Instances of Proximity in Ebb and Flow for Saxophone Quartet
Instances of Proximity in Ebb and Flow for Saxophone Quartet
Written for the Quasar Saxophone Quartet
Composer: Andrés Gutiérrez Martínez
Performers: Quasar Saxophone Quartet: Marie-Chantal Leclair, Soprano Saxophone; Mathieu Leclair, Alto Saxophone; André Leroux, Tenor Saxophone; Jean-Marc Bouchard, Baritone Saxophone.
Introduction
My musical sensibility focuses on gradual timbral transformations. From a very early stage in my training as a composer, I centred my attention on the malleability of musical material. This led me to think of sonic material as something that can be shaped—not just through conventional musical gestures but through extended playing techniques. In doing so, I developed an aesthetic approach rooted in the discursive potential of acoustic phenomena[1] from which I derive the musical structure.
In sound-based composition, gradual transitions can be made by the sequential ordering of closely related sonic elements with slightly different timbral qualities. This is where the notion of proximity comes into play in my musical thought: for each composition, proximity serves, both as a guiding principle in the process of generation of musical material, and as an organizing principle for the articulation and arrangement of said material into larger units (gestures, phrases, sections). An arrangement of sounds based on slight timbral differences allows me to conceive of gradual timbral transformations as means of creating an organic sense of progression and continuity in my music. The aim of the paper, however, is not to elaborate on the concept of proximity as an inspiration in the composition process but show how this concept was operative in the generation of musical material, and the creation of musical situations that would allow for gradual timbral transitions, spectral expansions or contractions.
Composing for the Saxophone Quartet
In my compositional practice, writing for homogeneous ensembles presents unique possibilities that differ markedly from those available with heterogeneous instrumental configurations. In the case of the saxophone quartet, for example, various acoustic factors—such as reed type, instrument make, and size—shape the timbral qualities of the instruments. Yet despite these differences, one can discern salient acoustic properties shared across the ensemble. My collaboration with the Quasar Saxophone Quartet focused on the use of multiphonics, reflecting the ensemble’s interest in sharing their catalog and encouraging composers to incorporate it. This project offered a valuable opportunity to deepen my understanding of saxophone multiphonics and to develop a compositional approach rooted in that engagement.
Multiphonics are sounds resulting from the interaction of two or more air columns in the resonant tube of the instrument brought about by special fingerings or different blowing techniques. They are common in wind instruments; however, it is possible to produce multiphonics on string instruments, and some percussion instruments as well. In the second half of the twentieth century, these sounds gradually became part of the repertoire of sounds available to performers and composers.
Research into the perceptual qualities of alto saxophone multiphonics has shown that listeners can reliably distinguish between different types based on their distinct auditory characteristics. A 2014 study by Riera et al. identified four perceptually distinct categories—multiharmonic, bichord, tremolo, and complex—despite a limited sample size. This categorization offered a useful conceptual framework for understanding the sonic attributes of multiphonics and sparked the initial impetus in the composition process. It led me to think of ways of combining different types, using their timbral qualities as organizational principles. Before developing this further, however, I needed to examine the catalog in more detail to i classify the multiphonics it contained.
A Timbre-Based Corpus Query
The compositional process entailed several steps starting with an initial selection of multiphonics from the Q-Phonics catalog, followed by its arrangement in terms of sonic quality and lastly, the ideation of principles for the simultaneous and sequential arrangement of the sounds In order to achieve a comprehensive survey of the available sounds, I analyzed the sounds using the advanced computational timbre analysis package FLUCOMA (Tremblay, 2019). The software package performs statistical analysis, among other things, on a user-determined sound collection. One of the features of this tool is to create a 2D visual representation/sampler containing in which each multiphonic is represented by a point in a 2-D plain as Figure 1. shows bellow. The FLUCOMA package was developed originally for performance purposes as a means of manipulating in real-time large sound collections in terms of timbral qualities, however, as I demonstrate in this paper, its analysis capabilities are also suited as a tool for computer assisted composition.
