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ABSTRACT space. In view of the continuing interplay in his life between terminology and concepts advanced by Varèse in relation to with associated commentary. along space, Varèse’s of to concepts relationship a have to comprises a variety of visual material that can be understood present part contains the second half of my investigation and thinking is covered in detail in the firstpart of my essay. The pronouncements on the subject. The verbal dimension of his current figures, underlay his quite radical considerations and particularly the writings of Helmholtz, and later, other more quentlythroughout life.Hisinteresthis psychoacoustics,in music. Varèse spoke and wrote about his spatial thinking fre of experience the in haverelationships can spatial that role manifests space and also interrogates existing music ideas His about senses. the metaphoric and literal its in both space, here, considers Edgard Varèse’s relationship to the subject of Thistwo-part essay [1],the second part ofwhich is published V The with remarkablelucidity. an arrayofspiraldiagrams,Varèse hisconcepts directlyportrayed marginalia,doodlesand Inoriginalartworks, and vocalperformance. ofelectroacousticsoundprojectionorvagariesinstrumental distortions within whichhisspatialideascouldbedirectlymanifestedwithoutthe withthevisualevidence,acontext publishedhere,isconcerned part, New Music),referencesVarèse’s writingsandlectures.Thesecond I:TheVisualImagination, Part Evidence”(publishedinPerspectivesof “TheLast article, ofatwo-part manifested. Thefirstpart WordIs: outlook wasbothconceptuallyandmusically(especiallyinIntégrales) “rotating planes,”“beams,”“projection”and“penetration.”His involving with science,hedevelopedanidiosyncraticvocabulary imaginative positionregardingmetaphoric“space.”Throughcontacts 20th century. yetuniquely Centraltohisthinkingwasaninformed Edgard Varèse wasoneofthesingularmusicalinnovators The LastWord Is:Imagination l a r e n e g ©2017 ISAST with thisissue. See forsupplementalfilesassociated Email: . California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, U.S.A. Roger Reynolds (composer, researcher), Department of Music, University of My aim is to seek corroborative evidence regarding the the regarding evidence corroborative seek to is aim My is u Edgard Varèse’s Work, Part II: Visual Evidence Visual Varèse’s II: Edgard Work,Part of Aspects Spatial the of Study A e g o R al

Evi doi:10.1162/LEON_a_01160 A e l c i t r den r o n y e R c e l d s

- ther Schuller: ther thatVarèse referredcomposer with Gun antoin interview - generated. Figure 1 shows the Saint Philibert de Tournus nave through their own weight and the interdependent forces they stabilize to structures allowed blocks stoneshapingof their and cuts their of precision the how work, at stonecutters observing of impact the about passion with spoke Varèse A 1. materials in the Sacher Archives—manifests art, marginalia, doodles and diagrams to be found among his tion. But in other ways, his work—musical sketches, graphic semination of sound, thwarted the demands of his imagina- manipulationelectronicavailable dis- forthe andstrategies the as well capacity, as performance of limitations because composition musical of realm the in case the not was This control.unimpeded had he which situationsover in did he what consider to useful is it logistical), contextual, logical, creative aspirations and barriers to their fulfillment (techno- tions, some only can be poorly understood. for consideration; some of it is straightforward in its implica a evidence range studysections, This lays ing. of five out, in atstage—evidently this relevant antoeventual understand - incompletenecessarily are—thoughherecommented upon and examined enumerated, relationships the Nevertheless, ear.Varèse’shis that accomplishedas as were eye and hand made is claim No addressed. be could desires his which in Saint-Philibert [3]. to it owe I music,my in beauty or strengthany is there If VarèseLouise quotes her husband as saying: other. every with balance and fit to had stone Every position to and insupport of one another [2]. op- in time elementssame at the thusthe structure,using total the stabilizes other the onpushingelement one how . conceptof the music in project thinking of Romanesque architecture . architecture Romanesque of thinking decoration. pure structural architecture—without frills or unnecessary rc h it e ct . . u . when I composed r e LEONARDO, Vol. 50, No.5,pp.477–485, 2017

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. - 477 The appeal of this rough and asymmetrical structure from the early 11th century is evident. The materials used in the larger edifice, their form-bearing capacity, the interplay of simple symmetries with canny imbalances—it all bespeaks a structuring that both is principled and yet was fashioned as it evolved. Such a relationship between ends and means can surely be understood as formative to Varèse’s creative life.

