The Intégrales of Edgard Varèse Space, Mass, Element, and Form.pdf

The Intégrales of Edgard Varèse Space, Mass, Element, and FormAuthor(s): John StrawnReviewed work(s):Source: Perspectives of New Music, Vol. 17, No. 1 (Autumn - Winter, 1978), pp. 138-160Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/832662 .

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THE INTEGRALES OF EDGARD VARESE SPACE, MASS, ELEMENT, AND FORM

JOHN STRAWN

Introduction

After a protracted and undeserved hiatus, the music of Edgard Varese has in the past few years experienced a sort of "comeback" in the literature. Several biographies have already appeared [13, 17, 26, 27];* reprints of Varese's own theoretical lectures and writings [1, 4, 5, 6, 19, 23, 24] as well as analyses by others [7, 29, 30, 31] are surfacing more and more frequently in publications devoted to music. But the literature to date has only occasionally [2, 11, 28] touched upon certain aspects of the music of Edgard Varese which will be treated in detail here.

Composed in 1924 and premiered in 1925 [26, pp. 216-25 passim], Inte'grales lends itself to a thorough analysis. Not only was it written during Varese's most creative period; a number of Varese's own statements about this work have also appeared in print. Integrales thus provides an excellent test case for examining the relationship between Varese's theoretical statements and his compositional prac- tice. The aspects of Integrales discussed here, as well as other important elements [14, 20] play a role in the rest of Varese's works which, however, can only be mentioned in passing.

The Concept of Space

Let us begin by examining Varese's own statements about Int'- grales. Varese was the author of the program notes for the premiere

* References cari be found at the end of this article.



THE INTEGRALES OF EDGARD VARESE 139

[26, pp. 227-28]. But another, lengthier passage from a lecture held in 1939 at the University of New Mexico (Santa Fe) is more inform- ative, and all the more significant, as Varese quoted the same passage again in his lecture at Princeton twenty years later:'1

Integrales was conceived for a spatial projection. I constructed the work to employ certain acoustical means which did not yet exist, but which I knew could be realized and would be used sooner or later... Whereas in our musical system we divide up quantities whose values are fixed, in the realization I wanted, the values would have been continually changing in relation to a constant. In other words, it would have been like a series of variations, the changes resulting from slight alterations of a function's form or from the transposition of one function to another. In order to make myself better understood-for the eye is quicker and more disciplined than the ear-let us transfer this conception into the visual sphere and consider the changing projection of a geometrical figure onto a plane surface, with both geometrical figure and plane surface moving in space, but each at its own changing and varying speeds of lateral movement and rotation. The form of the projection at any given instant is determined by the relative orientation of the figure and the surface at that instant. But by allowing both figure and surface to have their own movements, one is able to represent with that projection an apparently unpredictable image of a high degree of complexity; moreover, these qualities can be increased subsequently by permitting the form of the geometrical figure to vary as well as its speeds . . . [17, p. 83]

A short, inconspicuous footnote in the score of Integrales is crucial for the interpretation of this idea of "spatial projection". In m. 203, a "solo" in the oboe is "accompanied" by four other instruments (see Ex. 1). A footnote in the same measure specifies: "Clarinettes, Cor, Trptte, Trbne.-tres homogenes et equilibres-lkgerement au 2me

plan". It would seem here that the four instruments listed are to form a single "plane" in juxtaposition to a second "plane" in the oboe alone.

This idea of "plane", along with such terms as "surface" or "mass", appears to play a crucial role in Varese's music. As Varese generalized

1 The lecture given by Var'se at Princeton in 1959 has apparently not yet been published in its entirety. Excerpts appear in [4, 19, 24]. A typewritten manuscript [25] exists, but in many places it does not match the printed versions cited; cf. note 2. Quotations from [24] translated by the present author.



140 PERSPECTIVES OF NEW MUSIC

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in his Princeton lecture, "My music is based on the motion of unrelated sound masses.. ." [25, p. 3]. In discussing Deserts, Varese wrote: "The musical language given to the instrumental ensemble may be said to be evolved in opposing planes and volumes..." [17, p. 184]. This idea of three-dimensional masses of sound can be traced back to an early experience in Varese's life:

As a child, I was tremendously impressed by the qualities and char- acter of the granite I found in Burgundy, where I often visited my grandfather.... And I used to watch the old stone cutters, mar- velling at the precision with which they worked. They didn't use cement, and every stone had to fit and balance with every other. [18, p. 36]

But it would seem that Varese chose to ignore the example of the stonemasons' precision when he was selecting words to describe his music. The writings and lectures of Varese contain several different terms which seem to have been used as synonymous labels for the same concept: "sound mass" or simply "mass", "plane", "zone", "volume", and "block". For the sake of clarity, "sound mass" and "mass" will be used throughout the rest of this paper.

