Renato Serrano

Music 521 C

Dr. Craig Walsh

May 12th, 2010.

Elogio de la Danza by Leo Brouwer,

a Comprehensive Analysis.

Introduction.

The cuban composer Leo Brouwer (b. 1939) wrote Elogio de la Danza in 1964. In a first

moment , the piece was thought as the complement of a major work, to be executed with ballet,

and it was world premiered by Brouwer himself on July 31st of 1964 at Unión Nacional de

Escritores y Artistas de Cuba.

Within Elogio de la Danza we will find a world full of contrasts, which are somehow connected

with each other. In this paper we will focus on the analysis of these relationships, providing a

complete explanation of how these elements are related within the piece.

In order to achieve that purpose, we will break down the corpus of the paper into three parts:

1-Structure and Form.

2-Harmony and Motives.

3-Rhythm.

Each of these parts will be organized according to Nº 1 (Structure and Form), with the purpose of

making easier the placement within the work.

1- Structure and Form.

As its overall plan, the work Elogio de la Danza features two contrasting movements, Lento and

Obstinato. The first one will present the more contemplative side of the work. Although, this

movement features a rhythmic part too (Part B), which will recall motivic material from Part A. In

order to give a clear contrast of the character within the work, the second movement, Obstinato,

will be developed in a more rhythmic fashion, but this emphasis on rhythm will find a break in a

few contrasting melodic moments.

a) Lento

The first movement of the work presents a ternary form, A-B-A’. As well as many of 20th

Century’s works, this ternary form is asymmetrical. Let’s analyze this unbalance:

-A: from mm. 1 to 24.

-Section 1: from mm. 1 to 9.

-Section 2: from mm. 10 to 16.

-Section 1’: from mm. 17 to 24.

-B: from mm. 25 to 44.

-A’: from mm. 45 to 54.

As an explanation for this unbalance, we may say that in A a contrasting section occurs from mm.

10 to 16. This sub-part or section (Section 2) is marked with a change of tempo (Piu Mosso) and

features several groups of triplets in quartal harmony (in arpeggios) and a pedal in B. In addition,

after Section 2, the music reassume elements from Section 1, creating Section 1’, which is also a

transition to B. However, neither of these two sections (Sections 2 and 1’) occur when A’ is

presented. Therefore, A’ is shorter than A.

Continuing in the same movement, B is spanned from mm. 25 to 44. It features a change of tempo

as well, turning the music into an Allegro Moderato. It features some of the motivic material of A,

presenting three-notes groups of E below the stave and fast ascending arpeggios. Although we

may say this material is taken from A, it will be the rhythmic character of B the main, more

contrasting difference between these two parts.

b) Obstinato.

The second movement of Elogio de la Danza presents and evident musical contrast with outer

parts of the former movement. It features a peculiar form: A-B-C-A’-B’. We also may understand

C as an extended version of B, due to the elaboration of material presented in B, but its length (40

measures) and its new elements (“rasgueados”, new melodic section from mm. 77 to 92, and

developed material) allow us to see it as a independent, more elaborated part (C).

Therefore, Obstinato’s parts will be:

A: from mm. 1 to 16.

B: from mm. 17 to 52.

-Section 1: from mm. 17 to 28.

-Section 2: from mm. 29 to 37.

-Section 1’: from mm. 38 to 52.

C: from mm. 53 to 92.

A’: from mm. 93 to 108

B’: from mm. 109 to 131

The emphasis on rhythm can be appreciated throughout the movement, and therefore non of the

parts features clear contrasts between each other. Although, the only exception is the melodic

section of C (from mm. 77 to 92), in which a melody is alternated with “rasgueados”, creating a

responsorial effect, which can be seeing as a milestone within the rhythmic activity that

characterizes the movement.

2- Harmony and Motives.

Even though this is not a tonal work in which the tonal center is established by traditional V7-I

cadence, still we are able to state that this music has a tonal center. As we know, the assertion of a

tonic may be made by several means, namely, through the use of reiteration, return, pedal point,

ostinato, accents, formal placement, and many other techniques used to draw the listener’s

attention to a particular pitch class.

In this manner, in Elogio de la Danza the pitch centricity will rely on “E” and we will discuss the

means that Brouwer used to make it possible.

a) Lento.

1) Part A

- Section 1: it opens with two motives that will be used in several places in the work. The first one

(M1) is constituted by a group of three E notes under the staff (Example 1). The second motive

(M2) is a fast ascendent arpeggio (Ex. 2), which features a pitch material with the prime form

[01348]. These two motives will be used again within the movement in B and A’.

In measure 5, motive 3 (M3), whose prime form is [012], is presented on a real sequence situation

four times in a row in descendent fourths with the exception of the one in the middle, whose

descendent motion is in a major third (Exs. 3 and 4).

