Generating Resonance and Illusions of Polyphony Using Methods of Heterophonic Diffusion (DMA Thesis)

1. Introduction

In a series of lectures given by Anton Webern in the 1930’s, entitled “The Path to New Music” and “The Path to Twelve-Tone Music,” Webern offers a teleological perspective of musical history which places twelve-tone music at its apex. He points to the fact that with the emergence and flourishing of polyphony in the late Middle Ages, a new musical space had opened up where the importance of the single voice had been replaced by homogeneous contrapuntal textures. As he continues to suggest, this polyphonic writing came to its peak in the works of J. S. Bach, before new ideas about accompaniment and melody emerged in the Classical era.

However, it was with the advent of twelve-tone music in the twentieth-century that melodic and harmonic parameters became synthesized in the design of the row. It is in this point of musical evolution where Webern found himself, a musical space where he could “sum up whole ideas in a single part, as an independent melody.”1

The word heterophony suggests a musical texture that contains simultaneous variation of a single melodic line.2 The combination of simultaneous musical lines creates verticalities, yet we cannot look at these verticalities as an independent harmonic parameter. There are multiple lines, but the lines are not coordinated as they would be within a contrapuntal structure. Therefore, it is difficult to fruitfully chart heterophony in terms of traditional harmony or counterpoint. However, we can talk about heterophony in terms of the resultant resonant and contrapuntal qualities that emerge from the “diffusion” of a linear melodic line. By diffusion, I mean the elementary extraction of a line through pitch, color and rhythmic displacement that can highlight or blur particular features of the line.3

There is no doubt that Webern’s influence was felt in the world of composition in years following World War II, since twelve-tone music, and later total or integral serial music,became the beau idéal for many post-war composers. In serial composition, the row encapsulates possibilities of melodic and harmonic expression, as if these parameters are inextricably unified.

In the second half of the twentieth-century, one begins to notice that composers such as Berio, Ligeti and Boulez, and later, spectral composers such as Grisey and Saariaho, begin to develop an affinity for heterophony as a method of composition. Later in the twentieth-century, composers of process-based and minimalist music, such as Reich and Glass,4 also appropriated heterophonic techniques and injected them into their music as seminal compositional methods. Perhaps then, it is that heterophony is a natural “fit” for these types of compositional methods, because they all seek to extract linear and vertical meaning from a single source.

This kind of thinking coincides with the dawn and proliferation of electronic music with in academic circles of the 1950’s – 70’s. Perhaps the adherence to rigorous compositional dogmata during this period led to the sonic similarities one hears between electronic and acoustic music. It would not be to difficult to surmise that heterophonic thinking penetrated its way into early electronic music, because electronic music also seeks to extract new meaning from the manipulation of a single sonic capsule – such as in Luciano Berio’s 1958 tape piece, Thema (Omaggio a Joyce). The ability for the composer to span across both the electronic and acoustic dominions, perhaps led them to think of their acoustic music as an analog to electronic manipulations of sound. Be it as it may, acoustic heterophonic music of the type produced by these composers presents certain recurrent technical features. Most important amongst these is a conception of verticality as resonance and the achievement of this resonance through a sophisticated use of melodic and rhythmic diffusion to unfold a primordial line.

My music adopts similar heterophonic techniques as the primary method of composition, in that these works are often derived from a single melodic source that is impregnated with a high degree of resonant qualities, allowing me to diffuse a melodic source to generate auxiliary melodic lines both vertically and horizontally. Constructing a melodic source with diffusion in mind allows control over the volume and density of the source’s resonance. By resonance here I mean reverberation, and borrowing terms from video, luminance and chrominance.5 It allows me to create an illusion of polyphony by extracting fragments of the source material and projecting them into vertical and hori- zontal space.

In the sections to follow, I will examine different methods of diffusion within my D.M.A. thesis composition, eating filumena lionheart (2009), as this work was composed from the above point of view.

The following analyses will show how auxiliary lines are extracted from the melodic source, and how timbre and the density of resonance are totally bound to its melodic and harmonic elements. The analyses will also show how eating filumena lionheart incorporates allusions to electronic music, such as delay, reverberation and harmonic filtration, to produced and develop highly resonant textures.

2. eating filumena lionheart

eating filumena lionheart: two cautionary tales on vanity and other curiosities (hereby referred to as filumena), is a concerto for oboe and chamber ensemble composed between January and February 2009 in Urbana, Illinois. filumena was composed for oboist Emma Coleman and was performed on 17 March 2009 by the University of Illinois at Urbana-Champaign New Music Ensemble, with myself conducting.

The concerto is scored for solo oboe, single winds and brass, two percussionists, harp, two pianos, soprano and single strings.6 Structurally, the piece is cast into two unbroken parts. Tale One, or, “she wanted all the pink facing beautiful,” is the fastest and most physically demanding of the two parts; Tale Two, or, “she is memories for lots of people,” is slow and lyrical. Each part lasts roughly ten minutes; Tale One is 311 measures long (mm. 1 – 311) and Tale Two is 184 measures long (mm. 312 – 456).


On Deception and Fantasy

As the title suggests, eating filumena lionheart was composed with the idea of deception and fantasy in mind.7 Musically,the piece strives to provide a mirage of both tonality and polyphony.

The chimerical qualities suggested can be observed from the vantage point of structure and expectation. In a traditional, romantic-era concerto setting, we might suspect the oboe to be the protagonist of the musical narrative, and that the concerto will live up to certain instilled and expected associations based on style, period and dogma.8 This work abandons these notions, as the subtitle suggests. The listener is warned and ultimately deceived in the end, as is customary in a cautionary tale. In a cautionary tale, the protagonist often disregards a warning of a taboo or object of danger, and always meets a surreal and macabre death.9

My music adopts similar heterophonic techniques as the primary method of composition, in that these works are often derived from a single melodic source that is impregnated with a high degree of resonant qualities, allowing me to diffuse a melodic source to generate auxiliary melodic lines both vertically and horizontally. Constructing a melodic source with diffusion in mind allows control over the volume and density of the source’s resonance. By resonance here I mean reverberation, and borrowing terms from video, luminance and chrominance.5 It allows me to create an illusion of polyphony by extracting fragments of the source material and projecting them into vertical and hori- zontal space.
In the sections to follow, I will examine different methods of diffusion within my D.M.A. thesis composition, eating filumena lionheart (2009), as this work was composed from the above point of view.

