Texture, Rhythmic Synchrony, and Tonal Fusion in Henry Threadgill’s In for a Penny, In for a Pound^*

Introduction

[0.1] In 2016, Henry Threadgill won the Pulitzer Prize for his recording and performance of In for a Penny, In for a Pound, an instrumental work in six movements that combines improvised and notated music. He composed the piece for his ensemble Zooid, which he founded in 2001.⁽¹⁾ In the following quote from 2010, Threadgill describes the primary (but not exclusive) texture of Zooid’s music, which continues to the present day:⁽²⁾

It’s contrapuntal music—everyone is playing these different melodies and phrases. Harmony happens, but the harmony is incidental to the counterpoint chatter. (Vitale 2010)

[0.2] The few exceptions to contrapuntal (polyphonic) textures in Penny are strategically placed and rhetorically charged. The effect is strongest when we encounter melodies performed by two musicians in rhythmic synchrony (concurrence) and parallel unisons or octaves. Describing one such moment in “Ceroepic,” the second movement of Penny, critic Nate Chinen writes, “every coordinated gesture, like the spiky phrase for flute and trombone in the final seconds of ‘Ceroepic,’ comes with a small jolt, a reminder of how many details have been whirring past” (2015). Example 1 provides the audio and score for this passage.⁽³⁾

[0.3] Chinen is not the only critic to have taken notice of this sort of unison passage in Zooid’s music. Reviewing a performance by Zooid of In Frontispiece, Ben Ratliff writes, “And the melody at the end, played in unison by Mr. Threadgill and Mr. Ellman, made the whole band cohere, as if by gravitational force. Suddenly the music seemed to signify properly as mystery” (2010).⁽⁴⁾

[0.4] In this paper, I am interested in interrogating how we can profitably explore form through these textural changes. I pay particular attention to melodies performed by two instruments in rhythmic synchrony (concurrence) and parallel pitch motion. I argue that 1) the concurrent passages create movement-wide forms through their contrasts with the polyphonic textures and 2) the presence or absence of parallel unisons or octaves—the most “tonally fused” two-note intervals (Huron 2001)—further articulate form. The analyses have implications for our understanding of Threadgill’s music writ large. In addition, this article has a point of contact with current research on the Association for the Advancement of Creative Musicians (AACM) (Hannaford 2019, Steinbeck 2022, Lewis 2008). More broadly, the findings interact in productive ways with theorists’ ongoing work on texture.⁽⁵⁾

[0.5] Because of the limited amount of research on Threadgill, section 1 opens the article with a brief biographical sketch. Section 2 provides an overview of pitch and form in Zooid’s music. Section 3 presents the article’s methodology. As a test case for my argument, sections 4 and 5 offer analyses of the second and sixth movements of Penny, the aforementioned “Ceroepic” as well as “Unoepic.” Section 6 suggests avenues for future research.

1. Biographical Sketch⁽⁶⁾

[1.1] Henry Luther Threadgill was born in Chicago on February 15, 1944. His musical activities began during childhood and continued through adolescence. He attended Wilson Junior College in Chicago from 1962 to 1964 as a music major, where in his words he received “a solid foundation in Western classical music and composition” (Threadgill 2023, 46). Other music students at Wilson at this time included Jack DeJohnette, Roscoe Mitchell, and Anthony Braxton. Later in 1964, Threadgill enrolled at the American Conservatory of Music in Chicago, where he studied until he volunteered for the draft and joined the US Army in August 1966 (60–61, 79).

[1.2] Threadgill served in Vietnam in 1967 and 1968. Upon returning to Chicago in 1969, he joined the AACM. Also in Chicago in 1969, Threadgill enrolled at Governors State University “as a composition and woodwinds major” (Threadgill 2023, 157). He soon left Governors and returned to the American Conservatory of Music, studying flute, piano, and composition, and received a BM degree there in 1973 (204). This marked the end of Threadgill’s formal music education.

[1.3] In 1972, Threadgill cofounded the ensemble Reflection with bassist Fred Hopkins and percussionist Steve McCall. The trio renamed itself Air in 1975, becoming the first in a series of important ensembles Threadgill has performed with and/or led.⁽⁷⁾ These ensembles include: X-75 (1974–circa 1979), the Henry Threadgill Sextett [sic] (1979–1989), The Society Situation Dance Band (late 1980s), Very Very Circus (1990–1995), Make A Move (circa 1997–2001), and Zooid (2001–present). The cumulative impact of Threadgill’s compositions and performances with these ensembles has been significant. Already in 1988, the New York Times called him “perhaps the most important jazz composer of his generation” (Watrous 1988), and the 2016 Pulitzer Prize committee wrote that he is “widely considered to be among the most important artists in jazz” (The Pulitzer Prizes 2016).

[1.4] Notwithstanding these accolades, Threadgill has never considered himself a jazz musician, for two reasons. In a 2010 interview, he stated,

I don’t really like the term jazz; I prefer creative improvised music, because there’s confusion about what jazz means now. I think it’s lost its meaning, and I don’t think it’s relevant anymore. (2010)

Further, none of his ensembles fully embrace the stylistic traits of any jazz subgenre (e.g., bebop, modal, free, fusion). While Threadgill declares a stylistic debt to Sonny Rollins and Ornette Coleman, he considers the influence of Debussy and Varèse to be equal in importance.⁽⁸⁾

2. Zooid: A Primer

[2.1] Threadgill explained the name of his ensemble as follows:

In biology, a zooid is an organic cell or organized body that moves independently within a living organism. It can function as part of an aggregate or colony, but it operates on its own volition. The name emphasizes the key characteristic of the ensemble working in the chromatic language: the individual voices are linked as elements in the whole, yet also utterly autonomous. (Threadgill 2023, 375)

The statement regarding “individual voices” recalls the Threadgill quote in [0.1]: “It’s contrapuntal music—everyone is playing these different melodies and phrases” (Vitale 2010). I shall discuss “the chromatic language” to which Threadgill refers in [2.4]–[2.9].

[2.2] Threadgill notates his compositions for Zooid using Western notation on five-line staves. Three features of the scores deserve mention. First, all instruments are notated at sounding pitch. This includes the guitar and bass flute, which are typically notated one octave higher than their sounding pitches. Second, all parts for pitched instruments are fully notated. Threadgill notates the drums and percussion parts in three ways. Threadgill explains the first and most common way as follows:

With the drummer in Zooid, I don’t write out the part in as much detail as I sometimes used to do with Air or with the Sextett [sic]. I just give the drummer meter. But the drummer doesn’t play the same meter the rest of the band is playing, because I don’t need him to do that. It would be redundant . . . If a given melodic phrase goes on for, say, twenty-one beats, then that’s the unit we’re working with. For the drummer, those twenty-one beats might be divided up in a different way from the rest of the band—he might be playing in ${}_4^7$ time and then ${}_4^3$ and then ${}_{\mathrm{ 4}}^{11}$, while the rest of the band is playing in ${}_4^5$ and then ${}_4^6$ and ${}_4^5$ and ${}_4^5$. When those various units of time are overlaid on top of one another, it creates tension and drive—that’s what gives the music its characteristic groove. (Threadgill 2023, 377)⁽⁹⁾

[2.3] To illustrate how Threadgill “overlays various units of time,” Example 2 reproduces rehearsal A from “Ceroepic.” The drum part begins with a measure of ${}_4^7$. For the remaining instruments, these seven beats appear as one measure of ${}_4^3$ followed by one measure of ${}_4^4$. Similarly, the second measure in the drum part is in ${}_4^6$, and these six beats appear as two measures of ${}_4^3$ in the remaining instruments. The rest of A works similarly: every measure in the drum part contains two measures of the remaining instrumental parts. The remaining two types of drum notation in Penny work as follows. Some passages bear the marking “drum solo” or “improvisation,” with no additional information or staff notation. Conversely, other passages contain fully notated rhythmic staff notation and dynamics. Throughout Penny, the drums/percussion do not participate in rhythmically concurrent passages such as that in Example 1.