2. Musical Sketches Varèse’s sketching for the seminal realization of relationships between the incantatory lines (“beams”) and chordal blocks (“masses”) in his composition Intégrales can be seen as pro- ceeding independently in the drafting examples in Figs 2–4. Figure 2 shows a detailed laying out of the linear element in a manner completely separated from parallel efforts to find a vertical sonority that will suitably complement it. The fashioning of the line was processed more rapidly and with more decisive nuance. Its chordal complement was still un- certain here with regard to density, pitch content, registral parsing and placement. Evidently, these two essential aspects of Intégrales—the most explicit of his middle-period works as regards spatial metaphor—were conceived of as independent elements. Varèse interacted substantively with the New York jazz Fig. 1. The Saint Philibert de Tournus nave. (Photo by Dougsim. Image scene in the mid-1950s, partially as a result of the urgings of source: . composer Earle Brown. During the period just before he left Creative Commons CC-BY.SA 3.0 License.) for Eindhoven to work on Poème électronique, there were a number of improvisatory sessions at his 188 Sullivan Street home in Manhattan. Oliva Mattis indicates there were as many as five during 1957. For one of them, Varèse prepared a graphic score that laid out a pitch-relative, time-coordinated mapping of gestural interplay for eight musicians (Fig. 3). The original was about two by three feet on onion-skin paper [4]. As no tempo marking is indicated, the anticipated energy level of this graphic prescription is unclear. The occasional rhythms indicated reflect Varèse’s frequent intermixing of differing beat subdivisions in rapid succession. One can infer that the eighth player is a trombonist as a result of the “slide” indications (rather than “gliss.,” which would have suggested contrabass). There are gestural imitations, repetitions and inversions, but most of the components are relatively brief, set off from one another by rests in staggered alignment. Significantly, Varèse utilized the same abstract graphic ma- terial as a point of reference for his work on Poème électro- nique, as can be seen in Fig. 4. New sources such as “pure sine wave generator” and “distorted sine wave filtered” (each with a relative band of frequency variation indicated) are speci- fied for the realization of part-identical gestural components. A specific scaling of dynamics in terms of decibel strengths is also shown at lower left. This precision is an interesting remnant of the interfacing between Varèse and the Philips engineers with whom he worked, not always easily, it would seem: “Varèse was in conflict with the Philips Corporation for demanding that their engineers create sounds which they considered too difficult to produce” [5]. Fig. 2. Edgard Varèse, page from the sketches for Intégrales. (Edgard Varèse Collection, Paul Sacher Foundation, Basel. Used by permission.)

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01160 by guest on 28 September 2021 Fig. 3. Edgard Varèse, graphic score for an improvisation. (Edgard Varèse Fig. 4. Edgard Varèse, improvisation score detail adapted for Poème Collection, Paul Sacher Foundation, Basel. Used by permission.) ­électronique. (Edgard Varèse Collection, Paul Sacher Foundation, Basel. Used by permission.)

Fig. 5. Edgard Varèse, marginalia from a letter to Louise. (Edgard Varèse Collection, Paul Sacher Foundation, Basel. Used by permission.)