The following analyses will show how auxiliary lines are extracted from the melodic source, and how timbre and the density of resonance are totally bound to its melodic and harmonic elements. The analyses will also show how eating filumena lionheart incorporates allusions to electronic music, such as delay, reverberation and harmonic filtration, to produced and develop highly resonant textures.

To reinforce the tenets of the genre, several literary-to-musical translations are employed. For example, this work is a concerto, yet the oboe solo never acts independently of the ensemble, as is traditionally seen in such a work, as it has no lengthy virtuosic or muscular moments to spotlight the soloist. The concerto’s traditional agon is retained solely as a dramatic device, yet the oboe never engages the ensemble to “argue” with it. This democratic, or perhaps communal relationship between the oboe and ensemble, is expressed in this simplest of musical analogies, in that the oboe is doubled nearly all the time. This analogy plays along well with a composition derived from a single melodic source.

Structurally, the piece does not end with a flourish or bang, nor does it conventionally resolve. Each tale leads toward a grisly climax, but then fades to an inconclusive and unsettling ending. The piece hinges around a harmonic “compass” that is set up within the first minute or two of the piece and orients the listener towards a predisposed resolution of this harmony. A slow construction of a dominant A7 chord begins the work, and the desire for that chord to properly resolve to D is suspended throughout the work. However, resolution never comes.

The musical tip-of-the-hat to illusion goes hand-in-hand with the hetero- phonic nature of the melodic source, as the melodic source is imbued with a multifold of references to assist in the narration of a harmonic and timbral trajectory. From it, auxiliary melodic lines can be extracted to give the appearance of simultaneous and independent musical lines.


The Illusion of Tonality

In filumena, the melodic source was constructed to contain minimal changes of harmony. Long periods of static harmony are abundant in this piece, which provides for enormous freedom of linear variation of the source while preserving a consistent resonance. For instance, during the first thirty-six measures of the piece (about one minute), only a single trichord of 036 is present; likewise, the opening of the second tale (mm. 312-356) contains only the last five pitches of an ascending D Major scale.

Example 1:   Th  e opening chords of   e  at  ing   fi  lumena lionheart.   A minor third followed by a minor third, followed by a Major third, constructing a dominant chord. 

Example 1: The opening chords of eating filumena lionheart. A minor third followed by a minor third, followed by a Major third, constructing a dominant chord. 

Example 2: Basic Harmonic Narrative for Tale One. Corresponding measure numbers are listed.

As mentioned earlier, the opening of the work sets up harmonic compass that governs all of Tale One, and the entire work: an A dominant 7th chord (Ex. 1). The slow build-up of the A7 chord in the first 36 measures represents the longest stretch of harmonic stasis in Tale One. This chord is not resolved in m. 41, where one expects a resolve to D, resolving instead to F# minor. At the end of Tale One where the A7 reappears, it does not resolve at all.10

The principal harmonic collection for Tale One of filumena is the dyad, 03. The minor 3rd is often paired with nearby minor thirds, usually a minor second above or below, which generates a 0347 tetrachord, or a Major/minor chord. The tonal ambiguity of this tetrachord, and the manner in which it is approached or moved from, gives this piece its sense of tonality.

Depending on which tones of this 0347 tetrachord are sounding, the quality either sounds major or minor (and in some cases diminished, a chord that lends itself to tonal ambiguity). Looking at the example below (Ex.2),in the area between measures 141-202, it is possible to construct complete E, Ab and Db major triads; C#, F and Ab minor triads; and an F diminished tetrachord. However, triads are rarely constructed, as the pitch collection does not allow for it. The perceived major or minor qualities of the music are based on the shifting of dyads alone.

These collections have naïve associations with traditional tonal harmonic movement “baked” into their construction. Tonal implications of traditional harmonic motion arise out of our pre-conditioned assumptions about where a diminished chord, a dominant chord, etc., should resolve.

3. she wanted all the pink facing beautiful

As the harmonic and melodic properties of the piece are minimal, and not musically interesting on their own, melodic diffusion is used to generate additional, or auxiliary, musical lines beyond the principal melodic source. In conjunction with melodic diffusion, timbre is also used to generate another stratum of narrative as well as to signal points of harmonic and structural change. Timbre further assists in defining auxiliary lines that are diffused from the source, by either clarifying or obfuscating the melodic source, using variations color to prolong illusions of polyphony and locally manage its resonant qualities.

In Tale One, the melodic source is almost always encapsulated in the oboe, and passed to the ensemble during periods of rest. The oboe line is enriched by diffusing it into the accompanying ensemble through various mechanisms that allow the solo line to resonate. At times though, the ensemble appropriates the melodic source as its own, even while the solo oboe continues to play.

The following examples from Tale One illustrate the use of melodic and rhythmic diffusion as well as orchestration to generate highly inventive varieties of resonance. The contrast between periods of harmonic stasis and dramatic change in both timbre and diffusion is perhaps what propels this piece forward.

All the types of resonance diffused from the melodic line in Part One can be broken down into these categories: Strict doubling of the melodic line; generating polyphony by linearly “diffusing” the melodic line to generate new lines; refracting rhythmic patterns to generate accompaniment, or rhythmic resonance and; using orchestration to help clarify diffused lines as well as tell its own narrative.

Having broken down the following types of diffusion into smaller groups, we can now look at them in closer detail.


Strict Doubling

Example 3: Strict doubling of the oboe line. eating filumena lionheart, mm. 261 – 267. 