[2.4] A second element of interest in Threadgill’s scores are the notations appearing above the “chords” staff. I shall refer to these notations as chord symbols. In m. 1 of Example 2, $\frac{AC}{F♯}$ indicates a chord with F♯ as the lowest pitch, A as the middle pitch, and C as the highest pitch. The chord symbols indicate relative registral positions only, not exact registers. F♯2 appears in the tuba while A3 and C4 appear in the cello. The number 2 under the F♯ indicates that the chord sounds for two beats. Still in m. 1, $\frac{F♯A}{F}$ indicates a chord with F as the lowest pitch, F♯ as the middle pitch, and A as the highest pitch. F2 appears in the tuba while F♯3 and A3 appear in the cello. The number 1 under the F indicates that the chord occupies one beat.⁽¹⁰⁾

[2.5] The guitar’s C♯4 and D4 in m. 1 are “non-chord tones” relative to $\frac{AC}{F♯}$ and $\frac{F♯A}{F}$. Threadgill uses ”non-chord tones” to create melodies that differ in pitch content (and often musical character) from the remaining pitched instruments. In Penny, this is always the case when a melody appears with chord symbols. As such, the composite texture might be described as melody/accompaniment (melody = guitar, tuba/cello = accompaniment, drums = an additional [non-pitched] element of the accompaniment). Such a description, however, runs counter to Threadgill’s earlier statement that “harmony happens, but the harmony is incidental to the counterpoint chatter.” This begs the question: why does Threadgill include the chords in the score? The answer is that the chords act as a basis for improvisation—an improvisor may treat them as a “chord progression” (Taylor 2015, 153–54). This is how the Zooid musicians treat the improvisations on chord symbols in “Unoepic” and “Ceroepic.”⁽¹¹⁾

[2.6] How and when improvisation occurs in Zooid’s music relates to Threadgill’s use of modular form. Threadgill addresses this point in the following quote:

My music with Zooid is modular above all else. Everything can be moved around. Because the intervallic system provides a foundation for everything, the order and arrangement of the parts can be switched without undermining the total effect . . . I almost always switch things up on my musicians once we get in the room. It keeps them on their toes and keeps them from relying on their technical expertise or ingrained habits.⁽¹²⁾ (Threadgill 2023, 378)

[2.7] Example 3 provides an illustration of the “intervallic system” mentioned by Threadgill in the preceding quote. The example reproduces the opening measure of rehearsal D of “Unoepic.” The notation “-23445-67” appears above every staff except that of the drum set.⁽¹³⁾ The numbers indicate the sizes of tonal intervals: 2 indicates a 2nd, 3 indicates a 3rd, and so forth. A hyphen (representing a minus sign) preceding a number indicates that the quality of the interval is minor, such as minor 2nd and minor 6th here. If no minus sign appears, the interval is major (for 2nds, 3rds, 6ths, and 7ths) or perfect (for 4ths and 5ths). A plus sign indicates an augmented interval (not present here). If the number(s) 2, 3, 6, and/or 7 appears twice, both major and minor qualities for that interval size are present. Similarly, if the number(s) 4 and/or 5 appears twice, such as “44” here, both perfect and augmented qualities for that interval size are present. Each interval can ascend or descend, and each simple interval can also appear as a compound interval. I shall refer to a collection of intervals such as -23445-67 as an interval set.

[2.8] Interval sets constrain the note-to-note melodic intervals in each instrumental part. For example, consider the tuba melody G2, C3, F2, C♯2, A1 in Example 3. The note-to-note intervals are: ascending perfect 4th (4), descending perfect 5th (5), descending diminished 4th/major 3rd (3) (enharmonic equivalence applies), and descending major 3rd (3). Each of these intervals belongs to the interval set. The melodies in the other instruments work similarly.⁽¹⁴⁾

[2.9] The interval set also exerts a harmonic influence, in the vertical intervals of the chord symbols on the score. Recall that each chord contains one low pitch, one middle pitch, and one high pitch. The interval formed by the low and middle pitches will belong to the interval set, as will the intervals formed by the middle and high pitches, and the low and high pitches. For example, the $\frac{C♯F♯}{C}$ chord contains a minor 2nd/augmented prime (-2) from C up to C♯, a perfect 4th (4) from C♯ up to F♯, and an augmented 4th from C up to F♯ (+4). Each of these intervals is a member of the interval set. (The F♯4 in the guitar part doubles the cello’s F♯3 one octave higher.) The following two chords, $\frac{F♯C}{F}$ and $\frac{CF♯}{C♯}$, work similarly. By contrast, the final chord, $\frac{CF♯}{A}$, contains a minor 3rd (-3) from A up to C, an interval that is not part of the interval set. The presence of vertical intervals that do not belong to the interval set occurs occasionally in Penny. In this case, it is possible that the minor 3rds serve to anticipate the minor 3rds in the interval set found in the following measure: 22334-67. Every movement of Penny except “Ceroepic” includes interval sets on its score.

3. Analytic Methodology

[3.1] To introduce the methodology underpinning the analyses in Sections 4 and 5, let us examine three concurrent passages in rehearsal D of “Unoepic.” Because each passage involves two instruments, I shall refer to them as concurrent duets.⁽¹⁵⁾ Example 4 provides an annotated score and audio for the passages.

[3.2] To begin, I shall address some rhythmic and instrumental features of the passage. The guitar and cello perform the first concurrent duet. In the third measure, their rhythms differ during the first two beats, then realign. The second concurrent duet involves the cello and alto saxophone; there are no deviations from the rhythmic synchrony. The alto saxophone and guitar perform the third concurrent duet, again with no deviations from the rhythmic synchrony. By retaining one instrument from duet to duet (guitar/cello → cello/alto saxophone → alto saxophone/guitar), Threadgill creates a thread of timbral continuity throughout the sequence of duets. The first concurrent duet uses two stringed instruments, one bowed and one plucked; the second retains the bowed instrument; and the third brings back the plucked instrument. This continuity notwithstanding, the degree to which the instruments blend fluctuates.⁽¹⁶⁾ The guitar’s attack is faster and less “scratchy” than that of the bowed cello (duet 1), the alto saxophone is brighter than the cello (duet 2), and the guitar notes decay faster than those of the alto saxophone (duet 3). In short, not all concurrent duets exhibit identical degrees of sonic unity. I return to this point in [3.10].

[3.3] Let us now turn to pitch and voice motion. In concurrent duet 1, the guitar and cello move in similar motion, save for two oblique motions indicated in Example 4. The guitar provides the highest pitch of each chord symbol, the cello provides the middle pitch, and the (rhythmically independent) tuba provides the lowest pitch. In concurrent duet 2, the cello and alto saxophone move in parallel unisons. The guitar now provides the high and middle pitches of each chord symbol (double stops) as the tuba continues with the lowest pitches. In concurrent duet 3, the alto saxophone and guitar continue the parallel unisons. The cello now provides the high and middle pitches of each chord symbol (double stops), and the tuba continues with the lowest pitches.

