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).