CUTS CD

CUTS is my new CD of compositions, out on the FREEFORM Association label.

cat no FFA-6342, distributed by ReR, Instantjazz, Metamkine, No Man's Land, Soundohm (Italy), Art Into Life
(Japan).

This is additional information for listeners who would like to know more about how these pieces were written.

*These rambles concern technical aspects of the pieces on this CD. In the first piece, a solo for bass clarinet, I did not apply any mathematical thinking to the time organisation. It is one of a series of pieces in which I set out to write for wind instrument + ring-modulation, and ended up ditching the modulation and finding ways to play some equivalent on the instrument itself. Experimenting with embouchure and breath, I came up with certain harmonics which I then interspersed with occasional multiphonics. I explored some harmonic combinations, wrote down the results, then practiced until I could play them more-or-less accurately, and then went on to record a set of improvised variations, so that the piece keeps returning to the same pitch material and approach, even as it develops. The complete score is downloadable on the SCORES page of this website.
A clarinet is an example of a cylindrical bore instrument closed at one end. The normal resonant modes must have a pressure maximum at the closed end (the mouthpiece) and a pressure minimum near the first open key (or the bell). These conditions result in the presence of only odd harmonics in the sound. This contrasts to the saxophone or oboe, which have a conical bore and hence include the even harmonics.
The effect of pressing the register key on a clarinet is therefore to make the frequency jump to the third harmonic, because the second harmonic is absent. Hence the instrument over-blows at the twelfth.
Following the system developed by Armand Angster for the Bb clarinet, I number the odd harmonics in Roman numerals.
When I write a note with (II), the (II) refers to the fact that the resultant harmonic would be the second of the series of uneven harmonics produced by the clarinet. This would be the fifth harmonic of the fundamental if you counted the even harmonics as well.
However, for the bass clarinet, I was finding the harmonics I wanted using the upper (clarino) register, i.e. with the register key pressed, which causes a slight divergence in the pitching of the harmonics from the ones given by Angster. The (II) is therefore the lowest harmonic to hand for the fingering including the register key.
For example, the first note in the extract below, which is the G# just above the treble staff, has the F above that for a (II), and would have the B quarter flat above that for a (III). This G# is, of course, the (I) of C# below the treble staff, which lies in the chalumeau register which is played without the register key.
As an example of how I use this, in bar 19 below, which you hear at about 1 minute 12 seconds into the piece, the (II) of the B above the treble clef is immediately followed by the (IV) of the C in the treble clef: what you hear is a faint quarter tone drop at the top, with a drop of a seventh in the bass at the same time.
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Now for the second and third pieces. Early in 2011, I got interested in the phenomenology of number. My notes go thusly:
On the one hand, maths is a formal ontology, not studying sensible objects but their forms of being. On the other hand, it seems totally concerned with a certain category of actions and these actions involve sensible objects. Numbers, in other words, happen in the first place as a result of acts of counting. Counting involves sub-actions of setting apart, selecting from the broader field, and retaining an awareness of the place or relative order of these sub-acts. Counting produces numerical groups perceived as wholes. It separates out what is counted from what is not counted. (As in: What counts... Count me in, etc.) Counting produces an awareness of an essential generic feature of the whole group. Numerosity is this generic unifying structure of the groups as we see them.
In Hans Freudenthal's *Didactical Phenomenology of Mathematical Structure,

Phew. In March 2012, everything got worse when my friend Robert Reigle complained to me: why do you use numbers at all in your compositions? I defended myself saying that numbers have a kind of identity beyond their mathematical function, in fact they appear in the human world as distinct characters: think of the three-ness of three. We arrive at a compromise whereby Robert would be happy if I only used numbers up to 5. Five fingers, maybe? Do spiders have a thing about 8? I had already been thinking that in music you could be inaccurate with numbers, using number but in an inexact way, swapping a 6 for a 7 if it seemed propitious at the time. Music is always inaccurate anyway. It measures, but you could always measure more precisely. The way that curves can translate into numbers is a case in point: you could either look at the curve on a grid, and it would give you numbers at the crossing points, and you could change the size of the grid and get fewer or more numbers, or you could locate where the curve changed direction, how fast it went up or down from that point to the next change of direction, and so on. All of which suggests that the relationship between reality and number is contingent: it just depends on how you feel like counting, and where you are going with it. The only restriction seems to be that reality, or our relation to it, is not completely smooth: stuff jumps between quantum states, it can't exist in between them, and its complexities arise from the complicated proportions between whole numbers ( rotations of moons against earths) and not from some implicit fuzziness at base level. The equations that govern regularly vibrating systems only work with whole numbers, and regular vibrations are harmonic, i.e. vibrating at different frequencies occurring in whole number steps.

Later in 2012 I wrote a piece following Robert's rule for Cornelius Dufallo, for solo violin in quarter tones and specified each note in the scale by two of the first five whole numbers. So the fifth quarter tone up from the bass note was 2.1 for example: the first note in the second group of five notes. But what about 5.5? That would be the 25th quarter tone, and there are only 24. Luckily for me, in my pattern this number never occurred. Phew. But the main interest was in the behaviour of groups of numbers that were going through certain processes, with sort of convection currents flowing through them. Causing them to swap their positions around within a pattern. This is really another form of serialism. Strictly speaking 12-tone serialism is highly repetitive because to really have an equal distribution of pitches you need to repeat the series endlessly: I wasn't interested in this, I was interested in patterns that went round until they had done what they had to: it was the character of the process that interested me: was it a kind of folding? Did the pattern turn itself inside out? Did it get to a certain point and then collapse? The joyful moment working on a later composition for clarinet (

I think my current interest in number answers to a problem that I have working with a more spectral approach to composition: where is the level of abstraction? where is whatever there is about the piece that could have translated into other sounds? What I like about maths, as opposed to say traditional music theory, is the way that you can apply the maths in totally diverse ways to the production of sounds. The two pieces for ensemble on this CD come from a phase in which I wanted to compose the processing of the sounds by different kinds of vibrato, glissando, etc, and leave the choice of pitch undetermined, as well as (mostly) the exact choice of timing. Both these pieces involve the use of the number patterns I have referred to, to decide what instrumental techniques are applied to the sound production, and the order in which different instruments enter, what register an instrument plays in (but not pitch and not exactly when it begins in relation to some measured regular pulse). So as a conductor I am laying down a rather complex pattern of cues, but these durations (with the exception, sometimes, of downbeat accents) are not audible on the surface, but are spaces in which the incidence of sounds is shown graphically in the score in relation to other sounds. (Violin just after trombone, cello just after violin etc) ... The choice of process integrates metaphorically with the kind of meaning the piece has for me whilst I am writing it - which doesn't necessarily belong to the public persona of the piece, but is something I need just to be able to get on with the work of writing it.

The extract from the score on the back of the CD cover corresponds to what is played from 2 minutes 30 seconds into

So far as composing these pieces goes, between sections you could tighten or loosen the grip of numbers. You would then take that into account in your next moves: each significant change becomes part of a pattern of changes. Rather than giving in to the stability and security offered by the numbers, you see them as giving you a series of problems to be solved in terms of working towards an imagined result. And of course the patterns come to an end, and have to be restarted. Differently.

So far as playing these pieces goes, oddly, or paradoxically, enough, this maths seems to have generated a kind of garden or environment for the musicians to inhabit.