Figure 1. Plot of mutliphonic collection distinguished by instrument: red = soprano; green = alto; blue = tenor; black = baritone. Dimensions 1 (horizontal-axis) and 2 (vertical axis) on the left, and dimension 3 (horizontal axis), and 2 (vertical axis) on the right.
Figure 1 presents the entire collection of multiphonics from the q-phonics catalog. The plots were created with FLUCOMA in SuperCollider (McCarthy, 2018). As mentioned above, each plot is also a sampler that allows playback so that one can hear a segment of each of the analyzed sounds by clicking on one of the points. This timbre-senstive, topological representation allowed me to listen to each of the points in the search for similar, compatible, or even contrasting sounds. In Figure 1, the distribution of sounds—arranged according to the normalized averaged minima and maxima—is the result of the analysis of the 13 MFCCs for each of the multiphonic sounds. The color intensity for each colour maps the relative loudness, and the size of each datapoint gives an estimate of fundamental frequency from low (small) to high (big). The latter were added to convey more information in addition to the spectral characteristics due to the fact that timbral similarities from MFCC’s are not exclusively bound to pitch. In figure 1, four dimensions are represented in to plots by projecting the positions onto dimensions 1 and 2 on the image on the left, and dimensions 3 and 2, on the image in the right whereby the first and third dimensions are placed along the x-axis and the second dimension along the y-axis.
Side by side, it is evident that the plot of dimensions 1 and 2 (left side) presents more separation and clustering in different areas, whereas the image on the right presents an arrangement with gaussian-like distribution around the center, albeit with clear spatial separation for the soprano and baritone. As is the case with multidimensional scaling, it is sometimes difficult to label the dimensions of the generated timbre space with regard to perceptually relevant features. However, the arrangement along the horizontal-axis on the left image places softer sounds on the left, and timbrally rich sounds on the right. This suggests that some kind of spectral richness descriptor is considered in the horizontal arrangement. Moreover, the arrangement of sounds along the vertical axis places a large number of soprano multiphonics on the lower end, and baritone multiphonics on the higher end. This might suggest that register-contingent timbral qualities are somewhat considered in dimension 2. A dedicated plot focusing on spectral brightness and the estimated pitch of the fundamental was also created (see Figure 2 below) to present an alternative arrangement of the collection.
Figure 2. Plot of spectral brightness (using the linear centroid value along the horizontal-axis), and pitch (using a logarithmic scale along the vertical axis).
Creating my own Collection
With the project centered on composing a piece that makes extensive use of multiphonics, the initial step was to create a repertoire of multiphonics for each instrument. Initially, I was drawn to those featuring narrow intervals, discernible pitches, and soft dynamics (p–mp). As briefly mentioned above, the use of a timbral-based visual representation of the multiphonic catalog in the compositional process enabled the efficient comparison and selection of all the multiphonics of the collection—something not as easily achieved through playback alone from the ensemble’s online catalog. The spatial configuration of sampler-visualizer supported rapid, comparative listening across instruments and created a relational map making it possible to think of manifold alternatives and combinations.
In the initial phase of the selection process, the criterion was based on the intrinsic appeal of the multiphonic sounds. I focused on those featuring narrow intervals, clearly discernible pitches, and soft dynamics (p–mp). I then queried the database for multiphonics that shared pitches across two or three instruments, adjacent multiphonics with similar timbral characteristics, and combinations that blended well together. Based on these considerations, I compiled an initial collection. Using the analysis software Spear, I conducted spectral analyses of each sound, considering only the most prominent spectral peaks. The selected multiphonics were then arranged from low to high, according to the lowest note in each sound (Figure 3).
Figure 3. Chart of selected multiphonics with their salient frequency components.