[3.4] Turning now to texture, the alto saxophone projects the melody in a melody/accompaniment texture for the entire passage—first as a solo instrument, then in rhythmic and pitch unison with the cello and guitar, respectively. The progression from solo instrument to duo with cello to duo with guitar (the featured instrument of the movement; see [4.1] and [4.7]) gradually strengthens the melody. Several factors contribute to the alto saxophone’s primary melodic role: registral isolation (the alto saxophone pitches are almost always higher than those in the other instruments); timbral isolation (the bright woodwind tone contrasts with the darker timbres of the string, brass, and percussion instruments); rapid sixteenth, quintuplet-sixteenth, and sextuplet-sixteenth runs not found in the other notated parts; rhythmic onsets distinct from those in the other notated parts; and pitch content distinct from that in the chord symbols (see [2.5]). Throughout “Ceroepic” and “Unoepic,” when two instruments in rhythmic concurrence realize chord symbols (such as the guitar and cello in concurrent duet 1), those instruments form the accompaniment in a melody/accompaniment texture. By contrast, when two instruments in rhythmic concurrence proceed in parallel unisons or octaves and avoid the notes in the chord symbols, those instruments form the melody in a melody/accompaniment texture.

[3.5] We are now in a position to generalize about the rhythmic features of the passage. Throughout, four distinct rhythmic parts are performed by five instruments: two instruments in rhythmic concurrence and three rhythmically distinct parts. I shall represent this texture numerically as an ordered pair of integers in the form of (p, i), where p indicates the number of rhythmically distinct instrumental parts and i indicates the number of active instruments; so in this case, the texture would be indicated as (4, 5). Notice that i indicates only the number of sounding instruments; it does not indicate which instruments are playing. Thus, two textures labeled (4, 5) may not be “the same texture” in terms of instrumentation. This is evident in Example 4, which in terms of instrumentation contains three distinct (4, 5) textures: first guitar/cello, alto saxophone, tuba, drums; then alto saxophone/cello, guitar, tuba, drums; and finally alto saxophone/guitar, cello, tuba, drums. I shall bear this point in mind in the analyses in Sections 4 and 5. First, though, I shall briefly digress to situate this model in the context of previous literature.

[3.6] The (p, i) ordered pairs adapt work on texture by Berry (1976) and De Souza (2020). Berry writes, “Two lines moving in parallel 3rds may in an important sense be said to constitute a single real textural factor consisting of two [sounding] components” (1976, 186, italics original).⁽¹⁷⁾ He refers to the number of sounding components as the density number (185). If the two lines move independently “in rhythm, in direction of motion, in the distance of motion, or in any other sense,” Berry views this as two real textural factors consisting of two sounding components (186). Berry uses the model as the basis for revealing analyses of passages by Milhaud, Purcell, Corelli, and others (186–89, 206–9, 213–16). De Souza (2020) updates Berry’s work in two ways. First, he replaces “components” with textural streams. “Stream” is shorthand for auditory stream, defined by Albert Bregman (1990, 9) as the “perceptual grouping of the parts of the neural spectrogram that go together.” By adopting Bregman’s work on auditory streaming, De Souza gains access to a conception of texture that foregrounds the role of human perception, which he characterizes as “emergent” (2020, 162). De Souza’s second update makes Berry’s integer formulations compatible with transformational theory (Lewin 1987; 1993) by “model[ing] textures as ordered pairs of the form (s, d), where s is the number of streams and d is Berry’s ‘density number’” (De Souza 2020, 168). From this, De Souza recasts Berry’s Milhaud analysis in the form of a transformation network.

[3.7] My (p, i) ordered pairs resemble De Souza’s (s, d) formulation. However, the analytic agenda I shall pursue with “Ceroepic” and “Unoepic” does not require the vast conceptual apparatus of auditory streaming theory because my focus is narrower, concentrating on the number of instrumental parts in rhythmic synchrony, the total number of sounding instruments, and tonal fusion (Huron 2001). With this information in place, we can consider the roles of pitch, voice motion, instrumental choice, timbre, and attack/decay characteristics in the concurrent duets (as will be elaborated in [3.10]). This is the motivation behind the (p, i) ordered pairs.

[3.8] Having formalized some rhythmic and textural aspects of the concurrent duets, I now consider harmonic dyads. The cello/alto saxophone and guitar/alto saxophone concurrent duets proceed in parallel unisons; no other interval can bind the two instruments’ pitches more strongly. By contrast, each instrument in the guitar/cello pairing is distinct with respect to pitch. However, the near-exclusive use of similar motion unites them to some degree, as do the occurrences of relatively consonant perfect 4ths (m. 1, C♯/F♯) and perfect 5ths (m. 3, B♭/F, E/B). To better understand this variety in the concurrent duets, David Huron’s work on tonal fusion permits us to locate harmonic dyads and their voice motions on a spectrum (2001; 2016). One end of the spectrum indicates maximal unity (fusion) between the pitches of each harmonic dyad, as well as the voice leading from dyad to dyad. The other end indicates maximal separation between them. Huron defines tonal fusion as:

the tendency for some concurrent sound combinations to cohere into a single image. Tonal fusion arises most commonly when the auditory system interprets certain frequency combinations as comprising partials of a single complex tone . . . [It] occurs most commonly when the frequencies of the component tones are related by simple integer ratios. The pitch interval that most encourages tonal fusion is the aptly named unison. The second most fused interval is the octave, whereas the third most fused interval is the perfect fifth. (Huron 2001, 18–19)

[3.9] Example 5 graphically represents a spectrum of tonal fusion. Huron groups the four traditional types of two-voice motion into two categories, semblant (parallel and similar) and nonsemblant (oblique and contrary) (2001, 36–38, 52–53; 2016, 93–94). The intervals that are most tonally fused—parallel perfect unisons, octaves, 5ths, and 4ths—appear on the left side, followed by parallel imperfect consonances (3rds and 6ths), and then parallel dissonances (2nds, 7ths, tritones). The least tonally fused intervals (regardless of size and/or quality) are those approached by similar motion, then oblique motion, and finally contrary motion.⁽¹⁸⁾ As the analyses will show, while concurrent passages appear throughout “Ceroepic” and “Unoepic,” Threadgill reserves the most tonally fused intervals (unisons and octaves) and voice motions (parallel) for strategic formal locations; ending the “Ceroepic” movement with the parallel octaves concurrent duet in Example 1 is one such example.⁽¹⁹⁾ To render the concept of tonal fusion vivid, Example 6 provides a sample musical realization of the spectrum, composed by the present writer.

[3.10] Huron also discusses the influence of timbre on tonal fusion (2001, 48–50). Not surprisingly, he states that homogenous timbral combinations strengthen tonal fusion, while heterogenous ones weaken it (49). Although several studies address the influence of homogenous versus heterogenous timbres on the perception of harmonic dyads, none involve the instrument pairings found in the concurrent duets of “Ceroepic” and “Unoepic” (Bregman 1990, 478–90; Kendall and Carterette 1991; Kendall and Carterette 1993; Sandell 1995; Lembke and McAdams 2015; Lembke et al. 2017). Nonetheless, the analyses in Sections 4 and 5 consider the role of timbre in the concurrent duets. As in Examples 1 and 4, each concurrent duet in “Ceroepic” and “Unoepic” pairs two different instruments. Thus, the analyses consider 1) the relative volume of each instrument, 2) the family to which each instrument belongs, 3) the attack and decay characteristics of each instrument (“temporal envelope”), and 4) the timbral brightness of each instrument (“spectral content”).⁽²⁰⁾

[3.11] The final component of the analytic methodology involves texture tables. Texture tables (illustrated in Example 7) graphically represent formal sections, rhythmically independent instrumental parts, instrumental parts in rhythmic concurrence, and melodic versus accompanimental roles.⁽²¹⁾ The table references the “Unoepic” passage in Example 4. Rehearsal letters and timestamps appear above the table, while (p, i) ordered pairs, dynamic markings (if provided), and tempo markings appear below it. The two leftmost columns indicate the performers’ last names and the instrument each is playing.⁽²²⁾ Pink highlighting indicates the featured performer and instrument of the movement (to be discussed in [4.1]). Each remaining column represents a distinct configuration of rhythmic parts (i.e., “a texture”). Green diagonal stripes indicate instruments in rhythmic synchrony that together perform a melodic role in a melody/accompaniment texture. Blue diagonal stripes indicate instruments in rhythmic synchrony that form (part of) the accompaniment in a melody/accompaniment texture. Dots indicate instrumental parts whose rhythms are distinct from those of the other parts. These instrumental parts are also distinct from one another with respect to pitch. Green dots indicate a melodic role, while blue dots indicate an accompanimental role. As such, pitch and rhythmic polyphony is present when a table column contains more than one distinct graphic pattern. The notation “Imp.” indicates an improvising soloist. As no improvisations occur in rehearsal D of “Unoepic,” I shall explain this notation as it arises in the analyses that follow.