Continuing our examination of Varese's statements, it would seem




that traditional instruments stood in Varese's way as he was trying to realize his ideas. In a letter to Leon Theremin, Varese wrote:

I no longer wish to compose for the old instruments played by men, and I am handicapped by a lack of adequate electrical instruments for which I conceive my music. [22, p. 44]

Varese was not merely interested in generating certain sound masses which until then existed only in his imagination; he also wanted to process these masses in his compositions, and to submit them to a certain spatial development:

Personally, for my conceptions, I need an entirely new medium of expression: a sound-producing machine.... And here are the ad- vantages I anticipate from such a machine: ... a sense of sound- projection in space by means of the emission of sound in any part or in as many parts of the hall as may be required by the score... [6, pp. 191-92]

This idea of space, by the way, has nothing to do with the more philosophical argument about "space in music"; Varese was thinking of the auditory impression of a number of sound masses, each moving in space. Varese's own observations also provided the inspiration for the idea of sound in motion, comparatively rare as a compositional element in pre-Varesian music:

I began listening to sounds around me from all directions, and imag- ined how such sounds, and in just such a complexity, could be transmuted into music. It excited and stimulated me to think about the possibility of such a metamorphosis, and I began to imagine the invention of new devices that would make spatial music possible. [1, p. 195]

Not until Podme Dlectronique did Varese have at his disposal the equipment necessary to achieve such spatial motion:

The music [on tape] was distributed by 425 loudspeakers; there were twenty amplifier combinations.... The loudspeakers were mounted in groups and in what is called "sound routes" to achieve various effects such as that of the music running around the pavilion, as well as coming from different directions.. . etc. For the first time I heard my music literally projected into space. [19, p. 207]

Although these sound masses were to be heard simultaneously, Varfse also wanted the listener to be able to perceive each mass as a separate




entity. Such a demarcation would have been a further advantage of the "sound-producing machine":

Moreover, such an acoustical arrangement would permit the de- limitation of what I call "zones of intensities." These zones would be differentiated by various timbres or colors and different loud- nesses.... The role of color or timbre would be completely changed from being incidental, anecdotal, sensual, or picturesque; it would become an agent of delineation, like the different colors on a map separating different areas, and an integral part of form. These zones would be felt as isolated, and the hitherto unobtainable non-blending (or at least the sensation of non-blending) would become possible. [19, p. 197]

During a radio interview years later, Varese made a comment which can leave no doubt that these ideas are to be applied to Integrales:2

I hope in the near future to have at my disposal, equipment which will allow for spatial relief. I would be interested, if only for the sake of proving my point, in realizing Inte'grales as they were orig- inally conceived.

We have thus reached a first stage in interpreting the footnote cited above: Varese wanted to compose these measures so that the listener would have the impression that the sound mass constructed in and of the four instruments listed, was separated, but still located "not too far away", from the mass outlined by the oboe.

Varese was more than aware of the problems inherent in such an undertaking:

Not until the air between the listener's ear and the instrument has been disturbed does music occur.... In order to anticipate the result, a composer must understand the mechanics of the instruments and must know just as much as possible about acoustics. [6, p. 188]

The question thus arises: if the position of a musical instrument relative to the listener is not changed, how can the composer or performer create the auditory impression that the sound produced by the instrument is moving in space? Normally, we rely on experience when localizing sounds from sources which are familiar [3, pp. 37, 155], and the visual component plays a decisive role for localizing sound sources which are visible. As for unfamiliar or invisible sound sources,

2 Translated from [24, p. 67]; not in [25]. I have not been able to find this passage in [5].




research to date has not been able to precisely define the relationship between the distance from the sound source to the hearer, and the auditory estimate of that distance.s However, it is currently assumed that three factors play a role in estimating the distance for an un- known source of sound: loudness, timbre, and reverberation. 1) The sound pressure level of a signal arriving at the ear decreases with increasing distance of the sound source from the hearer, and thus the perceived loudness of the signal decreases as well. [3, pp. 96, 99] In everyday experiences, loudness of the sound source and distance of the associated auditory image are directly related. 2) For comparatively large distances, it is assumed that a change. in timbre is brought about by the non-linear transmission characteristics of the atmosphere, which is also a factor in estimating the distance of a source of sound (but see [3, pp. 233 ff.]). It is also interesting to note at this juncture that the timbre of an instrument is related to dynamics: if an instrument is played loudly, a brighter, richer sound is produced. [16, p. 256] 3) In closed rooms, reverberation apparently plays an important role. The more reverberant, the more diffuse a signal which reaches the ear, the greater the distance perceived. [3, p. 223]

The extraordinary orchestration and the carefully notated, compli- cated dynamic markings in Integrales would strongly suggest that Varese thought of a loud, brilliant, present sound (sound source) as creating a sound mass (auditory image) located in the vicinity of the listener. A soft, dull sound, on the other hand, is to be heard and understood as being "far away". Diminuendi, crescendi, and other transformations would represent intermediate steps between these two extremes.

