My goal as a theorist is to understand tonality broadly enough so that I can fluently compose music that is pleasing, comprehensible, and fresh. I have recently argued that any notes can act like a scale, with analogous motion occurring along multiple nested collections; I describe this as a “hierarchical set theory” where transposition and inversion are available at multiple musical levels. In Tonality: an owner’s manual, I explored this picture as a theorist. In Swells, I explore it compositionally.

The piece was written as a demonstration exercise for a Princeton graduate seminar called “Composing Fast.” My pedagogical goal was to help students develop techniques for quickly producing interesting music. This, for me, is the great value of theory: enabling composers to come up with good ideas quickly, rather than telling listeners what to do.

Every even-cardinality collection has two distinguished subsets, each containing every other note of that collection: for the chromatic scale, these are the two whole-tone scales; for the octatonic scale, the two diminished sevenths. These subcollections are interesting because they are preserved when melodies move by an even number of scale steps, and exchanged when melodies move by an odd number of scale steps. This makes it easy to compose or improvise complex contrapuntal passages moving between even and odd subsets. Musicians from Wagner and Stravinsky to Barry Harris have used this technique.

A good portion of Swells uses “semichromatic” hexachords, or six-note scales containing exactly one 012 trichord. These combine an “even” triad with an “odd” 02x trichord, with 5 ≤ x ≤ 9. Swells opens with harmonies built from dyadic patterns such as even-even-odd, odd-odd-even, and so on. The piece also explores the “approximate sets” I discussed in a recent JMT article. And like all of my music, it makes extensive use of hierarchical transposition along both chord and scale. These “dual transpositions” are aurally distinctive in preserving both set class and voicing, understood as the pattern of pitch intervals measured along the octave-repeating scale formed by a chord’s own notes (its “intrinsic” scale).

The story behind the piece lies in the composer’s Russian background. This piece was a reflection on her ancestors from the father’s side who lived in a small town nestled in the Ural Mountains, 56°40’ N, which is roughly the latitude of Quebec. The imagery that the composer had in mind while writing this piece is a cold snowy winter night in a rural area with no electricity where a person sings a lullaby for their child, not sure if they will make it through the night.

The piece is through-composed. To make it cohesive, recurring textures and motives are used several times creating a hauntingly resonant atmosphere. The basic idea of the piece is a short three-note motive that evokes folk-like melodies inherent in Russian lullabies. The drones in strings played sul ponticello create an ethereal, cold and freezing soundscape, akin to the icy breath of a desolate winter night. The repetitive arpeggios in the piano in the opening imitate the rhythmic sway of a cradle. Faster sections with guitar-like arpeggiated textures in the piano part evoke the blowing winds that buffet the isolated landscape. In several spots, imitative counterpoint is used and evokes traditional folk music.

The piece is tonal, happening primarily in F# minor, then modulating to C# minor in the middle of the piece, and coming back to F# minor in the last section. The last chord, F# major, is in the second inversion, which is not the most common chord to end a piece with. This unconventional resolution maintains the stepwise motion in the bass line.

Laerciando is an original Brazilian choro-samba, composed for this special session and in honor of its flautist Cynthia Folio, emeritus Professor of Music Theory at Temple University and my first music theory teacher.

Choro is a composer-based tradition with a built-in practice of oral history. In a gathering or performance, players retell stories about composers and their compositions before or after they are played. This storytelling is an important part of how choro generates a sense of community that transcends borders of time, place, and even language. In this context, I compose choros that memorialize new diasporic choro communities and their stories and that meditate on the musical ideas and idiolects of those composers to have gone before.

Two ideas motivated Laerciando. First, the piece would modulate frequently with simple ii7-V7 pairings, both closely and remotely, both implied and confirmed. Second, its key centers would be determined by abstract manipulations of a harmonic motive from the development of the first movement of Beethoven’s Appassionata sonata—a connection neither arbitrary nor idolatrous. The first idea constitutes my generalization of the harmonic style of Afro-Brazilian pianist Laércio de Freitas (b.1941) heard on his seminal album São Paulo no Balanço do Choro (1980, Eldorado). The second idea has long haunted me and has precedent (often in the same keys) in choro, samba, and MPB (música popular brasileira). Its use also embodies the characteristic Brazilian fuzziness between art and popular music (música erudita and música popular, respectively), as does the very context of the performance of this piece.

In addition to laying out the basic cultural context and my relation to it, my presentation ahead of the performance will show how Laerciando uses the Appassionata harmonic motive in various ways to generate its highly mobile, Laércio-like tonal plan.

If there is a dead thing still rotting (2021) is a solo work for flute and recited text based on a poem from Muriel Leung’s Bone Confetti. The piece uses a variety of challenging extended techniques, including multiphonics, vocalizations, key clicks, tongue rams, timbral trills, and a variety of air sounds; as such, the consideration of the performer’s physicality becomes a fundamental necessity when utilizing such sonorities in melodic compositional contexts.

Focusing particularly on the twelve multiphonics used throughout the piece, I discuss how collaborative precompositional approaches and methodologies can begin to mitigate the performance challenges of such extended techniques. I detail the collaborative undertakings with the first performer of the work to dramatically reduce the burden of successive multiphonic chords to the greatest extent possible; to preserve variables of specific dissonances, of volumes, and of harmonic functions, I limit the selection of multiphonic progressions to only those which (1) have been demonstrated to speak most easily, and (2) are separated from one another by only a single shift in fingering.