4. “Unoepic”

[4.1] Threadgill writes that “each quintet [in Penny] focuses on a different instrument” (Zooid 2015). While he does not explain how this focus takes shape musically, careful listening reveals that the quintets do not resemble concerti, nor do they consistently treat their featured instruments as soloists.⁽²³⁾ In “Unoepic,” the guitar gains prominence through the locations of its solo passages, improvisations, and participation in concurrent duets using parallel unisons (one appeared in Example 4). I shall return to these points in [4.7].

[4.2] In “Unoepic,” Liberty Ellman plays guitar, Christopher Hoffman plays cello, and Elliot Humberto Kavee plays drums/percussion. Jose Davila plays tuba or trombone, while Threadgill alternates between alto saxophone, flute, and bass flute. At any given moment, between one and five instruments are playing. The duration of the movement on the commercially available recording performed by Zooid is 17:52 (Zooid 2015).

[4.3] Example 8 provides a texture table for “Unoepic.” I begin by explaining the features of the table not covered in [3.11]. An empty column, such as that at 2:29, indicates a prominent pause. Four such pauses occur at the end of a section, creating formal boundaries at 2:46, 6:27, 8:29, and 14:59. Two types of improvisations are present in the table. When “Imp.” appears in a column that contains blue dots, such as that at 2:48, the performer is improvising on the chord symbols for that section. An uppercase letter “I” before a rehearsal letter indicates an improvisation on the chord symbols in that section (IA, ID, IG). Threadgill does not use “I” to indicate improvisations; this usage is my own. By contrast, when “Imp.” appears in a column that does not contain blue dots, such as that at 13:27, this indicates an absence of chord symbols and staff notation. Instead, Threadgill provides written directions on the score. For example, the following instructions appear at D1: “non tempo (short section), cello & drums improvisation, add intervals gradually, 3 steps, 22-34-677; add kit, one by one parts” (see Ex. 4, final measure). Numbers after rehearsal letters (D1, F1) appear in the score. Finally, at 4:40, there is a period of overlap between the end of the guitar improvisation and the start of the cello one. When the musicians improvise on a section that contains notated rhythmically concurrent passages, such as the improvisation IG on section G, they omit the concurrent rhythms.

[4.4] Upon inspecting the rehearsal letters above the table, one immediately notices that they do not appear in alphabetical order. Nevertheless, this is the order in which they appear on the score. It is also the order in which Zooid performs the movement both on their commercially available recording (Zooid 2015) and in a 2014 live performance (Roulette 2014).⁽²⁴⁾

[4.5] Let us further inspect the texture table for “Unoepic” (Ex. 8). I shall begin by making a few observations of a general nature. First, the opening five rehearsal letters (B, C, IA, A, E) contain no concurrent duets. The sole presence of dotted boxes (tantamount to the absence of striped boxes) conveys this information. A quick inspection of the table confirms that every number of instruments for a quintet are present in B through E: (1, 1) in B, C, and E; (2, 2) in B and C; (3, 3) in B; (4, 4) in IA and A; (5, 5) in A. The ordered pairs below the table also convey this information.

[4.6] Second, the first two concurrent duets are accompanimental (F, and cello/guitar in D), while the remaining three are melodic (cello/alto saxophone and alto saxophone/guitar in D, then guitar/trombone in G). In [3.2], I mentioned that the adjacent concurrent duets in D share one instrument. The table shows that every consecutive pair of concurrent duets in F through G follows this logic, whether the pairs are temporally adjacent (those in D) or not (F to D, D to G).

[4.7] Finally, the texture table indicates some of the ways in which Threadgill features Ellman and the guitar in “Unoepic.” In B, the movement opens with a guitar solo passage punctuated by interjections from the cello and tuba. In IA, Ellman has the first improvisation on chord symbols of the movement; the decrescendo and pause before IA set off this moment. The next pause, just before E, draws attention to Ellman’s first solo passage since the opening B section. Both solos have the tempo marking of = 66 and are generally quiet. By recalling the B solo, the E solo suggests a return to opening material, reinforced by the formal placements and dynamic levels of the drum solos; quiet drum solos in C follow the first guitar solo in B, and a second quiet drum solo in F1 follows the second guitar solo in E. To my ear, the material that separates E and F1 does not sever the connection between the second drum solo and the second guitar solo: it lasts less than one minute and the piano dynamic level holds throughout. Two final ways in which the guitar gains prominence in “Unoepic” include Ellman’s improvisation in ID, whose gradual decrescendo ending prepares the piano dynamic of D1, and Ellman’s participation in the final section of the movement, G. That section contains one of the movement’s three concurrent duets in parallel unisons; Ellman participates in two of the three.

[4.8] By considering the formal locations of the concurrent duets, the number of instruments active in each texture, the number of instruments that enter or exit at each texture change, and the voice motion and degree of tonal fusion present in each concurrent duet, a movement-wide perspective on texture in “Unoepic” emerges. As a reference for the analysis that follows, Example 9 graphically represents the number of instruments in distinct textures. The x-axis indicates distinct textures. The y-axis indicates the number of instruments in each. The number of rhythmically distinct parts is not shown. All but one of the adjacent texture pairs in B and C add or subtract only one instrument. That is, the i of their (p, i) values differs by ± 1. The exception occurs at the end of B, involving (1, 1) → (3, 3).⁽²⁵⁾ The texture analysis of “Unoepic” involves a six-stage narrative:

• Stage 1: The opening sections B and C contain no concurrent duets. They feature small changes in the number of instruments (± 1 or 2).
• Stage 2: The remaining textures preceding the first concurrent duet—C, IA, A, E—introduce larger changes in the number of instruments (± 3 or 4). For example, the IA texture (4, 4) adds three instruments to the preceding C texture (1, 1). Similarly, the A texture at 6:15, in which all five instruments play, leads to a guitar solo in E, a reduction of four instruments.
• Stage 3: Another large change in the number of instruments, from the (1, 1) E solo to the (4, 5) concurrent duet in F, draws attention to the first concurrent duet.
• Stage 4: The first two F1 textures—(3, 3) and (4, 4)—restore a small change in the number of instruments—one. The remainder of the movement combines small and large changes.
• Stage 5: The concurrent duets in D introduce changes of instrumentation during the duets (not changes in the number of instruments; see [3.2]).
• Stage 6: The remaining polyphonic textures in ID, D1, and IG prepare the parallel unisons concurrent duet in G that closes the movement.