Vermeulen's research and the so-called Frannsen Effect have furthermore cast some light on the ability of the ear to perceive different sound sources as a single entity. [3, pp. 223 ff.] These discoveries strongly suggest that a passage, such as in m. 19 (see Ex. 2), where the A# in the oboe is continued by the trumpet, is to be understood as an attempt to synthesize a new sound. The entrance of the oboe is undoubtedly masked by the sixteenth note in the trumpet, which is carefully notated with an accent. Even if the oboe entrance were

3German-language publications conveniently distinguish between the Schall- ereignis, or the physical process outside of the listener, and the Hdirereignis, which includes the idea of the listener's "ear", a distinction which forms the basis for the following argument. Cf. [15, pp. Iv-vi].




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audible in performance, this passage is a striking example of Varise's desire to overcome the "handicaps" of traditional instruments, creating a single sound mass outlined by two instruments.

Masses

Let us then return to the two sound masses mentioned in Varise's footnote cited above (Ex. 1). This passage has been composed so that several factors make it possible to differentiate between the two masses: 1) Except for a single F?, all of the pitches played by the oboe are above those of the accompanying chord. 2) The dynamic markings for the instruments playing the chord are completely different from those for the oboe. 3) An extended series of pitches is presented by the oboe, while the pitch content of the chord in the other instruments remains constant. 4) The mass in and of the chord is orchestrated such that it can sound "tres homogenes", which further separates it from the more penetrating quality of the mass outlined by the oboe. 5) The chords in mm. 199-205 might be divided into two major groupings, whereas the oboe, although it enters later (m. 200), plays a longer series of notes without major breaks.

There are three other footnotes in Varese's works which would lend support to such an analysis. In m. 43 of the second movement of Octandre, the footnote reads: "en-dehors-au meme plan que le Trombone jusqu'a 5", where "5" refers to m. 50. Here, a mass con- sisting of the horn, trombone, and double bass is separated from two other masses: one in the clarinet, oboe, and bassoon; the other in the trumpet.

Two more footnotes are to be found in m. 178 of Integrales: "Clarinettes = Sonorite creuse (lIgerement dominantes)" and "Cor., Trptte. en ut, 3me Trombone, tres equilibr&s-presque au 2me plan Ptes.Fls., Hb.-Trptte. en re a l'arriere plan". As in the passage already examined, the masses are again separated by the use of different pitch ranges, dynamic markings, etc. It should also be pointed out that in these footnotes from Intigrales and Octandre, a single instrument is specifically labelled "mass" or "plane". Finally, the desire to create a spatial impression has been spelled out here in so many words: the mass of the trumpet is supposed to sound as though it were farther away from the listener than the other masses.




Varese's statement-cited above in an abbreviated form--can now be understood in its entirety:

My music is based on the movement of unrelated sound masses which I always conceived as moving simultaneously at different speeds. [25, p. 3]

Speed is not to be understood here as the tempo with which a number of notes is played, or the number of notes per second. Rather, this concept provides a basis for a deeper understanding of the rhythmic relationships among the four masses in mm. 174-182 just discussed: a given number, density, and length of appearances charac- terize each individual mass. This would certainly not rule out a simultaneous entrance of two or more masses. On the contrary, it would appear in many passages that two or more masses enter together for a short time due to their nearly identical, so to speak, periods-analogous to a similar process in the music of such people as Steve Reich.

It would be appropriate at this juncture to divide Intigrales into its constituent sound masses. In general, it will be assumed here that Varese had a single sound mass in mind whenever a given group of instruments appears together consistently in a characteristic manner." For the sake of simplicity, such a listing is reproduced here as Table I. (See pp. 147-150.)

The two passages cited above (m. 178 and m. 203) have been incorporated into this table as Masses 65-70 and 95-96, respectively. The percussion in mm. 173-176 has been divided into two Masses, 65 and 67, based upon the auditory impression that the Chinese blocks sound closer, more vivid than the diffuse sounds of the chains, sleighbells, and drums. Masses 6, 18-22, 31-34, and 57-58 can clearly be separated in an analogous fashion, and require no further comment.