In the next measure, a new sequence situation of four ascendent fourths in a row is presented in

motive 4 (M4, the ascendent major [01]-minor [02] seventh). Therefore we may start to think that

sequenced patterns in fourth motion (ascendent or descendent) will be used as recurrent material

in the rest of the movement (Exs. 5 and 6).

The section ends with a repetition of pitch class “B”, which is related to “E” in a descending fifth,

creating the motion of V-I. In addition, if we analyze the first pitch class (“E”) and the two last

ones of this section (“G” and “B”), we will recognize clearly the chord of E minor, and that is

what sounds when the section is repeated, as it is required with the repetition bar at the end of the

section (Ex 7).

-Section 2: it overlaps the pedal in pitch class “B” with the quartal harmony in arpeggios

(descendent and ascendent). We may say that these elements were previously presented in Section

1, with the repetition of pitch class “B” at the end of Section 1 and the leaps in fourths motion of

musical cells.

-Section 1’: it reassumes M4 from Section 1, transposed a descending minor third though, so this

variation will be called “Motive 4,1” (M4,1). After M4,1, the music continues with groups of

clusters [0135] and a final tertian-split chord [0145], a C7 Major (3!, and missing fifth). All of

these chords are used in as a transition to the new part.

2) Part B

It features a repetition of pitch class “E” in a new tempo (Tempo II, Allegro Moderato). This

reiteration is made in groups of triplets, which resembles with certainty to M1 (opening motive),

so we will call it “Motive M1,1” (M1,1; see Ex. 8). The first melodic gesture is done in an “E

Aeolian” (measure 26), reaffirming our thesis of E as a tonal center (Ex. 9). Two bars later, M2

will be featured with some variations. Now, its prime form is [013578], but its placement,

although in a more rhythmic context, is the same that the one of M2: right after a group of pitch

class “E”. Therefore, we will call it “Motive 2,1 ” (M2,1; see Ex. 10).

In measure 32, a new melodic gesture occurs, again in “E Aeolian”, with a tiny difference though.

A foreign pitch class appears (an “F”), but its rhythmic placement (in the second sixteenth note of

the third beat) and its ephemeral nature will exclude it from our consideration.

In the next measure, a new situation of sequence will occur, again in four-in-a-row ascendent

fourths motion. This time, the prime form that features the motion is [025] in the first two groups,

[026] in the third one and [015] in the last one. This sequence is repeated and displayed along

with M1 and silence measures in the rest B, in order to create an effect of rallentando and a

transition to A’.

3) Part A’

Back in Tempo I, for second time in the work, we can hear a variation of M2. In measure 45, M2

appears with a slightly different prime form [013478], so we will call this variation “Motive

2,2” (M2,2; see Ex. 11). After M2,2, motives M4,1 and M1,1 (this time, in a slow tempo) will

occur.

Finally, M2 is quoted literally three times, featuring a “rallentando” and “morendo” in order to

close the movement with a fade out in the music.

b) Obstinato.

1) Part A

Reaffirming the thesis of the pitch centricity towards “E”, in the first three bars, the second

movement opens with two dyads in the upper voices (G-B and E-G#), which, if segmented

together, produces the sonority of the split chord E (3!), whose prime form is [0347]. In addition,

below we find another plane of harmony, which will remain during the part: a pedal of pitch class

“E” is sounding in the lower voice.

In this manner, in mm. 1 to 3, the first motive are the two pairs of sixteenth notes (G-B and E-

G#), which will be called “Motive 5” and we will add the transposition level, in this case:

“E” (because it belongs to the “E (3!)” chord), so finally its name will be “Motive 5E” (M5E; see

Ex. 12). The second motive are the three pars of sixteen notes (G-B, E-G# and G-B), and in the

same logic, this motive will be named Motive 6E (M6E; see Ex. 13). Later, a combination of

both, M5E and M6E occurs (actually, its ordering is M6E+M5E; see Ex. 14), so the result of this

will be five pairs of dyads (with just four different pitch classes) figuring the harmony of E (3!).

In mm. 4 to 6, a real planing situation occurs in upper voices (Ex. 15). The same prime form

[0347] (and exactly the same chord) is transposed in a parallel motion several times, doing the

following progression: F# (3!)-A (3!)-G# (3!)-E# (3!). Now the two pairs of dyads of the opening

bar are played as a tetrachord (confirming the segmentation), and the repetition of the harmonic

situation (real planing) is evident. When this situation happens, each tetrachord lasts one eighth

note (except for the final ones, that last two eighth notes). In other words, this progression has a

faster harmonic rhythm than the one presented in the first three measures. Also, it is remarkable

the intervalic relationships that we found when comparing the pairs of dyads and the tetrachords.

