Before I elaborated any structure, the first thing I did was to workshop the sonic and technical space of the piece with Hannah in a couple of sessions. I quickly realised that since the underblowing technique the work was based on provided many ‘passages’ through the same set of fingerings, the work could well be a sequence of different approaches to the one ‘isofingering’. I roughly thought would be made up of 20-odd fingerings.
Each instantiation of the isofingering I decided would be of a different temporal expansion (inspired by Stockhausen’s method of formula composition). But the question was how to get the right proportional relations between the durations of iterations. I wanted to have a slow exponential increase from the smallest to the largest expansion since this would, for perception, represent a more real differentiation than an increase by stable number. Here’s the sequence that I came up with:
In which the degree of increase of the increase (starting with 0.5 secs) itself increases arithmetically by 0.25 secs each iteration. Such a formula could be mathematically represented, of course, but I was still doing things quite intuitively at this stage (something that has very much changed while writing this piece), so I just tried a couple different ways of having an increase from one iteration to the next until I reached this sequence. This meant that the total number of 14 iterations was a result, not predetermined (except that I wanted more than 10 iterations and less than 14). Likewise the total duration of the work, 9’07.5”, was a result of this experimentation, rather than planned in advance (except, also, that I wanted it to be less than 10 mins and greater than 8 mins).
Ok, with that done I decided that each iteration would have 25 fixed fingerings and 5 rests in variable positions in the sequence. This is the ‘isofingering’:
(In which the top note is the fingered pitch and any lower notes are possible underblowings… Different flutes might have slightly different results, and the specified accidentals aren’t exact, only more or less accurate but dependent on various factors).
This was quite ‘intuitive’; I think it has a good balance of disjoint motion, stepwise ascent and descent (which are ‘warped’, as you can see, in the underblown layers).
I also then arranged the expansions in a sequence that I liked:
Which is the interpolation of two divergent sequences: 5,6,4,7,3,8,2,9,1,10, and 13,12,14,11.
To determine tempi for each section it’s quite simple: you just divide the number of fingerings (30 in each case) by the duration of the iteration, and then multiply by 60secs to get the tempo (which I would give in quaver = x bpm). In the case of very fast passages, I would divide the final result by two and give only a semiquaver to each fingering; in the case of very slow passages, I would double or quadruple the bpm and then give either a crotchet or minim to each fingering.
For example. The 5sec iteration would be: 30/5=6; 6*60=360; 360/2=180. Therefore quaver=180 and each fingering takes 1 semiquaver.
Another example. The 79.25sec iteration would be: 30/79.25=0.3786; 0.3786*60=22.7129; 22.7129*4=90.8517. Therefore quaver=91 and each fingering takes 1 minim.
After this I began basic determinations for each section (and here’s where it get’s interesting I promise). These are the parameters that I structured for each iteration at this level of the work:
- determinacy level (1=pitch determination; 2=pitch determination with deviations; 3=action notation determined, pitch result indeterminate; 4=fingerings determined, other parameters improvised)
- pitch/underblowing layers present
- number of rhythmic groupings (5,6,10,12,15,30)
- temporal tendency, or denominator of rhythmic groups (expansion, stable, contraction)
- degree of ‘mediation’ or ‘refraction’ of the tendency, or numerator of rhythmic groups (even, uneven, radically/exponentially uneven)
In my next post I’ll pick apart each of those parameters and show how they are structured.