The sections using strict doubling, while few, are designed for purely dramatic effect. For example, in the climactic moments of Tale One, such as in the tutti sections at m. 72 and m. 230, the oboe line is fully, and strictly doubled in octaves. 11 In example 3, the oboe is lightly doubled by harp, then by the baritone saxophone and contrabassoon before the entrance of the full ensemble at m. 263. At this moment the ensemble emerges with a rhythmically independent line, with all of the pitch material vertically extracted from the oboe line. A melodically separate (but harmonically identical) secondary line occurs in the low winds, strings and piano before the ensemble unifies with the oboe (see § 3.3 on Rhythmic Resonance).


Generating “polyphony” by means of distillation

Perhaps the most utilized method of diffusion in Tale One, as well as through- out the piece is “distillation,” or, the vertical extraction of pitch material from the melodic source to create auxiliary lines. By extracting some pitches and not others from the source, it is possible to generate rhythmically and directionally unique auxiliary lines. Much like polyphonic writing, where secondary lines serve to complement and contrast the rhythm and contour of the primary line, the goal of this method is to generate quasi-contrapuntal gestures by vertically reflecting the melodic source. All derivative lines must retain the vertical pitch content of the melodic source and may not be entirely independent in melodic content; in other words, all distilled pitches are replicated at the unison or in octaves. Therefore, using this technique, it is possible to create an illusion of a new, independent melodic line sounding concurrently with the source, giving the music polyphonic attributes while retaining its heterophonic properties.12

The faux-polyphony that is manufactured from this parent-child manner of thinking, can be any number of apparatus borrowed from polyphonic writing, such as an illusion of (or allusion to): countermelodies, augmentation and diminution, bass lines, driving-tones, and points of ellipsis, punctuation and cadence.13

Example 4: Extracting a melody from a moving, primary melodic line. Michael Torke, Green. p. 9. 

The example (Ex. 4) demonstrates the concept of distillation. In his orchestral work, Green, Michael Torke vertically extracts pitches from the moving melodic source (as seen in the winds, second violins and violas). By extracting some pitches and not others, Torke is effectively able to create a sense of mul- tiple and seemingly independent musical lines. Furthermore, Torke sustains specific pitches from the melodic source to generate a melody from the moving line, which is locked into a set, “quantized” grid. The bass line, while clearly harmonically related, is independent from the source.
In filumena, I diffuse the melodic source in much the same way, though unlike Torke, the bass line is not independent, and my source melody contains only one simultaneity, versus dyads, per sixteenth note.

Example 5: Two auxiliary lines diffused from the melodic source in m. 138. eating filumena lionheart, mm. 136 – 140 

For example, in measures 138 – 39, two auxiliary independent lines emerge, serving to punctuate the oboe line, eliding two similar gestural thoughts (Ex. 5). Here, as proposed above, the distilled auxiliary lines strictly double the pitch of the oboe, but are independent in melodic character and vectoring. While the oboe line has a rather narrow ambitus, the bassoon has an ascending scalar line, punctuated by a low C# (found in the piano, synthesizer, cello and bass), before descending to a low E.

A tertiary line appears immediately after the entrance of the bassoon. Here the clarinet and harp have an accented 4-against-3 descending line. This line overlaps and merges with the bassoon line before continuing on with a previous driving tone accompaniment (in the english horn).

It is also worthy to note that rests are incorporated into the melodic source. This provides some latitude with regards to what, if any, pitches can be inserted within that space. For example, in the same measures, an enigmatic, and heavily accented low C# appears during a rest in the oboe line.

This apostrophic C# can be analyzed from multiple viewpoints: The C3 could be viewed as part of the melodic source, but divorced from it, like a hocketed note; or, as an apostrophe, in that it is wholly unique “speaking” from a con- textually sound, but a foreign locale in the ensemble’s tessitura.

It is possible, from an inverse panorama, the melodic source is not present in the oboe in m. 138, but is in fact passed from the last note of the oboe in m. 137 to the bassoon, then back to the oboe on the last eighth-note of m. 138.

Example 6 and 7: The melodic source and its diffused lines and the extracted countermelody. eating filumena lionheart mm. 154 – 158. Below, Generating an auxiliary countermelody (in the horn line) from the melodic source (oboe). mm. 155 – 160 (extract). 

This plausible alternative would suggest that the oboe line is derived from the scalar bassoon line, not the other way around. This suggests that the oboe line was refracted from the bassoon, and thus could be analyzed from the vista of “rhythmic resonance” (something I will describe below) rather than distillation.

Be it as it may, a meaningful analysis here, and with any other works composed or explored in this vein, would be better approached from a subjective rather than objective point of view. It is a matter of how the oboe (the soloist, after all) is aurally perceived to be interacting with the ensemble that accompanies it, and not what is actually inscribed on paper.

Another method of distillation in Tale One is the extraction of countermelodies from the principal line. As shown in Example 6 and 7, a contrasting and independent countermelody is presented in the horn. Here the contrast is severe: the sustained, legato horn line is projected against the dry, staccato oboe (much like Torke’s Green). As expected, this line is distilled vertically in octaves from the arpeggiated oboe line, yet retains its own independent melodic characteristics and vectoring.


Rhythmic Resonance

Throughout the piece there are varying levels of “rhythmic resonance” which emerge rhythmically independent from the melodic source. By “rhythmic resonance” I mean resonance not as an acoustical phenomenon, but as a concept that can be expressed in several parameters including rhythm. It can be thought of as an echoing impulse of the source projected onto the surrounding texture and space, like the refraction of light waves through media.

As in the previous section, where I describe how a melodic source can be diffused vertically to create auxiliary lines to create false vertical polyphony, rhythmic resonance diffuses pitches from the source and refracts them horizontally into a quantized temporal grid. By doing so, the refracted line retains the melodic material and rhythmic thrust of the source, while increasing its horizontal resonant qualities. This notion of refraction brings to mind delay units, in that any singular verticality in the source can be re-sounded after the attack, and in many instances before. This results in a sense of delay or echo (or pre-delay) and pitch relevance and resonance.

In his piece Mémoriale, Pierre Boulez utilizes the concept of rhythmic resonance where, as in filumena, he refracts the melodic source to generate both density and highly inventive resonant textures.14

Example 8:   Th  e   fi  xed series of   M  émoriale. 

Example 8: The fixed series of Mémoriale. 