If we analyze this topic, we will find that the first two pairs of dyads of M5E are a minor 3rd apart

(G-B / E-G#). This intervalic relationship of minor 3rd will be kept in measure 4, when a group of

four tetrachords occur. Within this group, the first two tetrachords (M5F# / M5A) and the last two

ones (M5G# / M5E#) present the same intervalic relationship of minor 3rd.

It is important to notice that in mm. 7-10, when the harmony is figured, it rests over two points:

F# (3!) in mm. 7-8 (M6F#+M5F#), and D (3!) in mm. 9-10 (M6D+M5D), doing the same gesture

of the beginning of the movement (let’s remember that in the beginning of the movement it rested

over E (3!), though). In this manner, Brouwer is surrounding the tonal center (E) by one tone

above (F#) and one tone below (D) with this harmonic rest points.

Therefore, we will understand that we find two clear musical planes in this part: the split chord

[0347] in the upper voices (presented as figured harmony in pairs of dyads or in tetrachords in

real planing) and the pedal in pitch class “E” in the lower voice.

2) Part B

The first motive that we can appreciate in Section 1 suggests immediately the tonal center. Motive

7 (M7) is a clear V-I cadential motion over E (Ex. 16). In addition, in mm. 19-20 it is followed by

the progression E (3!) - F# (3!) - E (3!), and later, in mm. 23 and 24, the same parallel

progression is expanded to E (3!) - F# (3!) - Ab (3!). Here, in the upper voice, we have to consider

Motive 8 (M8) in a melodic way, because it will provide important material to part C (Ex. 17).

Besides, used in its expanded version (as in mm. 23 to 24), M8 will outline important pitch

classes for tonal center “E”, like E-G-A-B (I-III-IV-V in “E”).

At the end of Section 1, in mm. 25 to 29, we may appreciate how the tonal center is again

established by an unconventional method. In this case, it is asserted by formal placement,

beginning in B and ending in E. These bars of the score may also be seeing as a connector of two

different sections of B (Section 1 and Section 2), but we will prefer to consider them as a part of

Section 1 due to its re-exposition in mm. 38 to 52, when these bars are related with Section 1.

As we just said, Sections 1 and 2 are very contrasting between each other. This contrast is due to

the textures of the music. Whereas Section 1 uses an homophonic texture, Section 2 will include

also a contrapuntal one. This polyphony of Section 2 is very naif, using just the imitation of M9

with a passive accompaniment after each entrance. Finally, a D Major (add. 9th in the bass) triad

is presented to finish Section 2. Then Section 1’ is exposed with the same material that Section 1.

Part C

This part will feature an array of variants of elements that have been used already. Also the

inclusion of some new elements will occur.

Opening this part, in mm. 53-54, M8 is presented one octave below. This motive has harmonic

implications, such as the formal placement, which means that it begins, goes through and ends in

notes of the triad of E minor (pitch classes G-E-B).

In mm. 56, another variation of M2 occurs. In this case, it is the inversion of M2 with a prime

form [01357],which is a subset of the prime form from M2,1, which is [013578]. After this chord,

in mm. 59 to 70, a variant of M8 is displayed, this time in the lowest octave of guitar’s register.

A new element, the “rasgueado” (typical element from flamenco tradition) will be featured in

combination with strokes in the top of the instrument, it adds a powerful effect. The chord

displayed in the “rasgueado” can be analyzed as an E (3!) add. 6th, with a prime form [01458].

Then, again is alternated a variation of M8 with the “rasgueado”.

Another new element is the inclusion of a melodic section from mm. 77 to 82. If we consider the

two first notes of this section as a “upbeat” or two “extra notes”, we will discover that the

following two motives are transpositionally symmetrical and have one common note (last note of

the first one is the first note of the second one). These motives will be named M9 and M9,1 and,

of course, they share its prime forms [012458] (Ex. 18).

The two last elements presenting new material appear in mm. 88 to 92. The first one, is the group

of notes in measure 88 (G#-C-B-A-E-G), whose prime form is [013458]. This prime form is very

similar to many that we have found throughout the piece (for instance, [01348], [013578],

[013478], [01458], [012458]), and this is a convergence that should be mentioned. In the same

manner, in the next measure, from mm. 89 to 92, we will find a group of notes (C-F#-E), whose

prime form is [026], and again, this is not the first time that such a prime form appears (its firts

appearance was in measure 33).

Parts A’ and B’

Both parts are repeated with the same harmonic material. Therefore, the piece will close with M7

with a clear cadential gesture over E as tonal center, and thus the last chord will be a E suspended

4th, so we are not able to precise if this final is on E Major or E Minor. Although, we are able to

sentence that E has been established as the tonal center.

3- Rhythm.