Similarly, I situate the challenges of this work within the context of other contemporary compositions for flute with textual components, including Kaija Saariaho’s Laconisme de l'aile (1982) and NoaNoa (1992), Kate Soper’s Only the Words Themselves Mean What They Say (2010–2011), and Michael Hersch’s unwrung, apart, always (2020). I discuss the different methodologies through which each composer’s work specifically adapts to the performance challenges of this medium, and I explore the resultant intelligibility of text from the vantage points of composer, performer, and listener.

In a 2019 article, I claim that, in some of his stretto fugues, J.S. Bach sought an abundance of variety among the fugue’s “canonic intervals,” a specific pitch-time relationship between dux and comes. While some of Bach’s stretto fugues have an impressive diversity of canonic interval, none exhausts all of one parameter’s options. For example, his first fugue from Book I of the Well-Tempered Clavier never uses stretto at the seventh above, and none of the three stretto fugues from Art of Fugue uses stretto at the third above (both modulo the octave). Many diatonic row classes can achieve entirely consonant first-species canons at all seven diatonic ordered pitch-class intervals (DOPCIs) and all non-zero time delays—what I call “pancanonic”—when they iterate intervals or interval sequences and are thus trivially pancanonic. However, the number of nontrivial consonant pancanonic row classes of eight notes, the fewest number of notes possible, is exactly one. This unique row class contains 224 strings each of seven DOPCIs that are all equivalent under inversion, retrograde, rotation (order-number transposition), and/or “incrementation,” which is the increase or decrease of each DOPCI in the row by a constant. My ninety-second fugue fully expresses the pancanonicism of one of these strings. The choice of a steady and intensifying reduction of successive stretto intervals’ time delays over the course of the fugue ineluctably produces both an idiomatic and arch-like tonal structure, and a stylistically appropriate interspersal of metric displacements of the subject halfway through the 4/4 measure.

Being (2022) depicts the human life cycle through five character pieces for cello and piano. Each movement attempts abstractly to evoke a state of being through a single musical texture and idea spun out for a relatively short length of time. Movements 1, 3, and 5 are the “anchors” of the piece and set for both instruments. Movements 2 and 4, set for solo piano and solo cello respectively, are shorter and intended to function as interludes in between the longer anchor movements. Mimicking loose states of being we may experience in our life cycle, this piece attempts to explore first our state of seeking belonging (mvt. 1, “(Be)longing”), followed by a lengthier period of living and within that believing whatever it is we need to believe in order to continue living (mvt. 3, “beLIeVING”), and concluding with an imagined state of the afterlife, once we die (mvt. 5, “Beyond”). The overarching extramusical goal of the suite is to portray the ephemerality of life.

The opening movement features a cascading chromatic piano accompaniment based on contrary motion between the hands and implying compound melody, implying shifting tonal centers without explicitly invoking functional tonality. A slower-moving cello part derives its materials from the faster moving piano accompaniment using transformative processes like augmentation and octave displacement. Movement 2 (“Beside”) uses interval inversion between the parts in each hand of the piano. The third movement plays with non-functional tertian-based harmony and timbre, using harmonics in the cello part that catch and rub against various chord tones in the piano. Movement 4 (“Between”) recalls melodic material from the second movement, now for solo cello, played pizzicato. Octave displacement exploits the single line’s potential for compound melody. The final movement offers a harmonically driven texture, enhanced by open fifths and other double and triple stops in the cello, exploring triads to create a lyrical quasi-tonality befitting one imagination of an afterlife.

The Spinning Wheel is an arrangement for flute, clarinet, violin, cello, and piano of the second movement of my woodwind quintet, Kisum Flowz, which takes its title from the German words for music (Musik) and twelve (zwölf) in retrograde. The work is based on a twelve-tone row (P₀ = 03469TE12578) and cast in an ABA' form. Each of the five original instruments was given a single row form from which nearly all pitch material in the movement is drawn. The rows of the four woodwind instruments were related by T₃ or T₆: P₅ (bassoon), P₈ (clarinet), P_E (oboe), and P₂ (flute). The horn’s retrograde form of the row (R_T) allows for quotation from the A section in the A' section. For the most part, pitch material within each section is limited to discrete tetrachords: order positions 0–3 of each row in the A section, 4–7 in the B section, and 8–11 in the A' section.

The A section begins with a canon between cello and clarinet at T₃ and displaced by a half note. The flute and violin begin their own canon at T₃, related to the first canon by T₆. This leads to a canon among the four instruments at time intervals less than a half note. The B section begins with duets in which one instrument plays a rhythmic ostinato while the other plays a long-breathed, expressive melody. Gradually, additional instruments join until they burst into raucous excitement. The A' section begins with a funky groove in the bassoon that introduces a walking bass in the piano. The flute and clarinet reprise the flute and violin duet from the A section, and the piano, playing pitches from the retrograde form of the row, quotes the opening canonic material. Grouping and displacement dissonances appear throughout the work before it ends on a unison.