[4.9] Paragraphs [3.1]–[3.4] examined the pitch content and voice motion of the three concurrent duets in D. Let us now study the remaining concurrent duets in “Unoepic.” Example 10 reproduces the first concurrent duet of the movement, in F.

[4.10] In F, Ellman performs a melody, accompanied by tuba, cello, and bass flute. Three features of Ellman’s part distinguish it from the other instruments: relatively active rhythms, its registral position above the other pitched instruments in beats 3 and 4 of mm. 1 and 3, and the fact that the guitar melody does not duplicate any sounding pitches in the accompanimental instruments. Despite the guitar part’s louder dynamic indication on the score relative to the other instruments (mezzo piano versus piano), the cello and bass flute sound louder than the guitar on this recording, probably because of their longer decay times.⁽²⁶⁾ While chord symbols do not appear on the score in F, the “low-middle-high” registral placements of the tuba, cello, and bass flute resemble passages that do include chord symbols.

[4.11] Threadgill (on bass flute) and Hoffman (cello) perform the concurrent duet. Their first three harmonic dyads are perfect 5ths in parallel motion. The remaining harmonic dyads, moving in similar or parallel motion, form a major 7th, major 2nd, diminished 7th/major 6th, and major 6th, respectively. Thus, the entire passage uses semblant voice leading.⁽²⁷⁾ While this suggests a relatively high degree of tonal fusion between the bass flute and cello, rhythmic factors separate the instruments. In keeping with the tempo rubato ensemble performance (not marked on the score), the cello and bass flute’s rhythmic onsets sometimes occur separately. Examples include the opening dyad of the passage (bass flute enters before cello), the first dyad of m. 2 (cello enters before bass flute), the first dyad of m. 3 (bass flute enters before cello), and the first dyad of m. 4 (cello enters before bass flute). Overall, Threadgill and Hoffman strike a balance between independence and interdependence in the recorded performance.

[4.12] Example 11 reproduces the concurrent duet in G, which ends the movement. Ellman and Davila (on trombone) perform the concurrent duet in parallel unisons. As we have come to expect, their pitches are distinct from those in the chord symbols. Throughout the concurrent duet, the cello part (pizz.) contains the low note of each chord symbol while the bass flute part contains the middle and high ones (with one exception in the first measure: C4, indicated on the example). While the parallel unisons create a high degree of unity between the guitar and trombone, several factors counteract that unity. The guitar timbre is brighter than that of the trombone, and its attack and decay are faster. Additionally, the rhythmic activity and pitch register of Threadgill’s bass flute part interact closely with the rhythms and pitches of the concurrent duet. Threadgill’s rhythms often fill gaps left by the rests in the concurrent duet, creating fleeting hocket textures.⁽²⁸⁾ Arrows above the bass flute staff indicate simultaneous notated attacks between the bass flute and guitar/trombone parts. Further, Threadgill’s pitches-in-register are close to those of the concurrent duet; the bass flute part “trespasses” on the registral bandwidth of the guitar/trombone duet. Ultimately, while this final concurrent duet of “Unoepic” clearly forms the (doubled) melody in a melody/accompaniment texture, the bass flute exerts a significant presence at the same time; it is not accompanimental in the way that the drums and cello are.

[4.13] To summarize the analysis of “Unoepic,” Example 12 situates the F, D, and G concurrent duets in the context of the entire movement. Across the span of the movement, the concurrent duets increase in textural prominence and degree of tonal fusion. The number of instruments that change between adjacent textures increases in the lead-up to the first concurrent duet in F, then decreases thereafter (see Ex. 9). The rightmost column indicates the interaction of the guitar, the featured instrument of “Unoepic,” with these textural features. The second column from the left correlates these interactions with the six stages of the textural narrative presented in [4.8].

5. “Ceroepic”

[5.1] “Ceroepic” is the second movement of Penny. The featured soloist is Kavee on drums and percussion. The instrumentation duplicates that of “Unoepic”: drums and percussion, guitar (Ellman), cello (Hoffman), trombone or tuba (Davila), and alto saxophone or flute or bass flute (Threadgill). The duration of the movement on Zooid 2015 is 19:37.

[5.2] Threadgill features Kavee in “Ceroepic” through several means. Kavee participates in the movement’s sole improvisation for multiple instruments (B, 4:47). In addition, all unaccompanied passages in the movement are for him (C2 and E). In C1, Kavee “previews” the rhythms that the pitched instruments will perform in C2. He improvises throughout C2 and D while the remaining instruments perform notated material. Finally, compared to the other movements of Penny, the score for “Ceroepic” contains more extensive instructions for the use of sticks or mallets, and drum set or percussion. E contains a notated passage for pitched bells; only one other such passage occurs in Penny (“Tresepic,” F).

[5.3] Example 13 presents a texture table for “Ceroepic.” As in the “Unoepic” texture table (Ex. 8), rehearsal letters other than IA, IC, and IF duplicate those found in the score, and the recording timestamp of each section appears above the table. Like “Unoepic,” “Ceroepic” features lengthy improvised sections on chord symbols: an improvisation on A immediately before A, an improvisation on C immediately following C, and an improvisation on F immediately before F. However, in contrast to “Unoepic,” the recorded performance of “Ceroepic” proceeds in alphabetical order through its rehearsal letters, matching the layout and page numbers of the score. As in “Ceroepic,” when the musicians improvise on a section that contains rhythmically concurrent passages (for “Unoepic”: IA and A; IC and C; IF and F), they omit the concurrent rhythms.

[5.4] I shall begin by making a few observations of a general nature regarding the unique texture of C2. C2 features a (2, 5) texture that appears nowhere else in the movement (or, indeed, in any of the six movements). The only other concurrent textures in “Ceroepic” are (4, 5) duets. In C2, the alto saxophone, guitar, cello, and tuba unite in a striking concurrent quartet. However, because each instrument has its own melodic material and a variety of melodic voice motions, the degree of tonal fusion is low. During the concurrent quartet, improvised drum hits occur during the rests of the pitched instruments, together creating a lively call-and-response passage. The (2, 5) concurrent texture in C2 contrasts so starkly with the textures before and after it that it emerges as the focal point of the movement’s textural design. Threadgill prepares this moment by introducing the instruments in C2 in the concurrent duets that precede it. The alto saxophone and guitar appear in the concurrent duet in A, the tuba appears in the concurrent duet in B, and the cello and guitar appear in the concurrent duet in C; these four instruments then unite in the C2 concurrent quartet. Additional preparation comes from Kavee’s rhythmic “preview” mentioned in [5.2].

[5.5] I now proceed to a more granular level of detail in this examination of “Ceroepic.” The following section will focus on the movement’s concurrent duet and quartet passages, with particular attention given to a) the impact of voice crossings on the independence of each pitched instrument in B and C2; b) fluctuations in the degree of tonal fusion, timbre, and blend; and c) two departure/return scripts. Each script models a linear process that influences the large-scale form of “Ceroepic.”⁽²⁹⁾ Script  1  involves motion in parallel octaves. They occur in the first and last sections of the work, A and F. Script  2  involves rhythmic concurrence without parallel motion. The first such passages occur in B and C. C1 contains no passages in rhythmic concurrence and thus marks the departure stage of Script  2 . Rhythmic concurrence returns in C2 and appears for the final time in D, thus marking the return stage of Script  2 .

[5.6] Example 14 reproduces the first concurrent duet of the movement, in A.⁽³⁰⁾ A marks the start of Script  1 : the guitar and alto saxophone parts move in parallel octaves. The initial concurrent duet thus exhibits the second-highest possible degree of tonal fusion. The attacks, volumes, and timbres of the two instruments blend well, creating a unified composite sound.