All of the pitch material of the piece is presented in the following series, which is fixed in register:

It is important to note that the flute and accompanying ensemble remain attached to this fixed registration except during explicit cadential points that serve to articulate the form. This is, of course, a very important pre-compositional tenet of the piece, in that the fixed registration allows for enormous freedom of linear variation while preserving a consistent resonance.

Boulez also clearly separates his ensemble into instrumental levels: on the one hand the solo flute acts as the principal melodic voice; on the other hand, the strings either diffuse or clarify the melodic material. The horns are used to signal cadential articulation. The clear division in instrumental roles is crucial to the understanding of the formal unfolding of the piece. However, toward the end of the piece these roles begin to merge, perhaps representing a sense of resolution.

Figure 1:   Categories of di  ff  usion in   M  émoriale.   Th  e numbers represent rehearsal marks in the score. 

Figure 1: Categories of diffusion in Mémoriale. The numbers represent rehearsal marks in the score. 

All of the types of resonance in Mémoriale can be broken down into five categories: pizzicato (or: pizzicato-like), tremolo, undulating, sustained and cadential. As shown in Fig. 1, the pizzicato sections are the most frequent while more resonant oscillating sections are the least frequent, in part because they don’t appear until the final sections of the work. These highly contrasting categories are used to vary the texture, perhaps bringing to mind variation technique, here applied to the realm of color and resonance.

The monolithic cadence points are the most static of these sections and act as formal markers throughout the piece.

For example, at Rehearsal 1 the pizzicati articulate and synchronize with the flute. At each iteration of these “pizzicato sections,” which occur eight times within the work, the flute and pizzicati increase their sense of detachedness from the flute (Ex. 9)

Example 9: Comparing pizzicato independence. (L) Reh. 5, (R) Reh. 23. (Violins 1 & 2 are playing pizzicato, as well as the violoncello.) Pierre Boulez, Mémoriale. 

Boulez also enriches the percussive aspect of pizzicati by varying modes of attack in each instrument, such as at Rehearsal 12 (Ex. 10), where arco, col legno, pizzicato and tremolo are all utilized. In this way, rhythmic independence and greater variegation of color is achieved.

Example 10: Differing modes of attack, Reh. 12. 

In filumena, rhythmic resonance is used to a much similar effect, in that resonating auxiliary lines reinforce the rhythmic design of the source by adhering to it’s rhythmic momentum, yet retaining a unique but quantized rhythmic independence.

In the opening of Tale One, the melodic source appears in the solo oboe in a series repeated attacks on the pitch E. The E is resonated through the ensemble in a strictly quantized, but independent space, much like a delay unit repeats the rhythmic impulses of the source with a pre-defined and set periodicity. Both of these spaces (the source and refracted lines) retain an underlying rhyth- mic grid of sixteenth notes. The resulting 4:3 polyrhythmic feel is a result of placing the oboe in one quantized space (dotted eighths) and the ensemble in another (eighths).

Example 11: The sketch score of the opening measures. Note the three distinct refracted lines. eating filumena lionheart, mm. 1 – 7. 

Example 11 shows the three distilled lines as originally conceived each in an independent space before any orchestrational choices were made.

Example 12: Final score of the opening of Tale One. Note how the orches- tration further diffuses the refracted lines. Ibid., mm. 1 – 4. 

The orchestration helps clarify the diffused lines, defining and articulating them within a timbral space. Interestingly, the lines are not orchestrated in such a way to define them as three individual lines, but rather the orchestration combines them into one resonating entity. Comparing the sketch score with the final score (Ex. 12), one sees that two of the three lines are orchestrationally woven together, passing the line between the instruments (see. Fig. 2). The third line, the pizzicato strings, remain separate throughout the opening. A fourth sustained line, played by the synthesizer (sounding as an accordion) changes pitch simultaneously with the oboe, filling any spaces within the dry texture.

Example 13: Comparing the sketch score (above) with the final score (p. 22) 

As the pitch content of the opening increases, the amount of rhythmic resonance increases proportionally. By measure 14, the number of independent rhythmic lines increases to eight. Only Line 1 has variation in timbral color, while the remaining lines retain a single timbral voice. As in the opening, the synthesizer continues to color the oboe’s pitch; however by this point, a contrabass is also sustaining these tones. Here, the contrabass anticipates the changes of pitch (an example of pre-delay). For example, in m. 14 the bass’s C# sounds an eighth note before the oboe attacks that note, and the bass’s E sounds seven sixteenths before the oboe’s E is attacked. (Ex. 13, Fig. 3).


Figure 2: Orchestrational breakdown of the lines in mm. 1-4. 

Figure 3: Orchestration of the distilled line in mm. 14–16. 


Creating timbral narratives

As mentioned above, the orchestration of the auxiliary lines is paramount to the timbral narrative of the piece, and to bring life to the slow expansion and exploration of the melodic and harmonic material.

Figure 4: Orchestrational narrative in Tale One. Note return to “original” orchestration. 

In Tale One, the orchestration transforms from simple – dry and staccato (paired with sustained “sine” waves) – to a more complex sound while adhering to relatively homogenous sound qualities. One could imagine something that is clean and virgin becoming increasingly dirtied and corrupt before returning to a cleaner, but stressed state; perhaps also an analogy as well to “turning up the dials” in electronic music. A similar process, and perhaps a less abstruse of a transformation, happens in Tale Two, as I will explain later. This clean to dirtied analogy brings to mind Ravel’s Bolero,15 where the piece grows from simple, homogenous timbres (flute, harp, etc.) to increasingly complex timbres (such as the iconic piccolo, horn, celesta iteration of the melody) over the course of this piece.

As Shown in Fig. 4, the orchestration begins with sine wave-like instruments (flute), paired with bell like instruments (bells, harp, piano, pizzicato strings). Throughout the opening of the work, more instruments are added, namely bass clarinet and contrabassoon, which are meant to color the trombone’s timbre.

At m. 41, a shift occurs to coincide with the first change of harmony (from the A7 chord to its false resolution to F# minor). The timbre qualities are roughly the same, but more complex: the bell sounds are now marimba, vibes and electric piano; the bass clarinet, contrabassoon and trombone have become the brass section; the flute and clarinet are now arco strings.

