Semiditonum, ad alterum Hexachordum maius esse reperiatur; & quae Ditonum Hexachordum minus; & quae Diatessaron, Diapente . . . unde props similem concentum auribus effeciunt. Et multb manifestius experimur Diapente, & Diatessaron esse tamquam germanas gemel- las eodem partu editas d Diapason; & solhm quantitate differre, quoniam altera minor, altera maior sit.

. . . Between the two extremes of an Oc- tave are distributed the consonances, where on the one hand may be found the Minor Third, and on the other the !Major Sixth; and the Fourth and Fifth . . . whence they produce an almost similar effect on the ears. And many effects are experienced in the Fifth and Fourth being like twin brothers within the parts of the Octave; and only differing in size, because it may be either minor or major.

23 Salinas, op. cit., p. 63. 24 Ibid., Cap. 25, p. go.

JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY

. -

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-9rith-Figure 2

This is actually considerably In the foregoing stud of conso-clearer than Zarlino's statement. nance it is interesting tbat, for the

In either case, while the final con- most part, the treatment is intervallic clusion is never reached, it is symp- rather than chordal. Yet, in the first tomatic of the new harmonic think- two quotations at the beginning of ing and shows a definite break from this study Zarlino is dealing with the the past. chordal combination of the third and

ZARLINO, T H E SENA RIO, AND TONALITY 3 7

fifth. It should be noted that at this time the term chord (Italian: la chorda) refers usually to interval, but also occasionally to a single tone, rather than a chord in our sense. Nevertheless, he is chord-conscious as the following passage will demon- strate: 25

Oltra di questo B da auertire, che quella Compositione si puo chiamar Perfetta, nella quale in ogni mutatione di chorda, tanto ueno '1 grave, quanto uerso I'acuto, sempre si odono tutte quelle Consonanze, che fanno uarieth di suono ne i loro estremi. E t quella 6 ueramente Hmmonia perfetta; ch' in essa si ode tal consonanze; ma i Suoni b Consonanze che possono far di- versith al sentimento sono due, la Quinta & la Tena , ouer le Replicate dell' una & dell' altra; percioche loro estremi non hanno tra loro alcuna simiglianza, come hanno quelli dell' Ottava; essendo che gli estremi delle Quinta non mouono l'Vdito nella maniera, che fanno quelli della T e n a , ne per il contrario; . .. dobbiamo per ogni mod0 (accioche habbiamo perfetta cotale hannonia) cercare con ogni mostro potere, di fare udir nelle mostre Compositione questa due consonanze pih che sia possi- bile, ouer le loro Replicate.

Another thing which you should heed is that that composition is called Perfect in which every change of harmony, whether up or down, always includes a variety of sounds within its limits. And such is in- deed truly the Perfect Harmony which includes in itself such Consonances; but the Tones or Consonances which can pro- duce this diversity of feeling are two, the Fifth and the Third, or the compound of

25 I,'istitutioni, Part 111, Cap. 59, pp. 299-300. The Harmonia fierfetta had many follow- ers. Lippius, Synofisis musicae novae (Argen-torati: Ledertz, 1612), p. 16, states: "In practica observa Triadem harmonicam." G. Doni, Compendia del trattato dB'generi, e de'modi (Rome: Fei, 1635)~ p. 387, says "In quanti modi si possa practicare l'accordo per- fetto nelle Viole." And Mersenne, Harmonie universelle (Paris : Cramoisy, 1636-37), First Book of Consonance, ". . . que I'on appeile ordinairement Harmonie parfaite."

each; for their limits do not have any similarity to each other, as do those of the Octave; since the limits of the Fifth do not incite the ear in the way which those of the Third do, nor contrariwise; . . . we ought in any case (in order that we have such a perfect harmony) t o find out how each of us can use in our Composi- tions those two consonances as much as possible, o r their Compounds.

The Harmonia perfetta, or the combination of the third and fifth, or their compounds, is indeed a chord, and this is the first reference to such a vertical structure.

Zarlino then continues: 26

E ben vero, che molte volte i Prattici pongono la Sesta in luogo della Quinta, & 1: ben fatto. Ma si de auertire, che quando si porrh in una delle parti la detta Sesta sopra'l Basso, di non porre alcun' altra pane; che sia distante per una Quinta sopra di esso; percioche queste due parti uerrbono ad esser distanti tra loro per un Tuono, ouer per un Semituono; di mani- era che si udirebbe la dissonanza . . . Os-seruarh adunque il Compositore questo, c'hb detto nelle sue compositione; cioh, di far pih ch'ello potra, che si ritroui la Terza, & la Quinta, & qualche siate la Sesta in luogo di questa, b le Replicate; accioche la sua Cantilena uenghi ad esser sonora & piena. . . .

It is indeed true that many times Com- posers use the Sixth in place of the Fifth, & this well done. But be forewarned that when one uses in one of the parts the said Sixth above the Bass, not to allow any other part to be a Fifth above this; for these two p a m should not have the space between them of a Tone, or a Semitone; so that the dissonance can be heard. . . . The Composer will then observe this that I have said in composition; that is, as much as possible, let the Third be met with, & the Fifth, & sometimes the Sixth in place of this, or the compounds; so that the Song may be sonorous & full.

