Composition as preparation
In written music, the score in itself is rarely the artistic goal. This is especially true for jazz scores. Jazz compositions can exist without them, and if there is a notion of the “musical work” in jazz, it is connected with live and recorded performances, and not with the sheet music players might use.1 The goal of a jazz composer is then to facilitate the invention of musicians, and not to crystallize an art object in notation. In this exposition, we therefore use the term “composition” to mean the preparatory work that frames the performance.
Stretch is a piece that involves theoretical systems with which most jazz performers are unfamiliar. To initiate and facilitate the performance, the bandleader prepared not only a score, but provided the players with instructions, suggestions, and some study materials. The theoretical framework was explained orally and papers on the fundamentals of spectral music were shared with the other band members.
Here is a list of the materials that the players were provided with:
2. A chart with the pitch aggregates that make up each of the spectral harmonies (the “spectral changes”).
3. A legenda.
Stretch: details of the composition
Stretch is divided in two parts: the body of the piece and the coda.
The body of the piece follows a rather traditional jazz chorus form, meaning that the piece starts with the exposition of a musical theme whose rhythmic and harmonic grid determines the structure for a subsequent improvised section. The chorus follows an AAB form. The improvised section is not built around ‘solos’ of the individual players, but as a collective improvisation within the form. The body of the piece ends with a variation on part B of the theme.
The coda (section C on the score) is built around a drum solo over a recurring cycle of 3 bars.
The piece progresses towards inharmonicity. The A sections go from a 0% to 4% distortion of the spectrum, and section B goes from 7% to 8%. This means that each chorus starts with a perfect harmonic spectrum and ends with a spectrum where the “octaves” are half-step apart. The coda reaches even higher values of distortion, going from 13% to 17%. With these distortion values, the harmonic series is stretched beyond recognition.
Next to its cycling harmonies, the coda is also structured by two gradual processes:
- The density of the drum part gradually increases.
- The electronics, added in post-production, evolve in the opposite direction. They start by filling the space between sparse drum hits, and evolve to playing less and longer notes, blending with the other pitched instruments.
In a way, the cymbals and the electronics exchange roles during the coda. This process was not planned during composition, but was a consequence of the way Luis Mora Matus played his drum solo. The score indicates cymbal hits in three “frequency areas” (med, low, and high). These cymbal hits go with the three different stretch percentages of the harmony, and they were supposed to be executed at the beginning of the pitch aggregates. Their purpose was to mask the attack of the individual instruments, and in so doing promote spectral fusion.
In the recording, Mora Matus chose to partially deviate from this indication. As his solo became denser, he took emphasis away from the cymbal hits, and in general he opted not to follow the prescribed differentiation of frequency areas. His choices helped shape the composition of the coda, which became a combination of decisions Pirro made before and after the recording session.
Pirro chose the deformation coefficients so that the amount of stretch per octave would be easy to memorize: no stretch, ¼-tone, half-step, ¾-tone, and full step stretch per octave values.
STRETCH | P1 P2 P4 P8 P16 | deviation per octave in semitones
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0% | D# D# D# D# D# | 0.00 (perfect octaves)
4% | Dd D D+ D# D#+ | 0.48 (1/4 step apart)
7% | C+ C#+ D D# E | 0.84
8% | C C# D D# E | 0.96 (1/2 step apart)
13% | A#+ C C#+ D# E+ | 1.56 (3/4 step apart)
14% | A# B+ C#+ D# E+ | 1.68
17% | A B C# D# F | 2.04 (a whole step apart)
An illustration of the formal structure of Stretch. The red bars with the percentages indicate the amount of distortion of the spectra used in each section. Section C is repeated 6 times.
The table above, taken from the legenda, shows the pitches of the fundamentals of the spectra, and of partial ranks that in a natural overtone series would relate to the fundamental in octaves (the partials with ranks 2n). Px indicates the ranks of these partials: P1 (fundamental), P2 (second partial), P4 (fourth partial), etc.
We use the following convention for accidentals: + for ¼ tone sharp; # for ½ tone sharp; d for ¼ tone flat; b for ½ tone flat.
When similar material returns in B1, the harmony adheres more strictly to the stretched spectra. This suggests a strategy for the players to use in their solos. They can use the C#m7-infused pitch reservoir in B, and adhere more strictly to the stretched spectrum on C in B1. This would take the listener from an “easier” to a “stricter” expression of the 7%- and 8%-stretched spectra. In any case, section B appears as a stepping stone towards the more ear-challenging B1.
Inside and outside of spectra
When playing in C major, one does not necessarily stick to the white keys. Chromatic approach tones, passing tones, tones belonging to secondary dominants, and superimpositions of notes outside of the scale are some of the many non-diatonic interlopers in the language of jazz. Jazz musicians refer to such negotiations of pitches that do or do not “fit” the reference harmony as playing “inside” and “outside” of the harmony. “Outside” notes help the musician mark the roles of the tones in the scale and trace the limits of the harmony itself. In that sense, the space outside of the harmony is just as important as the space inside of it.
In spectral music, the pitches that “fit” a harmony are determined by the spectrum that serves as a model for the harmony. In other words, the partials of the spectral model serve as a reservoir for pitches “inside” the harmony. While composing Stretch, it soon became clear that staying within the spectra was creatively too limiting. It was not enough to just stick to the partials of each spectrum, to put the spectra on display. Pirro wanted to provoke the emergence of an idiom built in and around these harmonic and timbral constructs. He wanted to better define them by relating them to the space outside their borders. To this end, he enriched the pitch material the spectra provided with “outside” pitches, and mediated the resulting structures with more traditional harmonies.
As an example of the first practice, take how the unstretched version of the spectrum (0%) is expressed in the first two bars of the piece. These spectra have few notes in the lower octaves. However, a groovy piece like Stretch requires the bass to fulfill its function of giving foundation to the rhythm. If the bass line would stick to the spectrum, it would essentially repeat the same one or two notes, which would be neither interesting nor a very convincing attempt at fulfilling its role. Consequently, the bass line contains a good share of notes outside of the spectrum.
Bars 19 and 20 of section B are a good example of how Stretch relates to “traditional” harmony. This section features a shift of the amount of stretch from 7% to 8%. In bar 20, at 8%, octaves are stretched a half-step apart. Partials 2, 8, and 16 are C#, D#, E. These belong to the key of C# minor. The harmonies in these two bars invoke a resolution on a minor C# chord. Pirro achieves this (1) by adding notes that belong to the chord of C#m7 (namely E and G#) to the pitch aggregate in bar 20,2 and (2) by suggesting a resolution to this chord with a “tension” harmony on C 3/4 sharp in bar 19.