What follows is a high level of variegation from m. 85 through 292. With the exception of both tutti sections at m. 85 and m. 230, the ensemble is always a changing subset of the full ensemble. This is in part to be kaleidoscopic, but also to highlight the diffusion of the source.

As Tale One concludes, the orchestration begins to return to its original, yet slightly altered state. By m. 300 the initial saxophone timbre has been substituted by the timbrally related clarinet, and the trombone has been substituted its timbral neighbor, the contrabassoon.

Finally, at the conclusion of the entire work, the orchestration returns again to its initial orchestra block: Flute, Horn (as trombone), Bells, Harp, and Piano. Here at the end of the piece, the dry, staccato notes (like the pizzicato strings) have metamorphosed into sustained tones, as if the pizzicati have been frozen into stasis.



In Tale One, the resonance is mainly obtained through three methods melodic diffusion: by extracting portions of the melodic source and distilling them as vertical simultaneities with independent melodic vectoring, or by rhythmic diffusion, where portions of the source are refracted into the temporal grid allowing them rhythmic independence but melodic dependence. Both of the methods of diffusion suggest variable levels of resonance and a striving to a maximal amount of polyphony with very limited options.

By using a relatively small collection of pitch materials and allowing only certain pitches to be refracted though the ensemble, the music gives a sense of diffusion that one can compare to delay units and filters in electronic music, which I will discuss in greater depth in the next chapter.

4. she is memories for lots of people

Building Resonant Textures

Unlike Tale One, where the musical trajectory is concerned with the juxtaposition of complementary and contrasting musical character, Tale Two unfolds in much the opposite way – as a single unbroken gesture in which several processes unfold simultaneously. These gradual processes unfold at different rates of speed, and while seemingly unrelated at first, together form a single gesture in which each process, and their subsidiary parts, act like gears in a larger machine.

The principal and most obvious process is the slow agglomeration of resonance over the first two-thirds of the movement, as if one were slowly turning the feedback knob on a delay unit (and distortion pedal) from 0 to 10. As a result, timbres that start as pure gradually become more distressed and corrupt, mimicking the accumulation of rhythmic resonance and auxiliary melodic strata distilled from the melodic source.

In Tale One, the melodic source lacks a great deal of content, however here in Tale Two, the amount of source content has been stripped down to an even more barren and nearly void state. Here, the material distilled from it is comprised of sustained pitches, which grow more dissonant with the layering of distilled and refracted lines. One can imagine something similar to the electroacoustic processes of Alvin Lucier’s I am sitting in a room and John Luther Adams’s The Mathematics of Resonant Bodies.16  In the latter work, Adams’s processes the live signal of a percussionist playing long sustained textures on various percussion instruments (rolled cymbal, rolled bass drum, etc.) and projects the sound quadraphonically around the performance space. In turn, the speakers in the hall are miked and remixed back into the hall. The result is much like Lucier’s and Adams’s piece, a gradual increase of resonance to transform noise into pitch, yet reversed in filumena.

Another running process is an acoustic analog of pitch shifting. As repeated notes “shift” up or down in pitch they either gain or lose speed based on the direction they shift.
All of these processes work in tandem to construct the overall musical narrative and structure of the movement. In the pages to follow, I will examine them more carefully.


Melodic Cycles and Distilled Lines

Melodically, Tale Two begins with a skeletal six-note melody, which, like a tape loop, loosely repeats itself six times. In addition to this repetition, the melody at each of the six iterations, or Cycles, gradually augments itself through a series of contractions and expansions. This augmentation coincides with the develop- ment of resonance, the transformation of timbre, and the increase in rhythmic resonance, so that each coexisting process reaches its apex simultaneously.

Example 14: The six Cycles of Tale Two 

Since the melodic source unfolds at a snail’s pace, I chose to use the melodic source as a background, rather than pushing it to the foreground as in Tale One. In other words, the notable musical lines, such as the soloist’s part, are a product of distilling and refracting the source. The source by itself generates the resonant landscape that the oboe floats over, and marks structural elements to orient the unfolding of the processes.

Example 15: Opening of Tale Two. Note the minimal amount of reso- nance in the texture – first in the violins and violoncello, then viola and contrabass. mm. 312 – 316 

The first cycle, outlines the first five pitches of D major, are clearly stated: A, G, A, F#, A, D. (Ex. 14). Cycle 2 states the same pitches again, though broken into two strata: a higher line stating A, F#, D and a lower, G, F#. Cycles 3 through 5 look the same, both descend, adding E to the gamut and eventually C# in the fifth cycle. The final cycle (Cycle 6), becomes more dissonant, adding F#, G#, B and Bb. In the end, each new cycle changes the way linear information is distilled from the source.

Example 16: The beginning of Cycle 4. Note how the oboe “anticipates” the next pitch of the cycle. First a G in m.332, then an E in m.336. 

The source is always played by a bell ensemble consisting of crotales, glockenspiel, harp, piano, celesta and assorted unpitched “found” metal instruments, and is quietly sustained by string harmonics, like a luminescent halo.17 In Cycle 1, the sustained tones only last until the next attack, in that they do not bleed over to the next attack; one can imagine a piano pedal being lifted at every attack of the source. In later cycles, the sustained pitches do bleed over (creating harmonies), one can imagine the piano pedal remaining down.(Ex. 15).18

Example 17: Beginning of the winds and metallic aleatoric section, Cycle 5. m. 357, extract. 

At first, there is no adornment of the source, as it is replicated at the unison. The only exception is a measured tremolo played by flowerpots, and pulses played by the celesta (see the next section). The oboe enters at Cycle 3 (m. 331), doubling the source at the unison. In this Cycle, the oboe’s auxiliary line is refracted from the source, disengaged from the singular attack points of the bell ensemble. However, the distilled pitches anticipate the next pitch of the melody, rather than follow it. This reversal of roles temporarily changes the bell ensemble from a melodic generator to a quasi-melodic echo. (Ex. 16). The oboe continues this treatment through this cycle, before the roles return to their original state.