This statement is interesting for -zel'istitutioni, Cap. 59, pp. 300-301.

38 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY

two reasons: ( I ) he is dealing with a lontani pih de quelli, che si pongono nell' first inversion chord but makes no altre parti; accioche le pane mezani pos-attempt to explain it as a harmony sin0 prwedere con movimenti eleganti, Ec

different from the same with congiunti, & massima mente il Soprano;

a fifth-thus, agdnindicating that he percioche questo 2 '1 suo proprio. Debbe adunque esser' il basso non molto diminu-did grasp the invenibility, of ito; ma procedere per la maggior pane con

chords; and (') he 'peaks of nell' altre parti; & debbe esser' ordinat0 di a "Sixth above the Bass." maniera, che faccia buoni effetti, & che

The idea of building intervals non sia difficil da cantare; & cosi l'altre above the bass is a new one, at least Parti si potranno collocare onimamente ne as far as theory is concerned. It i propij luoghi nella cantilena. I1 Tenore would seem that it had been done in segue immediatamente 1'Basso uerso l'acuto, practice for some considerable time, ilqual' 6 quells pane, che regge, & governa

since practice usually precedes la cantilena, & & quella, che mantiene '1

theory. At any rate, in the chapter Mode, 0 Tuono, nelquale 6 composto; . . . osseruando di far le Cadenze A i luoghijust before the above statement, Zar- proprij, Pr con proposito~lino speaks in the following man-

ner: 27 TRANSLATION

. . .1 Musici neUe lor cantilene sogliono il . The Musicians in their

pih dklle uolte porre Quanro pani, nelle Of the time put them in four parts* quali dicono contenersi mas la perfettione in which are 'Ontained the Per-dell'harmonia. Et perche si compongono fections of the harmony. And because it is principalmente de cotalai per- le c O m ~ s e dOf such pans, that reason chiamarono Elementali dells compositione, the Of the

guisa de i quactro Elementi la onde si after the manner of the four Elements come F~~~~ et cagione di far whence as the Fire is fed and is the cause

produrre ogni cosa naturale the si troua producing every thing which is

ad omamento et a conservatione del Mondo found in the ornamentation and conserva-

cosi il ~~~~~~i~~~~si sforzara di far tion of the world so the Composer strives

la parte piu acuta della sua cantilena hab- make the upper part Of the more

bia hello, ornato ed elegante procedere di Ornate, and in a way maniera nutrisca et pasta which feeds and maintains the listening

ascoltano. E t si come la Terra e posts per 'pirit. And as the is to be the

fondamento de gli altri Elementi; cosi fundament of all the other elements; so

16Bassoh i tal proprieti, the sostiene, stabi- the Bass has such a propriety$ which

lisce, fortifica, & da accrescimento all' altre tains, stabilizes, fortifies, and gives support

pd; conciosiache posto per Bass & to all the other pans; because it is the Base fondamento dell'Harmonia; onde & detto and fundament Of the whence Basso quasi, Basa, & sostenimento dell' altre it is the Bass, as a Base and

panis M~ si come auerebbe, quando of the other parts. But as when an Element

mento dells Terra mancasse (se cib fusse the Earth is missing (and this may be

possible) the tanto bell' ordine di case possible) which Illin the good Order

ruinarebbe, & si guastarebbe la mondana, & things and 'poi' the and the

la humans ~ ~ ~ ~ ~ i ~ ;cosi quando 61 Basso human Harmony, so when the Bass is lack-

mancasse, tuna la cantilena si emperebbe di ing, the whole song is filled with confusion