Mass 1, like Masses 66 and 96, is outlined by a "solo" line, presented in succession by four different instruments (cf. Ex. 2). The impression of motion "toward" and "away from" the listener is especially apparent in those passages in which other masses do not predominate (mm. 1-4, 12-13, 19-22). Mass 2, distilled from soft percussion sounds, is perhaps the "most distant" mass. As with Masses 65-70, discussed above, a characteristic selection of pitch range, dynamics, orchestration, etc., is used to separate Masses 3 and 4. To continue Varese's visual analogy, the image of two pulsating entities

4A more rigorous algorithm based on an apparently analogous model and used to analyze Density 21.5 is discussed in [21].




TABLE 1 The "Masses" in Inte'grales Mass Measure Instruments No.

1 1-25 clarinet I 10-11 trumpet II 12-13, 19 oboe 18-21 trumpet I

2 4-23 gong, tam-tam, triangle, crash cymbal, cymbals (except m. 8)

16-20 suspended cymbal 16-17 bass drum

3 5-25 piccolo I, II, clarinet II 4 5-23 trombone I, II, III 5 6-23 tenor drum, snare drum, castanets, sleighbells,

chains, tambourine, twigs 8 cymbals 9-15, 18-20 bass drum 10-14, 22 suspended cymbal

6 15-19 Chinese blocks 7 25 clarinet I (from the last eighth note in m. 25)

trumpet I, II 26-29 tutti

8 29-31 percussion 9 32-54 horn, trombone II, III

32-52 snare drum, tenor drum, cymbals, Chinese blocks, chains, tam-tam, bass drum

44-45 piccolo I, oboe, clarinet II 10 36-52 woodwinds (except m. 44-45), trumpet I, II,

trombone I, suspended cymbal (missing in m. 38-typographical error?), gong, crash cymbal

11 53-62 clarinet I, II, trumpet I, percussion 12 54-70 trumpet II 13 62-70 trumpet I 14 62-70 trombone II 15 63-66 oboe, clarinet II

63-70 horn 16 63-70 trombone I 17 67-70 trombone III 18 71-771 piccolo I, II 19 72-75 percussion 20 72-77j clarinet I, II 21 74-76 horn, trumpet I, II




TABLE I (cont.) Mass Measure Instruments No.

22 76-771 trombone I, II 23 771-78 woodwinds 24 771-78 brass 25 79-93 percussion 26 80-93 clarinet I, II 27 80-92 horn, trumpet I, II 28 82-90 trombone I, II, III 29 93-100 horn, trumpet I, II 30 93-100 trombone I, II, III

percussion (bass drum starting in m. 90, crash cymbal in m. 92)

31 101-105 oboe 32 101-105 piccolo I, II 33 102-105 trombone II, III 34 102-104 percussion (except for the tam-tam in m. 103) 35 103-104 tam-tam

105-119 trumpet I, II, trombone I, percussion 36 106-117 woodwinds, horn, trombone II 37 117-121 trombone II, III 38 119-120 woodwinds 39 120-121 horn, trombone I 40 121 oboe, clarinet I, II 41 121-126 horn 42 121-126 trumpet II 43 121-126 trombone I 44 121-126 trombone II 45 121-126 trombone III 46 124-126 trumpet I 47 126 woodwinds 48 127-130 clarinet II, horn, tenor drum 49 131-134 clarinet I, II, trumpet II 50 131-134 trombone I, II, III, cymbals, bass drum 51 134-135 horn, trumpet I, snare drum, suspended cymbal 52 134-143 trombone I, II, III

141-143 bass drum 53 135-143 woodwinds

138 castanets 141-143 cymbals

54 140 string drum, sleighbells, tam-tam




TABLE I (cont.)

Mass Measure Instruments No.

(54) 141-143 suspended cymbal, snare drum, tenor drum, gong

55 144-154 horn, trumpet I, II 56 151-154 tutti 57 155-161 percussion except Chinese blocks 58 158-160 Chinese blocks 59 161-172 oboe 60 168-172 piccolo I, clarinet I, II 61 168-172 trumpet II 62 171-173 horn 63 172-173 trombone I, II, III 64 173 tam-tam, bass drum 65 173-175 sleighbells

174-176 snare drum, tenor drum, chains 66 174-181 trumpet I 67 175-176 Chinese blocks 68 175-181 piccolo I, II, oboe 69 178-182 clarinet I, II 70 178-181 horn, trumpet II, trombone III 71 183 percussion 72 184-186 piccolo I, oboe 73 185-186 clarinet II 74 185-186 horn, trumpet I, II 75 185-186 trombone I 76 186 Chinese blocks 77 187-190 trombone I, II, III, string drum, tam-tam, bass

drum 188 horn

78 189-190 piccolo I, II, clarinet I, II, horn, trumpet I, II, suspended cymbal, snare drum, tenor drum, gong, crash cymbal

79 190-198 oboe 80 194 trumpet I, II 81 194 trombone I, II, III 82 194-198 clarinet I 83 195-197 castanets 84 195-197 trombone II, III, bass drum 85 195-198 horn 86 195-197 snare drum




TABLE I (cont.)