[5.7] Example 15 reproduces the second concurrent duet, in B. Set for tuba and bass flute, the concurrent duet in B initiates Script  2 : it contains no parallel motion, a moderate amount of similar motion, many instances of contrary motion, and two instances of oblique motion. Thus, nonsemblant motions outnumber semblant ones, resulting in a weaker sense of unity in the two concurrent instrumental parts. The paucity of intervals with high degrees of tonal fusion—no octaves, two perfect 5ths, two perfect 4ths—also foster the independence of each line in the concurrent duet. The introduction of voice crossings further compromises the unity of the tuba and bass flute lines in B. As indicated by arrows in Example 15, the tuba’s F4 is higher than the bass flute’s C4. Similarly, the tuba’s D4 is higher than the bass flute’s A♭3. These crossings form exceptions to the general registral “tiers” of the duet, in which the tuba’s pitches are lower than the bass flute’s. During the voice crossings, the similar timbres of the tuba and bass flute will likely complicate efforts to distinguish their lines. The primary element of unity between the tuba and bass flute is their shared sustained attacks, despite rubato rhythmic misalignments throughout.

[5.8] Example 16 shows the C concurrent duet.⁽³¹⁾ By contrast, the concurrent duet in C (Hoffman/Ellman) contains no voice crossings because the cello and guitar are realizing the middle (cello) and high (guitar) notes of a series of chord symbols. Davila’s tuba part provides the low note in each chord symbol. For example, in the initial $\frac{DG}{C♯}$, Davila sounds C♯2, Hoffman sounds D3, and Ellman sounds G3. The alto saxophone’s high registral position and distinct pitch-class content contributes to its status as the melody in a melody/accompaniment texture (see [3.4]). Regarding the voice leading of the harmonic dyads in the concurrent duet, similar motion occurs most frequently, followed in descending order by oblique, parallel, and contrary motions. Given the general registral zones dictated by the chord symbols, it comes as no surprise that similar motion in the cello/guitar duet predominates: because the cello’s pitches occupy a middle registral tier, and the guitar occupies a high tier, residing within the assigned tier while realizing intervals of differing sizes and qualities naturally creates similar voice motions. The similar motion combines with frequent melodic leaps within parts, and dissonant harmonic dyads between the cello and guitar parts, to isolate each instrument in the concurrent duet.

[5.9] The (2, 5) concurrent quartet of C2 then follows. As stated in [5.2], in C1 Kavee’s drum part quietly “previews” the loud concurrent quartet rhythm of C2. Example 17 thus provides a score and audio for C1 and C2. The rhythmic design involves an additive process. In C2, the passage begins with four three-note figures, with the third note accented, and rests after each figure (accents do not appear in C1, although crescendo marks usually climax on the final note of each figure). Next comes four five-note figures, with the fifth note accented and rests after each figure. The section ends with three (not four) seven-note figures, with the seventh note accented and rests after each figure. While the duration of each attack in each figure remains the same throughout (one sixteenth-note), the lengths of the rests within and between sections fluctuate, which counterbalances the strictness of the additive process. Similarly, changes in dynamic levels do not entirely align with changes in the lengths of the figures. For example, the dynamic level drops to mezzo piano halfway through the five-note figures, not at the beginning of them. In like fashion, the dynamic level rises from mezzo forte to forte during the seven-note figures, not at the outset of them.

[5.10] In C2, as the figures grow in length from three to five to seven, voice crossings undermine the independence of each instrumental line. In the section containing three-note figures, instrumental and registral voice leading are in alignment: in an imaginary SATB texture, the tuba always has the “bass” pitch, the cello always has the “tenor” pitch, the guitar always has the “alto” pitch, and the alto saxophone always has the “soprano” pitch. This yields a texture in which all four pitched instruments are on an equal footing. Alternately, the bright timbre and high register of the alto saxophone may suggest a melody/accompaniment texture (melody = alto saxophone, accompaniment = guitar/cello/tuba). Finally, because the alto saxophone and tuba perform the outer voices, a parsing of the texture into wind/brass versus stringed instruments might also emerge. Other than one instance of parallel minor 7ths (m. 34, tuba and alto saxophone, F♯/E and D/C), all voice motions in this opening section are similar, oblique, or contrary.

[5.11] In the section containing five-note figures, rampant voice crossings take hold that blur the SATB texture. The tuba and cello swap registral positions: the cello becomes the “bass” voice and the tuba becomes the “tenor” voice. The alto saxophone and guitar also swap registral positions, although more gradually and less consistently than the tuba and cello. The voice crossings will likely impact one’s perception of each “chorale voice.” However, if one deems the tuba timbre to be sufficiently similar to the cello timbre, one can follow the tenor line as it passes from the cello to the tuba (and likewise follow the bass line as it passes from the tuba to the cello). This is perhaps less likely with the five-note figures in the alto saxophone and guitar because the soprano line rapidly (and somewhat unpredictably) alternates between those two instruments, and likewise for the alto line.⁽³²⁾

[5.12] In the culminating seven-note figure section, voice crossings manifest in less predictable ways that continue to impact the SATB texture. Here, only the alto saxophone part contains “soprano” pitches, thus restoring the opening section’s strict alignment of this instrument with this register. For this reason, a melody/accompaniment texture may result, as discussed in [5.10]. The guitar part changes clefs from soprano to bass, effecting an overall descent in its pitches, which now impinge on the tenor and bass registers. The upshot is that, for the entire seven-note figure section, the guitar occupies the tenor and bass registers, the tuba occupies the alto and tenor registers, and the cello scampers among the alto, tenor, and bass registers.

[5.13] At first blush, the rupture of instrumental and registral voice leadings just described poses challenges to identifying parallel voice leading in the concurrent quartet. Given the role of Script  1  (parallel octaves) in the large-scale design of “Ceroepic,” it will be necessary to tease apart registral and instrumental voice leading. To this end, Example 18 renotates the quartet, with each staff (SATB) showing registral (not instrumental) voice leading. On the example, colored circles indicate parallel motions between two (or occasionally three) voices. The example conveys that 1) the sheer amount of parallel voice leading is low; 2) the amount of parallel motion involving intervals with a high degree of tonal fusion is even lower; and 3) other than an instance of parallel semitones in the soprano/alto voices (m. 3), which creates a screechy, fingernails-on-the-chalkboard series of dissonances, parallel motion plays a minor (even incidental) role in the concurrent quartet. For this reason, I do not consider Script  1  to be active in C2.

[5.14] As we saw in Example 1, the flute/trombone concurrent duet that closes “Ceroepic” in F moves in parallel octaves. This marks the return portion of Script  1 . Thus, it remains only to examine the penultimate concurrent duet of the movement in D. This appears in Example 19.⁽³³⁾ In the large-scale textural design of “Ceroepic,” the role of D is to keep the spotlight on the featured instrument of the movement. Kavee begins an improvisation during the concurrent quartet in C2, continues improvising in the unaccompanied portion of C2, and concludes his final improvisation of the movement in D. While D marks the return portion of Script  2 , it is perhaps a concurrent duet in notation only—the difference between score and sound is vast. This owes primarily to the marking “freely, slow tempo” and the absence of a meter signature and barlines. Let us begin by examining the notation. The concurrent duet is for Hoffman (cello) and Ellman (guitar). They perform the middle and high notes respectively of the chord symbols; Davila (on tuba) performs the low notes. In the concurrent duet, the harmonic dyads exhibit a low degree of tonal fusion: there are only two perfect intervals (B2/E3 and A♭/E♭), and nonsemblant voice motions outnumber semblant ones (contrary and oblique motions are both present). The alto saxophone acts as the melodic instrument in a melody/accompaniment texture: its pitch classes are distinct from, and higher in register than, those in the chord symbols (an annotation on the example indicates an instance of voice crossing).