confusione, & di dissonanza, & ogni cosa and dissonance and e v e ~ h i n ggoes

andarebbe in ruins. Quando dunque il ruin' When then the

~~~~~~i~~~~componer~l~Bassodella sua the Bass of his composition, he will pro-

compositione, procederA per mouimenti al- ceed in a manner 'Ornewhat more 'low,

quanta tardi, & separad alquanto, ouer and different as far as possible, from the other parts; so that the middle parts can

27 Ibid., Cap. 58, pp. 293-94. proceed with elegant and united animation,

ZARLINO, THE SENA.RIO, AND TONALITY 3 9

and particularly the Soprano; since this is its right. The .bass then ought not to be diminished much; but proceed for the most part with notes of somewhat greater value than those which are used in the other parts; and ought to be ordered in such a fashion that it may produce a good effect, and that it be not too difficult to sing, and all the other Parts should be well arranged in their proper places in the song. The Tenor follows immediately the Bass in the upper part and is that part which rules and governs the Song and is that which maintains the Mode or Tone in which it is written . . . observing when to make the Cadence in its proper place and position.

The latter part is very interesting, for he still refers to the tenor as the "part which rules and governs the Song" and "maintains the Mode or Tone;" which is the view generally held UD until this time.28

~ev'ertheless, four pages later Zar- lino qualifies this view, since it is not really in keeping with the rest of the ~ t a t e r n e n t . ~ ~

Ma si debbe anco ouertire, che quantunque il basso possa alle uolte tenere il luogo del Tenore, & Cosi l'una dell' altre parti, quel dell'altra; nondimeno si d& fare, che '1 Basso finisca sempre sopra la Chorda rego- lare & finale del Modo, sopra '1 quale i. composta la cantilena, & cosi 1' altre parti B i lor luoghi proprii; .percioche da tal chorda haueremo B giulcare il Modo. E t se bene il Tenore uenisse B finire in altra chorda, che nella finale, questo non sarebbe di molto importanza; pur che si habbia proceduto nella sua modulatione secundo la natura del Modo del Cantilena. . . .

But also one should be warned, that al- though the bass may be able in turn to take the place of the Tenor, and thus the one take the part of the other, and vice

2 8 E.g., Pietro Aaron, Trattato della natura e cognizione di tutti gli toni di canto figurato; in Oliver Strunk, Source Readings in Music History (New York, 1950), p. 209.

29 L'istitutioni, Cap. 59, p. 298.

versa; nevertheless if this is done, the Bass always will finish so as to govern the Tone and final of the Mode upon which the piece is composed, and thus the other parts in their proper places; since by such tone we can judge the Mode. And if in- deed the Tenor comes to finish on another note than on the final, this will not be of much importance; although it may have proceeded in its modulation according to the Mode of the Song. . . .

This certainly seems to complete the final reduction of the importance of the tenor.

Before proceeding to the last part of Zarlino's harmonic theory, as re- spects the needs of this study, we should like to digress briefly and en- large somewhat on the above topic of maintaining the mode or tone of a composition.

In the middle of the 16th century there was a growing desire for the expressive treatment of the text in what Adrian Coclico described as mzlsica reservata, a style of treatment which could scarcely fail to disrupt the character of the modes, which is precisely what happened. I t is inter- esting to read what another contem- porary of Zarlino's had to say concerning this problem. W e are referring to Nicolo Vicentino (ca. 1511-7z), who was one of the first theorists to experiment with the res- toration of the Greek modes and genera which he considered as more expressive, since the Greek philoso- phers had ascribed great powers t o their music. A t any rate, he was well aware of the need for digression from modal restrictions in order to better express the affections of the text. Thus, he says: 30

Quando comporra cose Ecclesiastiche, & che quelle aspetteranno le risposte dal Choro, ?I dal'organo, come saranno alcune

30 N. Vicentino, L'antica musica ridotta alla moderna prattica (Roma : A. Barre, 1 5 5 5 ) ~Lib. 111, Cap. 15, p. 48.

ZARLINO, THE SENARIO, AND TONALITY 4'

of harmony which indicate the changes whlch will lead to a concept of tonality.

The importance of consonance as the basis of composition was, of course, emphasized by all theorists and made abundantly clear by Zar- lino, who says: 32

Le Compositione si debbono comporre prirnieramente di Consonanze & dopoi per accidente di Dissonanze.

TRANSLATION Compositions ought to be made up pri- marily of Consonance & thereafter per-chance by Dissonance.

He then continues: 3a

. . . La Dissonanza fa parer la Consonanza, la quale immediatemente la seque, pih diletteuole.

TRANSLATION . . . Dissonance prepares Consonance, & what follows is therefore more delightful.

The principle of this statement is that dissonance enhances the value of consonance and exists for this pur- pose. Furthermore, it prepares the consonance, and here, we feel, is an implication of considerable impor- tance for the further development of tonality. It suggests that Zarlino un- derstood the basic principle of func- tional harmony. (We have already indicated that he was the first theo- rist to begin a serious consideration of chordal structure with his Har-monia perfetta, or common chord.) The increasin use of both the V7 and the I in t\e final cadence shows that Zarbno's opinion was pretty

88 L'istitutioni, Part 111, Cap. 27, p. 212. 3 3 Ibid.

generally held. It is also indicative of the growing awareness of the verti- cal concept. In analyzing the music of the period 1500 to 1700 we pointed earlier to the almost uni- versal use of the third in the final chord during Zarlino's time. In ad- dition to its significance as the Har- nzonia perfetta is the added impor- tance of the inclusion of the final third for the use of the passing pen- ultimate dominant seventh. Zarhno's feeling for functional harmony is clearly supported by the practice of the times, as exemplified by the in- creasing use of the V7 and the 1: in the final cadence. During the forty years from 1580 to 1620 the music examined shows a total use of the V7 in almost ten per cent of all closes, and of the I ;in eleven per cent. In both cases this represents a five fold increase over the preceding forty years. The greatest use of the V, in the period around I 600 is to be found with the English composers, who used it in some 22.2% of all final cadences. If I may quote from my article referred to above: "The im- portance of the V7in delineating the tonic triad can scarcely be overesti- mated and, coupled with England's over-all tonal feeling, is of the great- est significance in the mutual inter- relationship of tonality and the au- thentic dominant-seventh ~adence."~'

In summation, Zarlino's Senario forced a dichotomization of modal theory which closely paralleled actual practice and pointed the way toward the major and minor tonalities.

San Fernando Valley State College 34 OP.cit., p. 382.