Mass Measure Instruments No.

87 195-197 Chinese blocks 88 195-197 sleighbells, chains 89 195-197 tenor drum 90 196-198 tambourine 91 196-198 suspended cymbal 92 196-198 piccolo II, clarinet II, trumpet II 93 196-198 piccolo I 94 196-198 trombone I 95 198 clarinet II

199-205 clarinet I, horn, trumpet I, trombone I 96 200-206 oboe 97 206-212 trumpet I, II, trombone I, string drum 98 212 piccolo I, II, clarinet I, II, suspended cymbal,

triangle 99 212-213 castanets

213 percussion 100 214-218 horn, trombone III 101 214-215 trumpet I, II, trombone I 102 215-217 woodwinds 103 217 percussion 104 218 oboe, clarinet I, II 105 218-2231 horn 106 218-2231 trumpet II 107 218-2231 trombone I 108 218-2231 trombone II, III 109 221-2231 trumpet I 110 223J-224 tutti

comes to mind, entities which repeatedly penetrate into and then dis- appear from the listener's field of hearing. The pulse of Mass 5 orig- inates "far away" in m. 6, springs into the immediate vicinity of the listener in m. 13, and starts fading away in m. 18 (cf. Ex. 2).

The following have been analyzed in a similar manner: Masses 9-10; 18-28; 31-34; 35-36 as well as 55 and 97; 37-40; 52-54; 59-64; 71-76; 79-94, where it should be noted that the percussion instruments can hardly be grouped into a single unit in light of the fact that their entrances are timed independently of each other;




99-103; and, recalling Mass 10: 47; 77-78; 98; 37-40; 102; and 104.

The singular entrance of piccolo I, oboe, and clarinet I in mm. 44-45 is especially noteworthy (Ex. 3). This is undoubtedly a further

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attempt on the part of Varese to "synthesize" a new sound with con- ventional instruments. As is well known, Varese had studied Helm- holtz. [17, p. 18] Helmholtz wrote that two sounds would sound as one "especially when all the sounds which are mixed have frequencies which are whole-number multiples of one and the same frequency".5 The C$ in the oboe, mm. 44-45, thus becomes the sixth harmonic of the F$ in the contrabass trombone; the Bb in the Bb clarinet and the A-B in the piccolo I represent the seventh and fourteenth harmonics of the C in the bass trombone; the effect of the mixture ranks in the pedal division of a well-built pipe organ comes to mind. Varese also took account of the fact that the seventh and fourteenth harmonics do not correspond exactly with a minor seventh (in this case, C-Bb), by color- ing the Bb in the clarinet with the change from A to B in the piccolo.

Mass 7 is set apart from Masses 1-6 and Mass 8 through the use of new instrumental groupings (cf. Mass 56). Masses 29-30 and 48-51 have been delineated due to the occurrence of a "melody" and a "pulse", both of which have already been encountered in other masses as well.

Only three groups of masses have not been touched upon thus far in this discussion. Masses 11 and 12 offer a third example of an attempt to generate a new sound, three of the pitches played by the trumpet II being echoed by-as though lightly etched upon-the other three instruments. Since there is no significant caesura in the trumpet II part, mm. 54-69, it is treated as representing a single mass. The other instruments in mm. 62 ff. have all been assigned to single masses (Nos. 13-17), because they remain independent of each other (see, for example, the extreme care with which the rhythms in m. 65 and m. 68 are notated, or the dynamic markings in m. 69). Masses

5 Translated from [9, p. 49] by the author; cf. [10, p. 30].




41-47 have been separated in an analogous fashion. Masses 105-109, on the other hand, involve more than a mere "transposition" of Masses 41-47 "a minor third higher"; thus, the writing for the trombones (cf. mm. 123-126 with mm. 220-223) necessitates a different division into masses.