Figure 3 presents the constituent pitches of the first collection of multiphonics from the q-phonics catalog arranged from low to high according to the lowest pitch of each sound. The colouring scheme for the labels follows that of the timbre space. This collection contained at least three discernible multiphonic types: one category of sounds consisting of a clear-sounding, narrow interval such is the case for multiphonics T.12, T.31, T.32, T.33, A.24, A.31, etc.; another category entails narrower intervals (minor and major seconds), which produce audible beatings (T.4, T.5, S.14…); and a final category with wide intervals (major seventh, minor ninth: B.45, B.46, B.47, B.50, T.47, T.48, A36, A.37, S.57, S.58). The multiphonics in Figure 3 match Riera et al.’s classification of bichord, and biharmonic multiphonics, respectively. The latter group of multiphonics are denominated “sons nuages” (cloud-sounds) due to their unstable, airy, and soft-sounding quality. I will expand on this category of multiphonics below.
The arrangement of multiphonics in Figure 3 follows the principle of proximity with regard to the lowest note. Rather than approaching complex sonorities in relation to a fundamental frequency or to apply an existing harmonic language, I sought to develop an additive principle.
I began to combine multiphonics from different instruments using common tones as nodes allowing for microtonal differences between the neighboring pitches. This yielded compound aggregates, some of which presented clusters in different regions of the spectrum conformed by component partials of several multiphonic sounds. Thinking additively, I began to conceive of the sound of the quartet as a single sonic entity: By projecting the acoustic interactions occurring within an instrument producing a multiphonic sound onto the entire ensemble, I conceived the resulting sound as a compound multiphonic aggregate formed by the sum of all instruments. In this case, the actual physical space of the performance became the site where the component sounds interacted with one another[2].
The initial collection was expanded to include multiphonics from a second catalog created by saxophonist Markus Weiss and composer Giorgio Netti, published by Bärenreiter (Weiss & Netti, 2010). In addition to the overlap of multiphonics contained in both catalogs, Weiss and Netti’s extensive catalog features several “microtonal relatives” of sounds found in q-phonics, produced through slight variations in fingering. Building on the notion of proximity as a guiding principle, I incorporated these multiphonics to enable gradual microtonal transformations while preserving the overall sonic quality.
Furthermore, some multiphonics appear in several instruments in a different transposition. For example, the fingering “1_4567_Bb” produces a multiphonic in the tenor, and the soprano saxophones consisting of a minor second between G and A-flat sounding an octave apart (G3+Ab3 on the tenor sax, and G4+Ab4 on the soprano sax). Another case concerns the collection of multiphonics mentioned earlier: the sons nuages. These sounds are present in all instruments and are produced using the same underlying fingering.
Figure 4. Table of sons nuages with approxiamte pitches and fingering (below).
As we can see in Figure 4, the same fingerings—represented in the lowest row of the figure—are employed to produce a series of timbrally related multiphonics in all instruments. The pitches in parentheses show the sounding pitches of those fingerings when played normally, followed by the constituent pitches of the multiphonic sound. This chart allows for an easy visualization of the ambitus of the fingering sequence for each instrument, as well as the overlapping regions of two or more instruments. For the creation of aggregate sounds, I developed a principle of concatenation based on the available sounds from Figure 4. From the chart, we can see that multiphonics A.1 and T.6 produce sonorities containing both F4 and E5 with corresponding microtonal variations. The upper note of both sounds overlaps approximately with the lower note of S.6, and the lower note with the upper note of Btone.2. This is a good example of the strategy used to create aggregate sounds throughout the piece: constituent partials of a given multiphonic are used as nodes or links to combine different multiphonics.
As shown in Figure 4, the same fingerings—represented in the lowest row of the figure—are employed to produce a series of timbrally related multiphonics across all instruments. The pitches in parentheses indicate the sounding pitches of those fingerings when played normally, followed by the constituent pitches of the multiphonic sounds. This chart facilitates an easy visualization of the ambitus of the fingering sequence for each instrument, as well as the overlapping pitch regions shared by two or more instruments.