3. Marginalia and Graphic Resources Around the same time as the improvisatory gesture-score, Varèse included a more nuanced graphic invention on the edge of a letter to Louise. Titled Voilà ton solo, it is aria-like (Fig. 5). The relative height of the line would appear to indi- cate (significantly) continuous pitch fluctuation up and down without the gestural separation of the eight-part improvisa- tion guide shown in Fig. 3. Whereas thickness suggests in- tensity to the eye, the hairpins and dynamic levels specified below are largely contradictory. There is a singular accent marking above, correlated with a graphic outcropping of the central calligraphy. An alternative possible significance to the variation of thickness—speculative, to be sure—might be the suggestion of proximity: thin = far, thick = near. Figure 6 shows a most intriguing page from the sketches Fig. 6. Edgard Varèse, page from the sketches for Déserts. (Edgard Varèse for Déserts. One would be hard pressed to imagine a more Collection, Paul Sacher Foundation, Basel. Used by permission.) explicit rendering of the notion of “projection,” raised in so many contexts by Varèse from the 1930s onward. The graphic reflection at the lower left of this page invokes the spirit of [C, G#, A, B] that then stretches out to a seven-note complex the gestural pitch successions on stave lines above. Which containing four repetitions so that it too contributes three preceded which? new elements toward saturating the chromatic space). Only The implication of a flowering out of germinal low-register the pitch class D remains unarticulated. The quasi-radial seg- elements (at the narrower end of the implied cone) parallels ments in the uppermost circle even suggest the repeated Fs the harmonic-gestural evolution sketched above, which can and As as “axes.” The linkage of the second and third circular be seen as three-staged (the low register chord [G, Ev, C#, E] focus (reading from the bottom up) could imply the tied-over is followed by another—now accumulating—four-note zone G#. Playing this sequence and listening to the ways in which

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01160 by guest on 28 September 2021 it builds a poignant harmonic tension through successive ad- of instruments, Varèse is not content here with a normative ditions, one experiences exactly the sort of sonic accretion range. He pushes the dimension of color toward a metallic proposed visually at the lower-left margin. An interrelated- spectrum by bringing gold and silver into his design, as if— ness cannot be doubted, and it is significant that Varèse used indeed—some “hyper” prism were at work. (They also subtly segments of spirals, circles and arcs to depict the elaborating support the implied regality of a crown-like overall form.) interconnectedness of this multimedial projection. The evo- Whatever the modality, Varèse’s sensibility demanded a di- cation is not merely logical as it might have been, but suggests mensionality that fully exercised the available, metaphoric also an outward radiation, or “projection.” space. The same fundamental concerns emerge whether he was working with sounds, texts or visual elements. A menu design (Fig. 8) depicts the spi- ral character of a snail shell, reinforcing consideration of shapes that were audi- torily represented by the curves in sonic space generated by sirens and lion’s roars as well as in the striking spiral sketches of the 1950s (cf. Figs 11 and 12). Later, as the prospect of electroacoustic resources was being realized, spiral shapes became some- thing of an obsession. Here, in Fig. 8, is a provocation happened upon and retained (one speculates) without clear notions of how it might be utilized. A photo of the eye of a hurricane posted in the composer’s studio in the later years carried forward the idea that certain abstract energy distribu- tions had parallels in the natural world [7]. One wonders whether, in their inter- actions at the time of the Philips project, Varèse and Xenakis discussed the idea of structuring sonic complexes in accord with natural phenomena, a line of think- ing that was powerfully influential in the latter’s work. Figure 9 shows a piece of paper, 39 × 51.5 cm, folded into four squares. Its quad- rants are suggestive of Varèse’s efforts to connect the spiral form with other physi- cal and sonic bases. An harmonic series on C, drawn with deliberate graphic weight- ing that favors the massive influence of the fundamental, is shown in the lower-right Fig. 7. Edgard Varèse, design for the cover of Hyperprism. (Edgard Varèse Collection, panel. Rudimentary numerical indica- Paul Sacher Foundation, Basel. Used by permission. tions suggest concern with the ratios im- plicated in tuning conventions. Given his While preparing the fair copy of the score for Hyperprism expressed interest in the microtonal precision of technology, ca. 1923, Varèse took the time to design an intricate, emblem- it is surprising that Varèse ignores the fact that an integral atic cover [6] (Fig. 7). It depicts, in two-dimensional space, succession of frequency values would necessitate microtonal with a variety of angular shapes, the essences of symmetry, adjustment. repulsion, energetic connectivities and lightning bolts sug- To the left of this panel are concentrically disposed spiral gestive of the ideas Varèse was verbally articulating about shapes, one marked by a circle of fifths beginning with C sonic space during the same period, especially in the text for at the top and proceeding clockwise. The upper-left panel his opera project The One-All-Alone. suggests a search for proportional values along a vertical One sees here how his sensibility requires balances to be axis that could form a basis for his later spiral diagrams. A unsettled. The larger wing on the left is rust while that on the rudimentary spiral unwinds in a clockwise direction toward right is red. The smaller internal sail-shapes are purple on the the lower-left edge of the panel. The upper-right panel is the right and green on the left. Further, as with the timbral colors most abstract and provocative, seeming to posit a planetary