[5.15] Let us now turn to the sound of the concurrent duet in the recording. Several factors combine with the harmonic dyads’ low degree of tonal fusion to separate the guitar and cello parts. Despite the notated rhythmic concurrence, Ellman and Hoffman’s onsets do not coincide. This may have to do with the “anticipate” performance marking, although it is not clear what should be anticipated (perhaps the next melody note in the alto saxophone?).⁽³⁴⁾ In addition, whereas Hoffman performs each notated pitch once, Ellman repeats each notated pitch multiple times. This is in the spirit of the “freely” and “sustain” markings—repeated attacks on the same pitch substitute for single sustained ones, which on a steel-string acoustic guitar are not possible at this tempo and dynamic (mp). The guitar part also gains independence by Ellman performing most of its pitches one octave higher on the repeat. For these reasons, the cello merges more with the tuba than the guitar.

[5.16] To summarize, Example 20 integrates the general (texture table) and granular (voice leading) observations. “Ceroepic” superimposes two departure/return scripts. The A and F duets act as starting and ending points for Script  1 , involving parallel octaves. Only parallel unisons are more tonally fused. Script  2  involves rhythmic concurrence without parallel motion. Script  2  primarily involves the concurrent duets, which frame the arresting concurrent quartet in C2. As detailed in the bottom row of the table, the three stages of Script  2  align with prominent moments for the drums and percussion, the featured instrument of the movement. Focusing one’s aural attention on the interaction of the two scripts can make for a rich listening experience; when the degree of tonal fusion is highest, the number of instruments in rhythmic concurrence is lowest, and vice versa.

Conclusion

[6.1] Given Threadgill’s description of his music for Zooid as contrapuntal, it follows that passages exhibiting other textures will be marked for consciousness.⁽³⁵⁾ For Nate Chinen, one such passage—the closing of “Ceroepic”—felt “spiky” and “created a small jolt” (2015). For Ben Ratliff, a similar passage in another piece “made the whole band cohere” and led the music to “signify as mystery” (2010). I have demonstrated that unison passages such as these, while brief, have movement-wide textural and formal consequences in two movements from In for a Penny, In for a Pound. Careful and sustained attention to texture, rhythmic synchrony, and tonal fusion can deepen our experience of Threadgill’s music and enrich our perception of its ebbs, flows, and formal designs.

[6.2] An important topic for future research involves alternate readings of texture in “Unoepic” and “Ceroepic.” As with musical meter, the listener creates texture. As such, it invites multiple interpretations (De Souza 2020, 160–62; Wang 2023). Accordingly, scholarship that weighs alternate readings of “Unoepic” and “Ceroepic” against those presented here holds promise. The discussions of melody-and-accompaniment textures versus polyphonic textures in [2.5], [5.10], and [5.12] provide a point of departure for such work.

Guy Capuzzo
University of North Carolina Greensboro
P. O. Box 26170
Greensboro, NC 27402-6170
guycapuzzo@uncg.edu

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Discography

Kronos Quartet. 2020. “Henry Threadgill—Sixfivetwo.” https://soundcloud.com/kronosquartet/henry-threadgill-sixfivetwo.

Zooid. 2012. Tomorrow Sunny / The Revelry, Spp. Pi Recordings PI43.

—————. 2015. In for a Penny, In for a Pound. Pi Recordings. B00V8JUAZ2.