In Elogio de la Danza, many rhythmic patterns will be used as recurrent material. We will discuss

how this material is developed, elaborated and repeated in order to create clear relationships

within the work.

a) Lento.

Part A

-Section 1: the first pattern that is repeated is the relationship between M1 and M2: a group of

three notes of the same pitch class (E) is followed by a fast ascendent arpeggio. This situation

happens twice during mm. 1 to 3, and will be featured also in M2’1 and its predecessor triplet

(mm. 27- 28), and in M2,2, with a slight variation though (measure 45). This time, the three-times

repetition of the same pith class will occur after the ascending arpeggio (not before, as in former

examples) and will be featured in the higher register (A#).

The next pattern is presented in the last beat of measure 3 and the entire measure 4, where the first

syncopation occurs, followed by a triplet. Also, this will be a rhythmic pattern within A. It

happens too in mm. 7 in Section 1, and in 20, 21 and 23 Section 1’.

The flexible, rhapsodical character of the movement is exposed with certain rhythmic effects such

as written accelerandos and rubatos. Some examples of this rushing effects can be seeing in

measures 5 and 6. In the first half of the measure 5, M3 (whose prime form is [012]), is presented

on a real sequence situation, but rhythmically it is featuring a written accelerando: at first, M3 is

presented in three sixteenth notes, then in a triplet of sixteenth notes and then in three thirty-

second notes.

-Section 2: Since the beginning of this section, the role of triplets will be promoted. The moto

(movement) of triplets will be executed all over the section, with one rest point in measure 14,

though (with a rest and an quarter note).

Part B

In this part, again the rhythm of triplets is overused. It may be consider too as an elaboration of

M1 (the group of three notes of pitch class “E”). In this manner the triplet will be featured in

several ways, namely: exposing the same pitch class (M1,1 in measure 25), in a melodic fashion

(E Aeolian in measure 26), and presenting a sequence of four-in-a-row ascendent fourths motion

with the progression [025]-[025]-[026]-[015] in measure 33.

From measure 44 on, the intermission of rest-measures will create an effect of ritardando, which

will be kept until the end of the movement.

Part A’

In this part, the same material of A is exposed with some variations, though. This time, through

the space or rests in-between the repetitions of M2, we can appreciate a written rallentando that

will lead us to a fade out effect in rhythm.

b) Obstinato.

Part A

An ostinato is defined as a rhythm and pitch pattern of the same length (Kostka, 2006, pp. 133).

Here we will analyze how this pattern is presented in this movement.

As we say before, we may perceive two different planes within A. In the plane above, we can see

that at the beginning M5E is presented in measure 1, followed by M6E in measure 2, and later by

M6E+M5E in measure 3. Therefore, if M6E has three pairs of dyads and M5E has two pairs of

dyads, then M6E+M5E will have five pairs of dyads. This conclusion might seem obvious,

although it has compositional implications. If we analyze the plane below (the pedal of pitch class

“E”), we will note that it is performed three times and then two times during mm. 1 to 3. We can

compare the nature of this situation with the one above and we will find that again the “3+2=5”

equation is developed.

In the same manner, we will be able to perceive that groups of 2, 3 and 5 dyads or tetrachords will

be the most constituent part of this ostinato. Each group is isolated by rests, so it is very easy to

find and define every single group within the ostinato.

Parts B and C

In these parts, we will be able to appreciate just the rhythmic repetition of new motives. Some of

them have cadential implications, such as M7 in measures 17 and 18 (and its reiterations),

supporting an accent in the downbeat of measure 18. And some other motives have melodic-

harmonic implications. This is the case of M8, whose division may be rhythmically defined in

3+3+1 (G-E-E / A-E-E / B). In the first note of each group, he is outlining an important part of the

harmony of E Minor, therefore the rhythmic aspect is helping to bring out the harmony.

Examples:

Examples:

1) M1: 2)M2:

3) M3: 4) Sequence with M3:

5) M4: 6) Sequence with M4:

7) -Ending of sequence with M4, 8) M1,1 -Syncopation before triplets, -Repetition of pitch class “B” (as a V of E).

9) Aeolian Mode: 10) M2,1:

11)M2,2 12)M5E

13) M6E: 14) M6E+M5E:

15) Real planing: 16) M7:

17) M8:

18) M9 (C-C#-F-E-D#-A) and M9,1(A-Bb-D-Db-C-F#):

References

Books:

-Brouwer, Leo. Gajes del oficio. Editorial Letras Cubanas 2004.

-Kostka, Stefan M. Materials and techniques of twentieth century music. Third Edition Pearson

Prentice Hall, New Jersey, 2006.

Website:

-http://chevalierdesaintgeorges.homestead.com/Brouwer.html

Score:

-Leo Brouwer, Elogio de la Danza.