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01160 by guest on 28 September 2021 Fig. 9. Edgard Varèse, a seminal four-panel sketch relating the overtone Fig. 8. Edgard Varèse, menu design. (Edgard Varèse Collection, series to various alternative representations. (Edgard Varèse Collection, Paul Sacher Foundation, Basel. Used by permission.) Paul Sacher Foundation, Basel. Used by permission.)

system of relationships combining magnitude, position and 4. Graphic Art path dependency. This seminal sketch shows Varèse in that According to Oliva Mattis, Varèse produced “numerous ab- act of seeking a means for elegantly “spatializing” the terms stract paintings” that remained at the time of his death [8]. of an ordered series by means of simple geometries. Nine are shown in her dissertation without discussion [9]. In Fig. 10, one sees a carefully rendered, sculptural im- Their chronology is unclear; some are untitled, and all that pression: three circular, almost totemic presences. The size Varèse produced are not accounted for in her list. gradation remains, but now the base plane is palpably mas- The pencil, ink and chalk design from 1952 (Color Plate C1) sive. Each of the circular shapes projects itself as a cylindrical is interesting in a number of ways. First, Varèse quite palpably “beam” that narrows and ends in a sketchy circle. There is represents two major “zones” defined by a roughly diagonal some ambiguity regarding whether these circles are meant to upper-left and lower-right subdivision of the picture plane; I represent oval shadows on the surface of the base or rather refer to them as upper and lower parts. The lower is evidently hang perpendicularly in the air above it. more “objective” in that it uses a rectilinear graphic grid as a There can be no doubt that these are “projections.” But of reference for what appear to be a collection of superimposed what? And what is to be understood as the common source oscilloscope tracings. But Varèse has not left them with solely of light/energy that causes the schematic shadows? Further, quotidian implications. Shaded areas adjoining the primary the centers of what seem to be three dimensional, donut- traces imply depth or mass (which a cathode-ray beam would like shapes are themselves shaded. To the right are two other not display). More interesting is the capricious slump of the sketched images that suggest a bracket of some sort. All in right-leaning shape at the far-right edge. It is a shape that all, one cannot say with any assurance what these intriguing could not have been generated on an oscilloscope (imply- shapes represent or how they relate to Déserts. What is nev- ing as it does more than one value for the same moment in ertheless evident is the care that Varèse exercised in depicting time). So, even in the more directly physical zone, Varèse has mass, orientation, plane and projection. allowed himself to think of the depicted space as “extended” in several ways.