In Cycle 4, the source is once again refracted forward into the temporal grid. Here the oboe’s auxiliary line is distilled, but contains additional pitches not found in the source. These pitches outline partials extracted from the sound- ing pitches of the bells and harmonics and are triadic in nature, alluding at times to A7 and DMajor7.

In Cycle 5 the pitch content of the source increases and thus the amount of diffusion as well. Here, the gamut of each attack of the source increases from dyads, as in Cycle 4, to pentads. As a result, the potential linear variation of pitch material for the oboe to refract increases, along with the harmonic density of the sustained tones. The sustained tones become more timbrally vivid (adding a flute, bowed vibraphone and trombone to the string harmonics), accessing wider vertical range.

Sub-auxiliary lines begin to emerge, as the oboe line is diffused into the sustaining instruments. At m. 358 the synthesizer (sounding a sine wave-like pad) and bowed vibraphone double the end of the oboe’s gestures, creating an acoustic reverberation of the oboe line.

Cycle 5 also signals a marked difference in the texture, primarily in terms of rhythm, as the fragmentation of the source’s attack points create richer resonant surroundings. The rhythmic resonance generated begins with the found metal instruments. At m. 357, the found metals enter an aleatoric environment, improvising their way through single attacks and tremolos, completely divorced from the temporal grid. In the same location, the long awaited entrance of the clarinet and bassoon amplifies the rhythmic disorientation (Ex. 17). Here, the winds are given a set of melodic gestures that have been distilled from the source line, which are to be performed quietly as background, in an improvisatory manner.

Cycle 6 (mm. 368 – 380) provides a glimpse of the most complex example of rhythmic resonance in filumena. Much like the Boulez example demonstrated earlier, the reinforcement that the bell ensemble provided of the source’s rhythmic and melodic presentation, begins to uncouple fully into distinct independent auxiliary lines. This moves the temporal grid further and further from view with the germinating number of rhythmic strata. Furthermore, up to this point, the horizontal auxiliary lines have been relatively simple, and it is here, as the resonant qualities increase, that the oboe line becomes more florid and achieves full rhythmic independence.

In addition to the increased rhythmic resonance, the pitch content of Cycle 6 grows more chromatic, hence generating more dissonance in the distilled auxiliary lines. Together, the dissonance, rhythmic resonance and the dilating ambitus of both the ensemble and oboe, propel the music towards the climax of Tale Two (Ex. 18).


Example 18: The ending of the resonance buildup and feedback loop just before the apex is reached. mm. 388 – 391. 

Timbral Transformation

Running in tandem with the gradual amplification of resonance through the melodic cycles, rhythmic resonance, and dense harmonic strata, is an ambient texture, which at first seems insignificant, but as it matures, takes on enough mass to become the dominant gesture of Tale Two. This gesture begins as a quiet tremolo played by flowerpots and celesta and ends with the full ensemble (plus two very large ratchets – “graggers” – and two suspended metal garbage cans) playing, of course, as loud as humanly possible. In conjunction, the tim- bral qualities of the tremolo transform over time. The timbral transformation may bring to mind, and was perhaps inspired by, similar processes of timbral development in works by György Ligeti, such as Clocks and Clouds or Lontano (Ex. 19).

Example 19: The opening measures of György Ligeti’s Lontano. Note the homogenous timbre of flutes, clarinets and bassoons slowly being paired with stopped horns and muted trumpet in m. 5 – 8. 

In Ligeti’s Lontano, the timbre slowly transforms from a sine wave-like sound to tremolo strings. In Example 18, the opening Ab begins with a simple timbre comprised of flutes, clarinets and bassoon. This timbre begins to transform with the entrance of the oboe, stopped horns and muted trumpet in mm. 5 –7. The timbre transforms again in m.11 with the entrance of the sustained strings (con sordini, flautando and sul tasto) doubled with the initial woodwind grouping before the sustained strings begin a staggered entrance of a tremolo which envelops the texture by m. 29.

Stage 1 of this process begins at the head of Tale Two. A fast measured tremolo is played by “tuned” flowerpots, while a slower tremolo is played by the celesta – slow enough that it sounds more like a pulse than a tremolo. The speed at which the measured tremolo occurs is directly related to the pitch it plays. For example, the flowerpot’s A is sextuplets, the following G (a step lower) is quintuplets, the F# below are sixteenth notes, and the E below, triplets (Ex. 20).

Example 20: The opening of Tale Two and Stage 1 where the timbral trans- formation of the tremolo (from flowerpots and celesta to full ensemble) begins. eating filumena lionheart, mm. 312 – 314, extract. 

This manner of slowing down the tremolo with relationship to the pitch is an outgrowth of an appropriated electronic music technique, “pitch shifting.” Pitch shifting occurs when a recording is slowed down or sped up, changing the source’s pitch with it, relative to the speed.19

The slower tremolo, can be understood as a “pitch shifted” tremolo in this con- text, in that it sounds an octave below the flowerpots, hence its speed is halved.

Example 21: Stage 2 of the transformation - The harp tremolo. Ibid., mm. 357 – 361, extract. 

This tremolo remains omnipresent for the next forty-four measures and relatively unchanged, except for a brief transference of the celesta line to the piano in mm. 325-30 to coincide with the beginning of Cycle 2. The pattern is eventually broken in m. 341, as the measured tremolo increases in speed transforming into the harp tremolo in Stage 2.

Example 22: Eliding Stages 3 and 4 – transferring the tremolo from harp to piano and strings. mm. 380 – 383, extract. 

Transitioning from Stage 1 to Stage 2, the Celesta slows down to quarter notes and stops in m. 354, while the flowerpots gradually speed up to an unmeasured tremolo at m. 357. Here, Stage 2 begins, as the tremolo is transferred to the harp, coinciding with the beginning of Cycle 6. The harp continues with this tremolo through Stage 2 and 3 until it becomes usurped by louder tremolos at m. 385 (Ex. 21).

