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MONO (2020)

Instrumentation: string orchestra

Around two years of deliberate work went into this piece, which is around a third of what I originally envisaged in its current state. On the other hand, it was the culmination of many of the compositional avenues I had explored earlier in my studies, so in that sense it was many years in the making.

It proved to be a colossal undertaking. Its genesis was simultaneously:

  • My desire to vouch for Elliott Carter’s pan-intervallic techniques by developing them to address some of the shortcomings a rather sacrilegious Roger Redgate pointed out to us during a postgraduate compositional-techniques module.

  • A desire to formalise a technique of notating acceleration and deceleration I believed I was capable of developing around the time.

  • A desire to make more use of the mass of pitch material I generated for Construction 1.

  • An interest in polytemporality and conceiving a means of formalising it.

  • A general taste for the sound stacks of minor seconds being struck simultaneously, gained perhaps from exposure to Toru Takemitsu’s music.

  • An interest in exploring that question of when one thing becomes another thing, gained both from work on various of my previous compositions and my burgeoning interest in Spectral music, on a mass scale.

  • An interest in being able to savour the quality and texture of a series of chords, taken both from the ideas I was introduced to for my earlier atonal chord exercise and an encounter with Jürg Frey’s 60 Pieces of Sound.

Construction 1 showed me that my long-range planning was lacking, so from the outset I directed the bulk of the work into the formal design itself. I chose to write for a twelve-piece string orchestra for ways that may well become clear to those who stay tuned and was stubbornly set on devising a way of writing for an orchestra and four totally independent string trios simultaneously. I had no idea whether this was possible or not before I started writing.

I started with the very same chord I used for Construction 1, transposed to accommodate my instrumentation’s range, but followed the transformation and transposition process through to completion this time to give a total of 528 chords. To put that number into perspective, if you printed those chords out and stacked them on top of one another, you'd have like a really big pile of chords. My pitch material was generated by assigning the intervallic sequence of that chord to my first instrument, the same sequence starting on the second interval for the second instrument, and so on for all twelve instruments. I then had to decide what to do with all this stuff. Having drawn this material from the information contained in my starting chord alone, I was determined that everything subsequent would draw from nothing outside of my starting material either. My rather novel idea was to a fractal-like thing where the DNA of the starting chord is applied at all of the individual instrument level, the trio level, and the ensemble or macro level.

Four trios, four transformations of the prime (P) chord. It seemed obvious that these two facts would correspond somehow. Trio 1 (the lowest) was assigned the intervallic sequence of P; trio 2 the intervallic sequence of the retrograde transformation of P (PR); trio 3 the inversion (PI); and trio 4 the retrograde-inversion (PRI). For each trio, I chose a note from each of the three instruments that would, when placed vertically, form a triad comprising the first two intervals of the trio’s intervallic sequence. I then refer to my chord bank, chose a chord that contained this triad, and filtered the other nine notes of this chord throughout the orchestra. In each section, all four trios undergo this procedure. This expanded pitch series is carried over into a new section where the process is repeated for the next two intervals in each trio’s intervallic sequence. The result is that each section contains four notes more than the section previous, since each iteration of the process adds one note for each of the trios.

Now things start to get kind of complicated. Using the powers of maths and spending hours staring out of a window, I was able to decide four separate tempi that, though audibly unrelated, can be played using (fairly) simple divisions of a mathematically generous master tempo. Bam—it turns out you can do the thing I said I was going to do. My idea was that I would I have one master conductor situated behind the players keeping the master tempo (perhaps just a machine or something), and four secondary conductors would count their tempi for each trio from this. Since each trio’s pitch series contains the same number of notes as each of the others, and they were all to start playing in different tempi, I now had a musical challenge to resolve.

By now, having composed my Parametric Study and two tempo studies to test the rigour of my methods, I had dragged my acceleration/deceleration calculator up to a usable standard and was pretty comfortable composing with it. With tempi and note-lengths of each section, I had all the maths I needed to calculate the durations of each section for each trio. I applied the calculator to each trio such that each concluded after the same specified amount of time that I decided would be appropriate for my purposes (I don’t entirely remember how I decided but it was more maths).

MONO temporal outline_edited.jpg

Thus, though part of a grand formal design, each trio is pretty much doing its own thing, playing at its own tempo. Now beckons the puppet master, for I am master of the notes—within each trio, further divisions of the sub-tempi are made, giving the aural impression that each instrument is playing at its own individual tempo. These tempi are determined by either ‘stretching’ or ‘shrinking’ the notes of each pitch series so that the notes chosen to form that trio’s intervallic combination for that section fall at the same point in time (for example, instrument one’s chosen note might be the fifth in its pitch series, while instrument two’s might be the eleventh. In each section, for each trio, one instrument is chosen as the one to be aligned to, so in this case, if instrument two were the one being aligned to, the point at which instrument two’s eleventh note is reached at instrument two’s tempo gives a duration which would be divided by five—the number of notes instrument one needs to play in that amount of time—to give the information needed to calculate instrument one’s tempo). Where the instrument being aligned to changes, or a tempo change is required for an instrument, I apply my acceleration/deceleration calculator and notate the result, achieving an effect that sounds almost improvised yet is actually precisely calculated, which, you may notice, is also pretty cool.
This process takes place during section one. But we’re not done there—throughout, the disorder of the piece is gradually assuaged as the process transmorphogates from the micro to the macro level and alignments begin to take place between trios (if that’s not a real word, how come you know exactly what it means?). Within a set of four, there are six possible combinations of two and four possible combinations of three. All combinations of two trios occur by using a similar process to the one that engenders alignments between instruments, before all alignments of three happen, and the piece concludes with a tutti chord, in effect closing the process by reaching the conclusion demanded by its internal logic.
By another process I can’t entirely remember, the number of minor seconds in each chord increases as the number of instruments involved in the alignments increases. I believe I decided that trios have to be ‘linked’ by a minor second, so each combination of two contains one minor second, combinations of three contain two minor seconds, and the chord at the conclusion contains an abrasive stack of three minor seconds. The idea here was for an antecedent force to oppose the overarching simplifying or ordering force of my process, creating a problem to be solved/dissonance to be resolved in a planned second movement. The basis of the second movement would have been answering the speculative question of what applying the process at the orchestral or most ‘macro’ level, but this piece alone proved to be such a colossal undertaking that I had neither the time nor the desire to go any further.
The effect, I believe (if the piece were to be performed), would be of a sound mass that the mind can choose either to hear as a single texture or a collection of individual compositions. The design of the process means that at different times one or the other might be more plausible. I like this idea—there is a threshold somewhere that separates a collection of individuals from a unified whole, and the piece traverses it repeatedly despite its precise location remaining unplaceable. The instrumentation serves this (told you): by working with a single class of instrument, I was able to achieve a homogeneity of texture at will, though the trade-off of course is that greater effort needed to be employed to achieve separation of them. Something about Elliott Carter’s solution of applying subjective ‘characters’ to instrumental groups felt unsatisfying to me, and I attempted to do what I could by using register and tempo, but this part of the design is perhaps the piece’s biggest weakness. Further work would look at ways of increasing the perceived conceptual distance between instruments when they are operating apart, creating an even greater plateau to be traversed on their way to unification that would, I believe, lead to more satisfying results.
The demand of this piece was such that only making it a full-time commitment would allow me to work on it further. A hypothetical PhD or commission would see me continue my research into polytemporality and notated deceleration and acceleration, and perhaps bring that second movement into reality. It was, to say the least, a lot of work.

Pitch series

Chord index

Tempo Study 1


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