Reynolds, The Last Word Is: Imagination 481

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01160 by guest on 28 September 2021 The upper part is far more intricate, a constructivist as- right, black and blue rectangles alternate with ambiguous red semblage of planes and volumes all in a decisively “collision/ verticals, in the same color contrast used in the top third of repulsion-driven” interplay. At the left center is what could the picture. The blue (B) rectangles are three-dimensionally be seen as a parallel to the categorical violations referred to specific, the two red (R) areas at the right, vague pillars that above in relation to the lower part’s objectivity. There is a function to separate. All in all there are 8 explicitly three- shape strongly suggesting a schematic eye (“the visionary”), dimensional rectangular planes of varied size and orientation resonantly ringed in concentric shapes that resolve them- depicted from left to right. (The sequence is R, R, B, R, B, B, selves differently above and below the central blue circle, in B, B.) Several extracted details will clarify. which an orange, quasi-trapezoidal “pupil” has been placed. Figure A1 (see the supplemental Appendix provided A chain of (now) five size-graded circles joins pyramids and with the online version of this article) shows a single three-­ latticed triangles in a tectonically fractured picture plane. The dimensional red plane rotated at an angle from the plane of primary elements of Varèse’s spatial vocabulary are repre- the picture surface. It is rectilinear, and both side and lower sented here: zones of intensity, masses, planes, projections, edges are clearly rendered. the traces of beams. The work is a graphic repository of the In Fig. A2 (Appendix), there are three planar elements. composer’s thinking about space, not terminological but The first five in the series referred to above are aligned in manifest in a nonsonic environment. an upward-moving arc, and the central red element in this Portes, from 1955 (?) (Color Plate C2), is both graphically detail is rotated 90 degrees with respect to its left neighbor. forceful and powerfully depictive of Varèse’s notions of in- The rightmost element resembles the first but is both smaller tersecting planes and of projection. Even more than in the and slightly rotated relative to its blue predecessor. This detail pencil, ink and chalk study, it is possible here to see explicit shows the kind of explicit planar rotation that Varèse invoked renderings of Varèse’s spatial concepts. in much earlier verbal descriptions, foreseeing such spatial The top portion of this work is occupied by a dynamic, phenomena. color-contrasted, cross-hatch-intensified elaboration of what Figure A3 (Appendix) shows the organically rooted energy appears to be a triangle-wave oscilloscope trace, a phenom- with which Varèse intends one blue planar element (surpris- enon with which Varèse was surely familiar at this time. More ingly the smallest of them) to be literally projected, pushing interesting is the lower two-thirds of the work (excepting out of the picture-plane of the depicted geometries. the jumble in the lower-right corner, where the planar sur- The top third ofPortes functions as a regular, though tex- faces and their orientations are less well-defined). At the far turally and color-contrasted, reference. The thin blue band

Fig. 10. A triad of totemic presences from the sketches for Déserts, from Edgard Varèse: Composer, Sound Sculptor, Visionary, edited by Felix Meyer and Heidi Zimmermann, p. 304. (Edgard Varèse Collection, Paul Sacher Foundation, Basel. Used by permission.)