Conceptualizing a Musical Synthax with Multiphonics
For the creation of aggregate sounds, I developed a principle of concatenation based on the available sounds depicted in Figure 4. The chart shows that multiphonics A.1 and T.6 produce sonorities containing both F4 and E5, with corresponding microtonal variations. The upper note of both sounds approximately overlaps with the lower note of S.6, while the lower note overlaps with the upper note of Btone.2. This example illustrates the strategy used to create aggregate sounds throughout the piece: constituent (or adjacent) partials of a given multiphonic function as nodes or links to combine different multiphonics.
The compound aggregate following this principle is presented at the beginning of the piece. There is a strong concentration of energy around the pitches F4 and E5 –with their respective microtonal variations for each instrument–framed by a low and high registral extension produced by the lower partial of the multiphonic of the baritone saxophone and the upper partial of the soprano multiphonic, correspondingly. Already at the end of bar 4, the sound aggregate gradually morphs away from the initial sonority expanding upwards and downwards. The step-by-step expansion of the initial sonority is reversed to arrive once more at the initial sonority in bar 12.
Figure 5. Beginning of the piece Bars 1 – 5. Presentation of initial sonority using only sons nuages.
This entire section, all the way through bar 25, makes use of the sons nuages mentioned above. For the sake of simplicity, the sounds were notated without taking into consideration the actual envelope of the multiphonics: in most cases, the lowest pitch is audible first while the second pitch sets in shortly after (1-2 seconds). The opening five bars present a “fixed sonority” that internally variated. // presents internal movement of the individual components.
Figure 6. Graph representation of opening section (bars 1 - 11). The color scheme for each saxophone is kept and overlapped.
Figure 6 presents a graph of the opening section (bars 1 to 25): a “Choral” of sorts. For the sake of simplicity, the representation focuses on the progression of sounding pitches through the opening section and leaves out the temporal phrasing. As we can see from the representation, the concentration around F4 and E5—with microtonal variations—gradually fans out giving way to a different distribution of pitches before returning to the initial sonority. The initial compound sound is not stable throughout the duration of the notated actions adding instability to the overall sonority. This instability concerns the envelope of the notated action as mentioned above, on the one hand, and to the sonic quality of the acoustic interactions between the different instruments:
Given the nature of multiphonics, the section presents a timbrally homogeneous sequence that gradually changes its harmonic constitution. The unstable quality of the multiphonics and phrasing of the section create a continuous texture with varying constituent elements.
Figure 7 Timbre space of entire collection (left) and zoom in of region with sons nuages (right).
Figure 7 presents once more the timbre space from the original catalog with a highlighted area on the lower left side. This area corresponds to the collection of sounds used in the opening section (bars 1 – 25). The clustering of sounds supports the argument that these sounds share timbral characteristics and that the computational analysis of MFCCs is a reliable strategy for a timbre-focused categorization of complex sounds. The image on the right shows the enlarged area with the labels for the multiphonics from Figure 4.
As I mentioned earlier regarding the choice of multiphonics in the opening section of the piece, I used constituent partials as connecting nodes. This organizational principle extends to adjacent pitches of constituent partials within multiphonics and operates throughout the piece, both in cases involving homogeneous multiphonics (those belonging to the same family) and heterogeneous multiphonics (those belonging to different families). This approach allows for variation within the complex sonorities and helps highlight specific regions within the sounding range established in each passage. In the opening section, the gradual trajectory of each instrument follows the concept of proximity sequentially. It is precisely this slow, stepwise movement that creates a gradual transformation in the musical texture.
Another application of fingering proximity takes place with a second subgroup of bichord multiphonics. As mentioned above, some multiphonics can be slightly altered by pressing or releasing adjacent keys, as is the case of the multiphonics in Figure 8. Here we can see that by altering the fingering, the multiphonic sound is slightly altered without loosing its intervallic quality.
Figure 8 Comparative chart with multiphonic variations through slight changes in fingering from the Weiss & Netti book of extended techniques for the saxophone.
Figure 8 presents a comparative chart with variations of given multiphonics for each instrument. The second multiphonic for each group only differs in one key from the first one. From the pitch diagram for each multiphonic, we can see whether the sounds are slightly lowered or raised depending on the key that is being pressed or released. In the piece, these multiphonics are concatenated vertically in order to get a complex sonority with similar sounding individual components.