Elements

A closer examination of the construction of each individual mass lends support to this dissection of Integrales into its constituent masses. Varese was fond of quoting Brahms as having said that composition was "the organization of disparate elements" (e.g., [6, p. 188]). At the risk of taking Varese too literally, we can apply the convenient label "element" to the constituents of a relatively small repertoire of motifs and procedures into which each of the masses in Table I can be dissected. Each element is listed here with a one-word caption title, a brief description, and representative examples of its use in solo (melodic and percussion) and ensemble situations:

1. Appoggiatura: the work begins with a quasi-appoggiatura figura- tion (m. 1, clarinet I), which occurs again and again throughout the piece (further examples: m. 36, trombone I; m. 13, snare drum; m. 63, oboe, clarinet I, horn). 2. Prolongation: a given note or chord is assigned a duration which is relatively long in comparison with the durations of the events im- mediately surrounding it, as in mm. 1-3, clarinet I (cf. also m. 161, oboe; m. 4, gong, tam-tam; mm. 145-147, horn, trumpet I-II). Dy- namics (mm. 32-33, trombone II-III), timbre (mm. 127-128, clarinet II and horn), and/or orchestration (m. 19, oboe and trumpet I) are often modified in the course of the sustained event. 3. Reiteration: a note or chord is repeated several times, as in the clarinet I, m. 4 (cf. mm. 164-166, oboe; mm. 175-176, Chinese blocks; mm. 74-75, horn, trumpet I-II). 4. Alternation: repeated alternation between two pitches, chords, etc., as in the clarinet line, mm. 7-9, which fluctuates between Ab and Bb (cf. mm. 106 ff., woodwinds, horn, trombone II; mm. 120-121, horn, trombone I); or alternation between three such "states", e.g., in the horn, mm. 195-198, or in the Chinese blocks, mm. 15-19. 5. Tutti: involves nearly all of the instruments in the ensemble. First




occurrence in mm. 25-28; but cf. also mm. 36, 38, etc., as well as mm. 194-198. 6. Pulse: a more or less regular beat is established, such as was already discussed in Mass 5 of m. 6; but cf. also mm. 93 ff. 7. Pitch curves: the sirens described in Helmholtz were an important inspiration for Varese in the development of his concept of spatial music. [26, p. 42] "Later I made some modest experiments of my own, and I found that I could obtain beautiful parabolic and hyperbolic curves of sound, which seemed to me equivalent to the parabolas and hyperbolas in the visual domain." [17, p. 18] Such instruments were actually used in other works by Vareise. But successions of pitches which follow the outlines suggested by parabolic and hyperbolic curves seem to have captured Varese's interest even when played by traditional instruments (mm. 62-69, trombone II; m. 168, piccolo I; m. 120, trombone II-III). 8. Selection of pitch content (vertical): as far as I know, no com- prehensive study has been published to date on the question of harmony in Varise's music.6 Vareise himself repeatedly emphasized that his music was not based on any "fixed set of intervals such as a scale or a series" [19, p. 206]. Not surprisingly, it seems impossible to derive the choice of pitches in the individual masses in Inte'grales from such a framework. Still, Vareise seems to have applied a few basic rules of thumb: octaves, for example, are usually avoided. On the other hand, "strong dissonances", such as major and minor seconds, augmented fourths, major and minor sevenths, and their octaves occur quite frequently, both in the selection of pitches for a single mass and in the distribution of pitches of masses presented simultaneously. An extreme case is the use of eleven different pitches for the eleven pitched instruments as in m. 28. 9. Selection of pitch content (horizontal): since a system of "harmony" is apparently not present in Inte'grales, it is accordingly diffi- cult to derive the selection of successive pitches from such a system. Rather, the distribution of pitches for the first presentation of a given series of notes seems to have been worked out in conjunction with the principles outlined in 8. above. One further principle apparently plays a role in the expansion of the pitch content through time: once a given pitch content has been presented, the stated note or interval

6 In [12], a computer study is made of the chords in the first 38 (!) measures of Inte'grales; but the conclusion reached there on p. 146 is hardly justified.




is expanded by neighbor-note motion, usually chromatically, some- times combined with octave jumps (cf. Mass 1; mm. 191-193, oboe; mm. 117-121, trombone II-III).

The separation of the masses is thus achieved not only through the selection of a characteristic range, orchestration, etc., for each mass, as was discussed above; a characteristic selection from this repertoire of elements is assigned to each mass as well. Mass 1, for example, is constructed from the "appoggiatura", the "prolongation", and the "alternation"; the "alternation" between two pitches is gradually expanded in chromatic steps in accordance with the principle discussed under "pitch selection (horizontal)" (but see also [14, p. 442]). Fur- thermore, the regular "pulse" occurs in one passage (mm. 14-16). The "prolongation" plays a major role in Masses 3 and 4 (the two instrumental blocks) as well as in Mass 2 (in some of the percussion instruments). Mass 5, the regular "pulse" in the other percussion mass, is molded almost exclusively from this one element.