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01160 by guest on 28 September 2021 at the very top does not have the same significance but also One could think of the hook-like shapes as visual analogs acts as a reference, asserting that the entire image complex is to the ornamental, but also anacrusic function of grace note rotated a few degrees counterclockwise from the horizontal. embellishments particularly, of course, with the incantatory Why did Varèse incorporate this angled reference? Most lines of Intégrales. This would imply in both instances a “left- probably it functions in the way that highly variegated inter- to-right” direction of flow, which makes intuitive sense. No- vallic combinations used harmonically in the music do: They tably, however, these impelling embellishments all originate create what might be termed inflected stabilizers. As would from “above,” whereas Varèse’s musical grace notes tend to be the case with strongly asserted low-register harmonies come from below. (consider the G, Ev, C#, E chord in Fig. 6), such elements act It is striking, though perhaps not surprising, as the same to root, to place in perspective the larger context (in that case, Varèsean sensibility was at work, that the curvatures and harmonic and melodic). They also inflect this effect by not al- proportions of these black and red lines are closely compa- lowing us to easily resolve the discordant intervallic elements rable to the disconnected segments used in the improvisatory within. The upper two slanted horizontal bands in Portes “score” (Figs 3 and 4). function in a similar way. They are a disquieting reference. One can see evidence that, in the lower linear counterpoint- The lower two-thirds of Portes is set off both in terms of ing, here, two of the elements are moving, by implication, its formal detailing and by the use of canary yellow. One from right to left across the picture plane. The dominant, ris- can imagine a circumstance where the planar elements of ing yellow-rose element includes along with its distinctively the lower part were aligned as are the triangles above. But jointed central tubing (this term used for this detail as a result it is rather the case that forces imagined and invoked here of the careful attention to three-dimensional shading that by Varèse have decisively unsettled the details of the planar Varèse includes) three biomorphic triangular cross-sections alignments depicted without obscuring their larger direc- with relatively straight backs (left side) and gently extruded tionality. Observing the ways in which this work parallels front surfaces. In the case of this line or element, a left-to- Varèse’s sonic architectures, it is also clear that he is far less right direction is implied by the shapes of these “penetrated assured in execution here, more pragmatic in his strategies. masses.” One can imagine the right-side extrusions as being In Portes, for instance, he felt the necessity of a reference- “caused by” the force of their left-to-right penetration by the invoking component that would not have been acceptable jointed tubing (read “beams”). in the music on a similar scale. In a musical context, local The subordinate, occluded green and gold lines are more regularities exist here and there, but never as formally promi- literally beam-like in their linear design, but both also have nent features lasting for long periods, let alone spanning an idiosyncratic, Dalí-esque graphic characteristics suggesting entire work. directionality. The green beam has, at the right, a pod-like The 1951 untitled oil-on-wood painting in Color Plate C3 expansion that is weighted at its left end; to the left of it, there is spatially explicit in complementary ways. Here, instead of is a somewhat less decisive mirroring of accenting features of planes in rotation and projection, it is rather lines (or beams) the already described yellow-rose continuity above. Finally, that are depicted. As with Portes, there is a jagged continuity the gold line includes a bamboo-like jointedness, vaguely that stretches across the entire picture plane. It too is remi- echoing the yellow-rose structure but without any angular niscent of an oscillographic trace, much more naturalistically displacements. Its segments emphasize a male-female suc- than the triangle-wave band at the top of Portes. It feels like cession, where each segment appears to be fitted into the one a reference of a different sort: phenomenological rather than that follows to its left. formal, and one notes that its role as reference is inflected by What seems clear from the visual creations commented a descending migration just as was true with its counterpart upon here is that Varèse’s thinking in the 1950s—a time in Portes. The prevalence of primarily horizontal, linear ele- during which his long-dreamed-of engagement with elec- ments in this work feels at the same time less cluttered than tric resource was actually coming to fruition—was entirely the works already examined and yet more complex in its con- consistent with the terminologies he had been using for trapuntal potential. It is notable that the word “counterpoint” three decades before in relation to informed conceptions of is not significant in Varèse’s discussions of musical space. This sonic space. If there was any doubt, from a musical perspec- graphic work is perhaps the most elaborate surviving contra- tive, whether Varèse intended his terminological repertoire puntal design to have come from his imagination. (plane, intersection, mass, penetration, rotation, etc.) in a There is unresolved ambiguity in the interwoven black and literal sense, the visual record decisively erases that doubt. red bands near the top. It is as though Varèse had determined to engage with these nonbeam-like lines but wanted them 5. Spirals (as the expressive doodle in the letter to Louise does [Fig. 5]) The most enigmatic element in Varèse’s visual record are the to meander in some significant way while crossing one an- 16 [10] extant pages on which he explored the spiral shapes other within an implied depth of pictorial plane. There are that had first been metaphorically introduced in his music two positions, at the left and at the right, where Varèse has through use of sirens in the 1920s. Recall the sketch in Fig. 8, either been unsure about which line should occlude the other from a restaurant encounter, that ratifies the organic signifi- spatially or has left it ambiguous by introducing a masking cance of the spiral as reflected in a snail’s shell. But Varèse element. abstracted these suggestions, utilizing, in page after page of

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01160 by guest on 28 September 2021 Fig. 11. Edgard Varèse, extended pentagon spiral. (Edgard Varèse Collection, Fig. 12. Edgard Varèse, extended pentagon spiral with associated Paul Sacher Foundation, Basel. Used by permission.) proportional timings. (Edgard Varèse Collection, Paul Sacher Foundation, Basel. Used by permission.)

Fig. 13. Edgard Varèse, detail from Fig. 12. (Edgard Varèse Collection, Paul Sacher Foundation, Basel. Used by permission.)