In addition to the harp tremolo, the found metals that were unshackled from the temporal grid begin occasionally to add tremolos as a mode of attack. These continue through Stage 2 and 3, up to m. 381.

Stage 3 begins at m. 365 and continues through m. 378. The orchestration of the tremolo remains the same, with occasional encroachments of tremolos from different areas of the ensemble, in anticipation of the emergence of this gesture from background to the foreground. For example, in m. 365 the con- trabass has a brief tremolo that pokes out from the texture. Five measures later, the glockenspiel has the same gesture. In mm. 372 - 378, the flute begins to add fluttertongue to its sustained pitches.

Example 23: The climax. Full tremolo in all instruments and the begin- ning of the pulsed piano. mm. 392 – 96. 

Up through Stage 3, the tremolo has remained an omnipresent background texture that is passed to different instrumental groupings. In the following two stages, 4 and 5, the tremolo begins to infiltrate the rest of the ensemble, as if this moment were the event horizon, where all of the running processes cannot escape the tremolo’s gravity. Stage 3 elides with Stage 4 as the tremolo is passed to the viola and piano 1 in mm. 378 – 79 (Ex. 22). These tremolos begin softly and crescendo as the tremolo takes on more mass, adding Piano 2, Glockenspiel and the remaining strings by m. 384. This coincides with the end of Cycle 6 in m. 380. From here on, the tremolo folds in a secondary glockenspiel and sleigh bells, while the strings play sul ponticello molto, which effectively turns the overall sonic qualities of the tremolo from pitch to pure noise.

Stage 5 occurs at the climax in m. 394. Here, the entire ensemble (minus the soloist) has a tremolo: Strings are in their upper ranges; the brass are playing fluttertongue; the winds are in their extreme ranges and; the pianos, harp and percussion play all noisemakers (Ex. 23).


Maximum Resonance and the Deus ex Machina

As mentioned above, the end of Cycle 6 synchronizes with the elision of Stages 3 into 4. To complement the shift from pitch to noise, the pitch material of the melodic source moves from diatonic qualities to chromatic while the amount of rhythmic resonance and volume is pushed to an extreme, as if the knobs of distortion, delay, and feedback pedals have been turned up to 11.

All of the aforementioned processes conclude at the summit of their gestures, climaxing at m. 394. For example, the pitch material has moved from octaves outlining the D Major to total chromatic saturation. The timbre of the distilled sustained tones has transformed from pure and simple to metallic and complex; the timbre of the tremolo, which began as dry and “earthy” trans- forms to metallic as well; the oboe which began in the middle of its tessitura, makes the most of its range, pushing itself into the uppermost ranges of the instrument, at maximum volume.

Example 24: The piano pulse: a slowed down tremolo. Cf. the orchestra- tion here with the opening of the work. mm. 441 – 446, extract. 

From the noise emerges a new and unexpected musical idea; its actual entrance is masked by the noise generated from the ensemble and we only realize it is there once the noise deteriorates by m. 403. What follows here is a quiet, word- less pop-song sung by a unique timbre, the heretofore tacet soprano doubled by the solo oboe at the unison or octave.

Here to the end of the work marks the only point in the piece where there is no melodic source, as the music in this section is comprised of only melody and an accompaniment. The accompaniment is provided by the pianos as pulsating quarter notes, colored by sustained strings (Ex. 24). This pulsating accompaniment can be viewed as a continuation of the tremolo, thus Stage 6, as it is no more than the initial tremolo pitch shifted down (and harmonized), and run through an orchestrational filter to make it appear more “mellow.”

Overall, the orchestration has returned to its original state as it was in the beginning of the work. Certain timbres have been altered to be more appropriately mellow; the saxophone has been replaced by horn, while the higher bell-like sounds in the pianos, glockenspiel and harp, have been smoothed out to crotales and glockenspiel, along with the vibraphone and harp in their middle ranges. The piano pulses can be viewed as a distant, lo-fi cousin of the pizzicato strings, while the sustained string section mirrors the aura-like sustained “accordion” in the opening.



In Tale Two, the melodic source was pre-compositionally fashioned to allow for both a maximum amount of resonance and for a high degree of distillation and refraction. This was accomplished by stripping the melodic source down to its bare essentials, leaving the distilled auxiliary lines to freely interpret the source freely within vertical and horizontal musical space.

The orchestration of this section was based upon choosing an ensemble that supports the lyrical properties of the oboe while supporting it with a resonant and homogenous texture, like a halo. The supporting texture is also elaborated upon with gradual processes including a long-term timbral transformation and a slow build-up of rhythmic resonance, growing like a feedback loop, serving both as connective tissue and as a dramatic device.

Furthermore, the diffusion of the lines was approached from a perspective of paying homage to “lo-fi” æsthetics. By lo-fi I mean an audio recording (or any visual medium) that has a degraded quality of sound (or image) that has been intentionally distressed to provide an aural (or visual) association of antiqueness and authenticity; this æsthetic encourages artifacts and impurities to be audibly present, providing both a sense of nostalgia and crudity. Translating this into an acoustic setting is perhaps ephemeral and subjective, and approached with a high degree of abstraction. It can be viewed as if I were notating all of the inconsistencies of an imagined ancient recording of the melodic source, slowed down, with copious amounts reverb and filters piled onto it. Thus the various timbres of bells, “detuned” found metals and flowerpots, diffusion of the melodic lines, rhythmic resonance, and the slow implementation of feedback and noise, can all be viewed as the artifacts, inconsistencies and other related phenomena of a highly distressed recording. From this vantage point, all of the ways diffusion was concretely charted and extracted in Tale One can be compared to in Tale Two as the abstracted effects of obsolescent media like wow and flutter, dropouts, loss of frequency, and so on.

5. Conclusion

As I have shown in my analyses, eating filumena lionheart uses various methods to diffuse the melodic source within the confines of the heterophonic nature of this composition. While Tale One seeks to obtain resonance and polyphony by diffusing a primordial line, Tale Two builds an increasing mass of sound from a through several processes meant to diffuse the line. However, we can understand both parts through a common analytical model.