Even such a "traditional"-sounding passage as mm. 93 ff. (also discussed in some detail in [14, p. 443]) can be broken into groups of constituent elements, which adds support to the division of this passage into two masses as discussed above. Mass 30 is quite obviously marked by the "pulse", and is set in juxtaposition to a mass formed from the following elements (presented in the following order) : "prolongation", "reiteration" (occasionally synchronous with the "pulse" in the other mass), and expansion of the "pitch content (horizontal)" combined with "alternation" above and below the initial pitch, D.

Form as Process

Having thus dissected Inte'grales in accordance with the ideas suggested by Varese's writings, the question now arises: can the "masses" and "elements" in Integrales be treated in terms of a unifying concept of "form"? As might be expected, Varese had ideas of his own about musical form:

Rhythm is too often confused with metrics.... In my own works, for instance, rhythm derives from the simultaneous interplay of unrelated elements that intervene at calculated, but not regular, time-lapses.... Form is a result-the result of a process. Each of my works discovers its own form. [19, pp. 202-203]




Varese found support for this idea in an analogy to the process of crystallization. He was fond of quoting the mineralogist, Nathaniel Arbiter:

The crystal is characterized by both a definite external form and a definite internal structure. The internal structure is based on the unit of crystal which is the smallest grouping of the atoms that has the order and composition of the substance. The extension of the unit into space forms the whole crystal. But in spite of the relatively limited variety of internal structures, the external forms of crystals are limitless. Crystal form itself is a resultant rather than a primary attribute. Crystal form is the consequence of the interaction of attractive and repulsive forces and the ordered packing of the atom. [19, p. 203]

From the totality of the available musical material, Varese has se- lected a repertoire of elements, the "atoms" in the above quotation. These elements are arranged into masses, at first conceived quite independently of each other. Reproductions of Varese's manuscripts would seem to suggest that he prepared various score fragments before fitting them together into the final score, not unlike solving a jigsaw puzzle.7

As for the manner in which the masses "intervene at calculated, but not regular, time-lapses", a few of the masses listed in Table I can be related to another in terms of e.g., "thematic" shape, as shown in Table II. This would represent nothing more than the framework of a "crystal"-but such a "crystal" would not represent a static, stable structure. Varise, continuing his discussion of the formation of crystals, speaks of form as a process, based on

an idea, the basis of an internal structure, expanded and split into different shapes or groups of sound constantly changing in shape, direction, and speed, attracted and repulsed by various forces. The form of the work is the consequence of this interaction. [19, p. 203]

Each sound mass (here "groups of sound") is thus modified every time it penetrates into the listener's field of hearing, by a process in which various elements are added or removed, this being the manner in which elements contribute to the process of form. Some justifica- tion is also provided for bringing various kinds of elements together: a principle, e.g., that of the chromatic expansion of pitch content, is

7 Cf. [1, pp. 192, 194]. The footnote on p. 192 is especially important.




TABLE II Superficial relationships among the masses listed in TABLE I.

1-9-17-61-66-77-82 2-57 (2-3-4)-(9-10) -(18-19-20-21-22) -(25-26-27-28) -(31-32-33-34-35-36) -

(52-53-54) -(66-68-69-70) -(84-92) 5-25-30-(48-50) -54-64-71 6-58-67-76-87 7-(9-10)-(13-14-15-16-17)-(23-24)-(41-42-43-44-45-46-47)-56-(77- 78)-110 9-77-84 10 (high woodwinds) -38-40-47-78-98-102-104 10-16-63- (74-75)-(84-94) 12-60-73-85 28-56-70-81 (29-30)-(49-50-51) (37-38-40-41-42-43-44-45-46-47) -(100-102-104-105-106-107-108-109- 110)-59-96

applied in much the same way as a quasi-thematic entity such as the "pulse" or the "appoggiatura". Especially clear examples of this

process of addition and subtraction are to be found in Mass 1, Masses 12-17, or Mass 59. Furthermore, each mass is subjected to a unique set of modifications-the general case of the speed discussed only in

rhythmic terms on p. 146 above. For example, in mm. 185 ff., the clarinet II (Mass 73) is at first dominated by the "appoggiatura", followed by the "alternation" between three pitches (m. 186). Mean- while the "reiteration" occurs in Mass 72 (oboe, piccolo I), followed by the "alternation", but only between two pitches. Finally, the

"appoggiatura" and the "reiteration" are prominent throughout the simultaneous presentation of Mass 75.

