Part of this activity falls under traditional musicological research (“academic” research). We gather knowledge about compositional methods and techniques by consulting writings by spectral composers and commentators. We then use this as a basis for the analysis of scores and recordings.
We studied music from both the classical and jazz traditions. A wealth of information is already available on the methods and techniques used by classical spectral composers. For the purpose of this project, we did not feel the need to tread new ground in that area.1 Instead, we chose to focus on existing knowledge regarding the composition methods of Gérard Grisey and Tristan Murail. This choice was in part pragmatic. We chose composers who wrote prolifically about their music and whose work has been the topic of much scholarship. But the choice for Grisey and Murail was also artistic. Grisey and Murail applied spectral techniques towards personal, intentional discourse, and this meshed well with the kind of jazz composition Pirro was interested in exploring.
For the composition of Stretch, Pirro was interested in a specific kind distortion of harmonic spectra that can be found in works like Vortex Temporum (1995) by Gérard Grisey2 or Désintegrations (1982) by Tristan Murail.3 Mathematically, this type of distortion translates to the following exponential function
fn = ndf0
where fn is the frequency of a given partial; f0 is the frequency of the fundamental; and n is the rank of a given partial, which is raised to the power of d (the distortion).
The formula to calculate the frequencies of the partials of a harmonic spectrum is fn = nf0. The frequency of the n-th partial (fn) is n times the fundamental f0. This can be expressed in the above distortion function if d = 1 (fn = n1f0).
For d > 1, the spectrum is expanded: each note of the new spectrum will be slightly higher than the ones of the harmonic spectrum, and the difference between the frequencies of the original and the deformed pitches will go up as the partial number goes up. For 0 < d < 1, the spectrum is contracted in a similar fashion. For one of the spectra in Vortex Temporum, Grisey uses d = 1.046, which Hasegawa notes stretches the spectrum with more or less a quarter tone per octave.4
In Stretch, Pirro defines different spectra that correspond to different values of d, and all the resulting spectra share the 8th partial, an E♭4. This way, the fundamental of the spectrum changes and becomes lower as the distortion factor rises, going from E♭1 down to A0. The resulting spectra are used as the harmonic framework for the piece, thus replacing the notion of chord changes with different values of the distortion factor d: 1.0 (labeled 0%), 1.04 (4%), 1.07 (7%), 1.08 (8%), 1.13 (13%), 1.14 (14%), 1.17 (17%).
While in classical spectralism one is spoilt for choice of literature, scholarship on the budding subgenre of spectral jazz is scant. It includes the 2012 doctoral dissertation of Stephen Lehman and his 2023 chapter in The Oxford Handbook of Spectral Music;5 a brief account written by Frédéric Maurin6 about the spectral episodes in his compositions for the big band Ping Machine; an unpublished essay about the music of Steve Lehman, written by guitarist Jacob Wiens in 2016 as part of his graduate work in music theory at McGill University;7 and an article by Scott Gleason that argues that the playing of double bass and violin player Henry Grimes can be interpreted as a sort of “Jazz spectralism.”8
Our literature study in this area therefore included our own analyses of works and methods that had not yet been covered in publication. Moreover, differently from our engagement with literature on classical spectralism, transcription (by Pirro) was the methodological cornerstone of these analyses.9 For the creation of Stretch, an analysis of Steve Lehman’s No Neighborhood Rough Enough10 was particularly inspirational.
The two pieces share some general features: they both use quarter-tone approximation and they deal with stretched spectra. But Lehman’s composition also influenced the writing of Stretch in two more specific ways. The first had to do with its use of changing time signatures. In a piece where the harmonic content does not relate to harmonic functions, the technique of constantly shifting meters is a way to achieve what functional harmony and consonance/dissonance afford in common-practice jazz: a series of tension-release episodes that punctuate the jazz chorus.
The second direct influence of No Neighborhood Rough Enough is the treatment of the bass part. Lehman partially frees the bass from the constraints of the spectra and lets it play lines that go in and out of the spectral harmony. As we will explain later on in Composition/Inside and outside spectra, Pirro did the same.
Notwithstanding all these similarities, there are many differences in the approach that these two pieces have towards composition and the integration of spectralism in a jazz piece.
Lehman largely derived his pitch aggregates from one kind of "stretched" spectrum: that of a piano note. This is not a spectrum that can be calculated with the formula Pirro used for Stretch. Rather, it is based on a harmonic spectrum in which partials number 16 and 22 are slightly raised. Lehman transposes this "spectral shape" onto different fundamentals. Conversely, Stretch uses seven different "spectral shapes" in the same composition, each with a different value for d in the formula fn = ndf0 (see explanation above). They all share the 8th partial, and the changing fundamental is a consequence of the various degrees of deformation.
Another difference between the two pieces is the use of repetition. No Neighborhood Rough Enough features very little repetition in its form. The only exceptions occur during the instrumental solos and in the last two bars. Other than that, the piece never repeats material and it has a long score to account for that. Stretch, on the other hand, is based on a traditional jazz chorus form. This makes it easier to memorize, and allows band members to negotiate personal contributions with the written score at any point in a performance.
A third difference we would like to point out is that Lehman gives soloists a smaller section of the spectrum to improvise with (from the 8th to the 16th partial, with the addition of the 22nd). In Stretch players can draw from the entirety of the spectra that Pirro uses as harmonic reservoirs for the various parts of the piece.