Figure 9 Vertical concatenation of similar sounding multiphonics following the rule adjacent partials.
Projection-Orchestration
Up to now, my work with multiphonics in this piece was concerned with a principled approach to combining multiphonics to create gradual transitions. One possibility that I explored was the use of ordinario sounds as a means of reorchestrating multiphonics. This resulted in a timbrally nuanced variation of certain multiphonics–used as both echo and anticipation in the piece.
Figure 10 Timbral echo using ordinario tones to extend the sonority of a multiphonic sound.
Figure 10 presents a passage of the middle section (bars 69 – 112) in which a multiphonic sound in the tenor is alternated with its reorchestration by the soprano and baritone saxophones using individual, ordinario tones. This passage introduces another manifestation of proximity: this time, it is applied to the nuance of a given sonority: The phrasing based on timbral variation articulates the quasi-periodic structure underlying this passage. The difference in granularity, the change of spatial localization, and the use of the upper register thickens and thinens the sonic line.
Figure 11 Graphic representation of bars 95-105. Red: soprano saxophone; Green: alto saxophone; Blue: tenor saxophone; Black: baritone saxophone.
Figure 11 shows a graphic reduction of bars 95-111. The graphic allows to identify the timbral phrasing of the passage. The pitches comprising the multiphonic played by the tenor saxophone (F#4 and G#4) are played by the baritone and the soprano saxophone creating an alternating pharse in which elements gradually fade in and out. The alternating sounds make up the elementary layer, and the extension of the sonority’s ambitus marks tension and conclusion. The activation of the higher register contributes to an intensification in the sonority: through the introduction of different multiphonics on the same pitches, the overall sonority becomes brighter providing a thinckening and expansion of the spectrum that mark the conclusion of the segment: on the first timbral swell, the soprano plays a similar multiphonic than that of the tenor, albeit an octave higher; the baritone plays a fragile sounding son nuage on a G4 with an minor 7th partial sounding in the same region as the higher partial of the soprano multiphonic; the alto introduces a new multiphonic also on G4 with a clear sounding partial at A5. This multiphonic on alto encapsulates the sounding register while the other multiphonics function as enriching elements to that sonority. The second swell introduces the soprano and baritone multiphonics first, and the alto is coupled with one of the tenor multiphonics employed earlier. The brash sound quality of these multiphonics introduces a change in timbre with regard to the granularity and spectral richness. This change is used to add intensity and gravity.
Conclusion
The compositional process behind Ebb and Flow for saxophone quartet focused on the use of multiphonics as the sole sound source, encouraging a musical context in which timbral qualities took on a structural role. Fragile sonorities such as sons nuages contributed to an unstable, evolving texture; alternations between a multiphonic sound and its reorchestrated version with conventional pitches articulated patterns of timbral granularity; and the gradual transformation of a stacked multiphonic chorale in the final third of the piece further exemplifies how proximity shaped the work’s phrasing and formal continuity.
In this paper, I presented several of these compositional strategies to illustrate how proximity functioned as an organizing principle across multiple stages of the creative process. From the use of visual timbre maps—where spatial proximity indicates timbral similarity—to pitch relationships based on the partials of multiphonics, to microtonal variations introduced through fingering adjustments, and ultimately to timbral echo as a form of instrumental resynthesis, the article demonstrates how a single concept can inform diverse aspects of the composition. It is pertinent, however, to point out, that this principle of organization is not precisely what the piece is about. As was stated at the beginning. The aim of the composition is not to represent the concept of proximity as an inspiration in the composition process but to utilize this concept to as an organizing principle for the composition.
To conclude, the compositional process I have described demonstrates that new analytical techniques, such as visual timbre mapping, can serve as effective tools within a creative workflow. This method allowed me to explore a large collection of sounds and afforded a conceptual framework that informed the subsequent stages of the composition. While such techniques remain rare in instrumental composition, this paper offers a practical example for how they might be used in other creative contexts.
Score and Recording
References
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