An analysis of this kind permits a deeper understanding of Varese's use and meaning of the term "projection", cited in the lengthy quotation at the beginning of this article. For Varese, "projection" means not only that the sounds produced by stationary instruments should create the auditory impression of being projected into the space where the performance occurs; these masses are also projected upon and

through each other during the process:

When new instruments will allow me to write music as I conceive it, the movement of sound-masses, of shifting planes, will be clearly




perceived in my work, taking the place of the linear counterpoint. When these sound-masses collide, the phenomena of penetration or repulsion will seem to occur. Certain transmutations taking place on certain planes will seem to be projected onto other planes, moving at different speeds and at different angles. [19, p. 197]

Thus, the distribution of certain elements among the various masses is modified in the course of time as a result of this interpenetration. For example, the element of "reiteration" in the oboe, m. 184, is taken over by the mass in clarinet II, m. 185, and "passed on" to trombone I (Mass 75) in mm. 185-186. At the same time, the element of "prolongation" leaves the oboe (mm. 184-185) for Mass 74 in the horn and trumpets. This process of addition and subtraction of various elements, as opposed to traditional thematic or harmonic development, accounts for the modifications in the successive occur- rences of some of the masses, as summarized in Table II. Each time a mass is presented, the distribution of elements is rearranged, which would, of course, include the pitch content of the mass. Thus, Masses 102, 104, and 105-110 are not only to be heard and understood as a mere transposition of Masses 38, 40, and 41-47, respectively; rather, the distribution of the elements has been modified in such a manner, especially in the trombones after m. 220, that the trombones must now be assigned to three different masses instead of the former two.

One is reminded of Varese's analogy of sound masses and granite blocks, blocks which are chosen and positioned to fit and balance without cement. This analogy can be applied almost literally to Varese's process of composition, i.e., the fitting together of various sound masses: the masses are bonded together via the exchange of elements. This also provides a viable explanation for avoiding octaves: the pitch content of one mass is, so to speak, fitted into and comple- mented by the pitch content of the others without duplicating pitches. Obviously, the various elements are distributed among the masses which are heard simultaneously or successively in such a manner that the very exchange of elements is made possible.

But the masses are not bound to each other in an immobile stasis, since the motion of the masses in space also participates in the formal process by allowing for a dynamic exchange of elements. For example, the "solo" mass in the oboe has moved "near" the listener in m. 12, as opposed to the more "distant" Mass 5 dominated by the "pulse" (cf. Ex. 2). In m. 13, this Mass 5 suddenly comes closer while the



158 PERSPECTIVES OF NEW MUSIC mass in the oboe moves away and returns (p ffff/). At the end of m. 13, while both masses are "close" to the listener, the "solo" mass takes over the "pulse" (m. 14, now in clarinet I), and the mass in the percussion disappears (m. 14: chains, sleighbells, suspended cymbals, snare drum). Gradually, the mass in the clarinet moves away from the listener (mm. 14-16); in m. 18, new elements are added to it (trumpet I), and the pulse is separated and returned (m. 17) to the mass in the percussion (but see also [14, p. 443]).

An important question remains to be answered: can Intigrales be divided into two or three "major formal sections" separated by "ca- dences" (e.g., in mm. 28, 78, and/or 153), as has been attempted [8, 31]? One objection to such a procedure is the fact that the measures which are thus arbitrarily tied together show no internal unity which would intrinsically separate them from the other "sections". Similarly, it is impossible to derive a 2-, 3-, or 4-part form by examining the relationships shown in Table II (see also [14, p. 445]). But the strongest objection derives from the fact that such an undertaking ignores the idiosyncrasies of the formal process in Varese's music. Varise was not interested in subjugating every musical entity in In- tegrales to two or three groupings which would determine the "form". Indeed, he warned against such thinking on more than one occasion [19, p. 206]. To use Varese's words, we are confronted here with a "series of variations" since, in a larger sense, every mass is related to every other mass. The central feature in Varese's compositions is not the manner in and the extent to which the composer repeats and develops the "themes", "harmonies", or "motifs" chosen by him. Varitse does not introduce here, modify there; he constantly varies.

Conclusion

Inte'grales was created from a defined repertoire of organized sound masses, each of which is to be heard as a three-dimensional entity moving through space, appearing, disappearing, and re-appearing in the course of performance. The "framework" of this composition, the non-rigid "crystal form", is given by the number and frequency of such recurrences. The masses, in turn, are constructed from a fixed number of elements, which are exchanged between simultaneously and/or successively appearing masses.




Acknowledgments:

This article is based on a paper submitted at the Oberlin Conservatory of Music, Oberlin, Ohio, in 1973, in partial fulfillment of the require- ments for the Bachelor of Music degree. I should like to thank Prof. Robert Drummond at Oberlin for his many helpful suggestions and comments. A modified version of this article first appeared (in German) in Melos/Neue Zeitschrift fiir Musik, 1:446-456, 1975.

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