mostly unannotated sketches, various polygons (triangle (sound, numerical formulations and graphic manifestation) through heptagon, as the seeming generators of spirals with was not diminishing but growing more explicit. What is varying angular compression. certain is the generative and conceptually unbounded ex- In Fig. 11, a pentagon spawns a four-layered spiral that ex- pansiveness implied in the spiral shape; a center becomes pands at a very gradual rate. Although it is tempting to see endlessly productive. the extended polygon sides (along with labeling and numeri- It would not be surprising were Varèse to have been af- cal suggestions on some pages) as a constructive device, the fected not only by influence from developments in science, unevenness of measurements as read off these sketches is so but also by the more extended of the serialists’ explorations— noticeable as to preclude proportion (at least with any preci- the so-called total in which there was an attempt to sion) as a guiding factor in the production of the associated apply to music specific sorts of scalar succession not only in spiral shapes. pitch but in the dimensions of time, dynamics and timbre. The hexagon with numbered vertices and the subordi- Varèse’s exploration of rhythmic serialization is discussed nate pentagon in Fig. 12 are of less interest than the band of in the companion essay to this present one [11]. Surprising proportional indications across the top (as oriented here) though these forays may be in light of Varèse’s steadfast and of this figure. Shown with increased size and detail in Fig. continuing disavowal of theories, even methodologies, of any 13, this area includes a tempo marking (MM 60), numerical kind, his immense curiosity about the relationship between dimension in seconds (0:15, 0:06, 0:11, 0:04, etc.) and graphic the felt and the manifested drove him to explore all seemingly proportionality. (The majority of the line segments, marked plausible pathways, even those that he would not publicly off with vertical hash marks in red, are more or less propor- admit. There was emerging at the time of his paintings, in tionally plausible.) It looks as though, in these spiral sketches, the 1950s, a more direct interaction between psychoacoustics Varèse is seeking rather than exercising an already grasped and musical thought both in Germany and the United States generative principle. Consultation with colleagues whose (e.g. Herbert Eimert’s interactions with Karlheinz Stockhau- professional expertise lies in mathematics has elicited no sen in Köln, ’s application of group theory to even speculative insight into the meaning of these diagrams. musical structuring). Even Stravinsky had felt impelled to One hopes that a close examination of the full set of 16 accommodate the serial idea shortly after Schoenberg’s death spiral sketches might provide a key to their significance. As in 1951. These forces appear to have impinged also upon even it is, they establish that, during the latter years of his life, so resolute an independent as Edgard Varèse. The last word Varèse’s interest in the relationships between various forms in his creative quest, was, indeed, not theory or methodology, of representation, the precision of such representation and but imagination. the complementary potential between differing modalities

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/LEON_a_01160 by guest on 28 September 2021 References and Notes 8 Olivia Mattis, “Edgard Varèse and the visual arts,” PhD dissertation, Univeristy Microfilms International, 1992, p. 221. 1 For the first part of this essay, see Roger Reynolds, “The Last Word Is: Imagination, Part I: Written Evidence,” Perspectives of New Music 9 Olivia Mattis, Varèse and the Visual Arts (, 1992). 51, No. 1, 196–255 (Winter 2013). 10 Noirjean [6]. 2 Gunther Schuller, “Interview with Varèse,” Perspectives of New Music 11 Reynolds [1]. 3, No. 2 (Summer 1965).

3 Louise Varèse, Varèse: A Looking-Glass Diary (Davis Poynter, 1972) Manuscript received 20 October 2014. p. 67.

4 Olivia Mattis, “From Bebop to Poo-wip: Jazz Influences in Varèse’s Pulitzer Prize–winning composer Roger Reynolds was Poème électronique,” in Felix Meyer and Heidy Zimmermann, eds, trained in Engineering Physics and Music. His compositions Edgard Varèse: Composer, Sound Sculptor, Visionary (Boydell, 2006) span solos to orchestral works; analog electronics to computer p. 313. algorithms; the purely sonic to the theatrical and inter-medial. 5 Mattis [4] p. 315. The has a Special Collection of his sketches, some of which are also housed at the Sacher Foundation, in 6 Per Michèle Noirjean, Sacher Foundation, 10 September 2010. Basel. He is Professor of Music at University of California San 7 Varèse [3] p. 228. Diego.

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3 Edgard Varèse, (1) pencil, ink and chalk design, 1952; (2) Portes, 1955 (?); (3) untitled oil on wood painting, 1951. (1–3 reproduced by permission of Jacques Besson.) (See article in this issue by Roger Reynolds.)

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