Footnotes

* Portions of this paper were read at the 2024 meeting of Music Theory Southeast (March 16, Lipscomb University, Nashville, TN). I wish to thank the anonymous reviewers for their assistance in preparing this article for publication. I also thank Henry Threadgill for permission to reproduce the scores and audio for In for a Penny, In for a Pound in the examples. All scores are © 2014 Henry Threadgill, all rights reserved; all audio examples are © Zooid 2015, all rights reserved (see Discography).
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1. The members of Zooid are Threadgill (alto saxophone, flute, bass flute), Jose Davila (tuba, trombone), Liberty Ellman (steel-string acoustic guitar), Christopher Hoffman (cello), and Elliot Humberto Kavee (drums, percussion). Penny contains six movements: “In for a Penny, In for a Pound (opening),” “Ceroepic (for drums and percussion)” (spelled “Ceropic” on the score), “Dosepic (for cello),” “Off the Prompt Box (exordium),” “Tresepic (for trombone and tuba),” and “Unoepic (for guitar).” Notice the use of the Spanish numbers cero, uno, dos, tres followed by the English word “epic.” It is unclear why the ordering of movements is not in numerical order.
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2. My definition for texture follows from Grove Music Online (s.v. “texture”): it applies “either to the vertical aspects of a work or passage, for example the way in which individual parts or voices are put together, or to attributes such as tone colour or rhythm, or to characteristics of performance such as articulation and dynamic level.” Other aspects of texture include “the spacing of chords, the ‘thickness’ of a sonority as determined by the number of parts, [and] the amount of doubling at the unison or octave.” Beginning in [3.11], I also use “texture” to indicate a specific combination of instruments.
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3. Section 3 of this paper explains the notation in the “chords” and “drums” staves. The “Ceroepic” recording contains some flute pitches that are octave transpositions of those in the score in Example 1. In m. 51, the flute’s sounding pitches are C♯6, D6, B♭5, A♭5, B5. (There may also be an unnotated attack between A♭5 and B5). Measures 51–53 sound as notated. In m. 54, the sounding pitches are B5, C♯6, D6 (one octave higher than notated), A♭4, F4, D4, E♭4 (sounds as notated). Measure 55 sounds as notated. Measures 56–57 sound one octave higher than notated. Finally, m. 58 sounds as notated.
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4. In Frontispiece is not to be confused with the Zooid piece titled “Put On Keep, Frontispiece, Spp” (Zooid 2012).
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5. This work includes De Souza 2020, Duane 2017, and two Society for Music Theory conference sessions. “Specters of Polyphony” (2023) included papers by Anna Yu Wang (cited in the present paper), Stephen Spencer, and Christopher Segall. “Reconceiving Texture: Style, Temporality, Expression, and Performance” included papers by Johanna Frymoyer, Robert Hatten, and Jonathan De Souza.
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6. The biographical sketch draws on Threadgill 2023, Baumgartner 2015, Iverson n.d., and Blumenfeld 2023. Information on Threadgill’s activities with the Association for the Advancement of Creative Musicians appears in Lewis 2008, Hannaford 2019, and Steinbeck 2022.
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7. Steinbeck 2022 contains a chapter devoted to Air.
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8. In the liner notes to the Penny recording, Threadgill writes: “I would like to give my endearing thanks and respect to two greatly beloved artists: Sonny Rollins and Ornette Coleman” (Zooid 2015). In his autobiography, Threadgill states, “Debussy and Varèse have remained important models for me” (Threadgill 2023, 52), and he discusses the influence of these composers (especially Varèse) elsewhere in the book.
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9. The drummer/percussionist for Zooid, Elliot Humberto Kavee, offers his perspective on meter in Zooid’s music in Micallef 2010: “My bars will be different from the other musicians’; their downbeats are in different places . . . Say you’ve got a meter of eleven. You can divide it as three, three, three, and two. But that can also imply a seven. If a rhythm is in seven as two, two, two, one, often we will play that as straight pulses. But sometimes we’ll ‘tripletize’ a rhythm, like swinging it. For example, if you play a bar of seven and it’s two, two, two, one and then you repeat it, you might do the triplet version played as three, three, three, two” (59–60).
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10. Threadgill’s chord symbols recall “slash chords” in jazz and popular harmony in that the note under the horizontal line (for Threadgill) or after the slash (for slash chords) acts as the lowest pitch or “bass note.” However, Threadgill’s chord symbols do not contain chordal roots. Threadgill’s chord symbols always contain three notes and indicate every chord tone. Some of Threadgill’s chord progressions involve techniques he refers to as “infolding” and “unfolding,” which he credits to Varèse (Threadgill 2023, 371; see also Hill 2017, 78–80; Taylor 2015, 37–42; and Forker 2019, 46–55). Bernard (1987, 74–75) offers a lucid introduction to unfolding and infolding in the music of Varèse.
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11. In this paper, “solos” refer to unaccompanied passages performed by “soloists,” not improvisations, which are performed by “improvisors.”
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12. Other AACM musicians who have employed modular form include Anthony Braxton (Steinbeck 2017, 254), Douglas Ewart (Steinbeck 2022, 153), and Roscoe Mitchell (Steinbeck 2017, 194–99).
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13. Above the rehearsal D marking, the Roman numeral I is not part of the interval set and is to be ignored. The interval sets in Examples 4, 10, and 11 have similar markings, such as Roman numerals and/or numbers in parentheses (e.g. (015) in Ex. 10). I emailed Threadgill to inquire about the meaning of these markings. His assistant, Declan Sheehy-Moss, forwarded me Threadgill’s response: “Those were just some temporary reference numbers. They don’t mean anything” (Declan Sheehy-Moss, email message to author, July 30, 2023).
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14. In many interviews, Threadgill discusses the role of interval sets in Zooid’s music. The interview in Iverson (n.d.) is representative. See also Threadgill 2023, 370–72, 374–75, and 381–82.
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15. The use of the term “duet” in this paper differs from conventional usage, in which the two parts typically contrast in some way/s. In the present paper, “concurrent duet” indicates two instruments playing in rhythmic synchrony.
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16. The term “blend” in this article follows the definition in McAdams, Goodchild, and Soden 2022, [4.1]: “cases in which two or more concurrently sounding instruments are fused perceptually.”
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17. I have added the word “sounding” to this quotation; Berry uses it in subsequent discussions. De Souza (2020, 167–70) also summarizes these excerpts from Berry.
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18. Huron’s work on tonal fusion involves musical contexts that typically employ functional tonal harmony, a system that Threadgill does not use in his music for Zooid (Threadgill 2023, 69). However, I contend that two lines moving in parallel unisons or octaves will exhibit a high degree of tonal fusion in many musical contexts since tonal fusion is not defined in terms of musical style, but rather in terms of acoustics—in particular, low-number interval ratios (“simple integer ratios” in the Huron quote in [3.8]). Studies that support this view include DeWitt and Crowder (1987, 73); Bregman (1990, 495–96); Sandell (1995, 214); and McAdams, Goodchild, and Soden (2022, [3.7], [4.1]). Huron also draws a distinction between tonal fusion and tonal consonance: “Following Stumpf, many music researchers have assumed that tonal fusion and tonal consonance are the same phenomenon and that both arise from simple interval frequency ratios. However, the extant psychoacoustic research does not support Stumpf’s view. Bregman (1990) has noted that the confusion arises from conflating ‘smooth sounding’ with ‘sounding as one’. [The extant psychoacoustic research] implicates critical band distances in the perception of tonal consonance or sensory dissonance. This work shows that sensory dissonance is only indirectly related to harmonicity or tonal fusion” (Huron 2001, 19).
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19. An anonymous reviewer noted that Threadgill’s formal placements of lines in parallel and similar motion recalls related textures in big band styles. Threadgill performed with the AACM big band in the late 1960s (Threadgill 2023, 164, 166, 168, 172, 244).
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20. The sources cited in notes 16, 18, and 32 ground my discussions of volume, instrument family, spectral content, and temporal envelope. These sources represent a fraction of the literature on these topics. Three accessible entry points are McAdams, Goodchild, and Soden 2022, Dolan and Rehding 2018, and The Timbre and Orchestration Resource: https://timbreandorchestration.org/about/tor.
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21. While original to this paper, the texture tables resemble Dolan’s “orchestral graphs” (2013).
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22. The texture tables employ the following abbreviations: Bfl = bass flute, Fl = flute, AS = alto saxophone, Gtr = guitar, Vc = cello, Tu = tuba, Tro = trombone, D/P = drums/percussion.
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23. I thank an anonymous reviewer for this observation.
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24. In the 2014 live performance, the ensemble omits rehearsal D, moving directly from F1 to D1. This perhaps reflects Threadgill’s statement in the liner notes to Zooid 2015: “I wanted to write something [the six movements of Penny] that Zooid could revisit and find a new perspective and arrangement with each performance.” For the 2014 live performance, on the left side of the screen (https://roulette.org/event/henry-threadgill/), the audio labeled “Ceroepic” should read “Unoepic” and the audio labeled “Unoepic” should read “Tresepic.”
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25. De Souza (2020, 169) defines operations that map one ordered pair onto another. Because the present paper does not adopt a transformational approach, I do not employ such operations.
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26. I credit an anonymous reviewer with this observation.
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27. I thank an anonymous reviewer for pointing out that the “no vib.” marking for the bass flute and cello may be meant to aid tonal fusion and/or prevent these instruments from overpowering the guitar melody. The tuba part also contains the “no vib.” marking.
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28. The cello also participates in the hocket-like texture: its rhythmic onsets generally do not coincide with the onsets in the bass flute or the concurrent duet.
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29. The scripts in the present paper recall Richard Cohn’s “departure → return scripts” involving chromatic triadic harmony (2012, 121–31).
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30. In m. 2 of the concurrent duet, the score shows E3 as the final attack for the alto saxophone and E4, F4 for the guitar. In the recording, it is possible that the alto saxophone performs E♭3, E♮3, F3 and the guitar performs E♭4, E♮4, F4.
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31. Measure 24 contains a minor rhythmic difference that affects the synchrony: the guitar begins with a dotted eighth note, while the cello begins with an eighth note.
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32. Studies of the relationship of voice crossing and timbre include Bregman 1990, 497–98; Huron 2001, 36; and McAdams, Goodchild, and Soden 2022, [5.4]. These studies find that distinctive timbres maintain the independence of a voice more effectively than similar or identical timbres. This view is consistent with that of [3.10] in the present paper.
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33. In rehearsal D of “Ceroepic” (Example 19), the alto saxophone’s E♭3, F♯3 is performed as E♭3, F3, F♯3 and B3, D4 is performed as B♭3, D4, both on the first repeat. On the second repeat, Threadgill ornaments and improvises throughout.
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34. One way to understand the lack of onset synchrony in this guitar and cello “concurrent duet” is by considering the rhythmically concurrent passages before and after it. In this performance, Zooid creates a gradated spectrum of rhythmic concurrence across the span of “Ceroepic.” “Strict” or “tight” concurrence occupies one end of the spectrum, while “free” or “loose” concurrence involving misalignments occupies the other end. The duets in A and C are performed in strict rhythmic concurrence. The B concurrent duet separating A and C provides contrast through extensive misalignments. The (2, 5) concurrent quartet in C2 is performed in strict time, as is the concurrent duet in F that closes the movement. In chronological order, this yields the following interpretation: strict A, loose B, strict C and C2, loose D, strict F.
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35. Sixfivetwo, a string quartet commissioned by the Kronos Quartet, is an example of a Threadgill work not composed for Zooid that eschews unison textures. See Kronos (2020) in the Discography.
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