In filumena, the melodic source was preconditioned to achieve a various outcomes. The melodic source in Tale One was designed to allow for a great deal of linear variation while retaining a consistent resonance throughout. The amount of vertical distillation was maximal, while the amount of rhythmic diffusion was kept to a minimum, as a quantized temporal grid rigidly controlled the refraction of the auxiliary lines. This achieves an illusion of polyphony, allowing the oboe’s gestures to be diffused as seemingly independent lines with the assistance of a kaleidoscopic orchestration. Furthermore, these independent lines seem to resonate across the ensemble, as if one were taking electronically filtered snippets of the solo line and projecting it into the performance space.

In Tale Two, a continuous stream of resonance is built up, much like a feedback loop, which defines the structure for the movement and transforms timbre homogeneously from one state to another. Here, both timbre and the source’s distilled auxiliary lines expand, synchronically metamorphosing from clean, pure and diatonic to cacophonic, before returning again to a simple, virgin state.

Musically, both of the cautionary tales of filumena can be construed as tell- ing the same narrative in different ways.20 Each tale is cyclical both in form, harmony, diffusion and timbre; the piece as a whole retains this cyclicality,much like the narrative of a cautionary tale suggests: something naïve becoming corrupted, and perishing, so the next callow victim can follow the same perilous fate.

Perhaps this naïveté is also reflected in the inadequacy of interesting melodic content encapsulated within the melodic source. In other words, the melodic source is not interesting enough to stand alone. It needs to be inflated with narcissistic musical devices to allow it to be effectively large and flamboyant – that is, it needs to be able to sing. In this case, the musical surface becomes a grotesque reflection of the source. All of the material, including polyphony, harmony and processes are derived from it, and ultimately synthesized with it, in the attempt to provide the illusion of its magnificence.

It would be interesting to further explore this phenomenon beyond the confines of this piece. Perhaps further investigation of how and why composers of the late twentieth-century, and later, chose to encapsulate total musical ideas within small pellets (like a row, single musical line, or harmonic fields) with the intent to magnify and amplify its heterophonic contents to generate a musical work, and is, so en vogue. Be it as it may, further examination and codification of methods of melodic and rhythmic diffusion would provide excellent grounds of research for scholars of the future.

1 Webern, Anton. “The Path to New Music.” p. 20. The lectures were given to a group of amateur musicians in Webern’s home in 1933-34 and were transcribed by one of the attendees.

2 Cooke, Peter: ‘Heterophony’, The New Grove Dictionary of Music and Musicians.

3 Webern’s approach to this kind of ‘refraction of a line’ can be seen in his 1935 orchestration of J.S. Bach’s Ricercar (from the Musikalisches Opfer.) In fact, this notion is summed up in Schoenberg’s concept of Klangfarbenmelodie.

4 This list also includes all of the subsequent genres appearing very late in the twentieth and early in the twenty-first centuries, such as postminimalism, totalism, “sincerialism.” Sincerialism is an ironic, and perhaps negative neologism coined by performing ensembles in the New York area. It is defined as music that is harmonically, melodically and rhythmically simple, often coupled with an honest, emotional subtext. My piano quartet (at times my sadness falls into would be an example of this type of music.

5 Luminance is defined as the brightness in an image, while chrominance is defined as the color information of an image.

6 See Appendix for full instrumentation.

7 Much could be written about other cautionary tales represented in the piece, mainly on the current state of American composers and their music. This exploration, unfortunately, would be out of the scope of this paper.

8 This may bring to mind the anti-concerto nature of Hector Berlioz’s Harold en Italie (1834), where the viola sola and orchestra are treated as equals. Niccolò Paganini, who encouraged Berlioz to write this piece, refused to perform it as he “expected to be playing continuously.”

9 Cf.the works of Edward Gorey, or Heinrich Hoffmann’s Der Struwwelpeter.

10 Initially, filumena was to have a third tale where the A7 chord would finally get resolved.I rejected this because it seemed that leaving the piece theoretically (and “romantically”) “hanging” would be more dramatically effective than resolving it.

11 See the Appendix for a full structural analysis.

12 The polyphony I am thinking of bears an uncanny resemblance to the polyphony of a Baroque aria, for instance. An aria from any one of J.S. Bach’s Cantatas usually contains the melodic line (solo voice), a countermelody (solo instrument), and a rhythmic driver (such as short notes punctuating the beats, like a moving bass line), all of which is derived from the motion of the harmony (continuo). Perhaps this is a good way of understanding and analyzing this movement.

13 By driving tones I mean background notes (or “ghost-tones”) that adhere to the rhythmic grid serving to “drive” the music forward (e.g. a ride cymbal, the off-beats in stride-piano music).

14 Mémoriale was written in 1985 and is a re-working of flute material from his ...explosante-fixe... (1972). It is scored for solo flute, two horns, 3 violins, 2 violas and violoncello. It is fruitful to note that ...explosante-fixe... was scored for solo flute with electronics, and perhaps the re-imagining of the electronic part had some hand in how he “analog-ized” electronic thinking.

15 An homage to this moment appears in filumena at m. 97 and is one of the rare moments of distilled pitches not being in unison or octaves.

16 In Lucier’s piece, a narrator reads a statement, which is amplified via loudspeakers in the performance space. A microphone array is simultaneously recording this performance. When the statement is finished being read, the recording of it is played back in the space while the narrator re-reads the statement again. This is also recorded. Overtime, resonant feedback begins to occur on the tape loop as more and more layers are added on top of each other. The piece ends when the initial iterations are lost to complete resonance.

17 Such as steel auto parts, railroad stakes, metal plates, metal bowls, etc.

18 In his program notes for Coptic Light (1985), Morton Feldman writes: “An important technical aspect of the composition was prompted by Sibelius’s observation that the orchestra differs mainly from the piano in that it has no pedal. With this in mind, I set to work to create an orchestral pedal continually varying in nuance. This ‘chiaroscuro’ is both the compositional and the instrumental focus of Coptic Light.”

19 The exact relationships of pitch to speed are relative here, and are not by any means exact.

20 Cf. the works of Samuel Beckett, specifically Waiting for Godot and Happy Days.