response to 9th April performance

from Simon Ellis

My experience was wonderfully dominated by the sonic. I felt part of - or immersed in - some huge rumbling organism, struggling for breath, reverberant, and inhabited by sibilant half sounds. This experience was quite different from any theoretical notion of the'finite but unbounded' ... the bounds of the conventional black box, its traditions of 'removal' from reality seemed at odds with an unbounded finity.

The mix of pre-recorded and live audio was deeply engaging.

I was often drawn to a notion of 'the unfinished' - of letters devoid of words, of partially completed sounds ... about mid way through the materials this sense of the 'incomplete' within the work felt quietly ecstatic.

Within the more formal conventions of the work - its location, use of light, crafted entrances and exits - I was excited by the presence of the 'unmanaged' ... when books fell, when one of the dancers dropped a book in the standing sequence, in the misshapen and subtly warped blackboards struggling to be aligned by the performers, in Marcus dealing with compass, ruler and ladder against a mobile blackboard.
The intrusion of these moments seemed to infect what was described as an oscillation between 'order and chaos' - as if I was occasionally reminded of just how much potential for the unplanned, the disordered there is in the act(s) of performance. These infections seemed to roughen the edges of the formal characteristics of the work (right down to their waistcoats etc).

This next thought is a little more uncertain - or incomplete. It has to do with embodiment, and with my memory of the act of solving mathematical equations at high school and university level, and now similar experiences in writing code. It represents a sort of collision between how 'mindful' those activities are, in which I
often approach a strong sense of the 'disembodied' ... they are experiences in which I find it hard to reconcile the dissolution of a mind-body split. And yet, seeing Marcus 'release' a solution onto the blackboard was extraordinary (his sense of embodiment was strongly contrasted with seeing the performer engage in that 'solving'conversation - she was so clearly writing something 'learned', not something 'experienced'). This tension - between states of (dis)embodiment - seems a difficult line to tread ... how much of the processes and conversations so clearly present in the development ought to be made transparent to viewers? (an old question I know but it seems to assume greate importance in a work 'about' mathematical concepts). At the same time, seeing Marcus write the solution disconcertingly reminded me of how Hollywood has portrayed the
'mathematical genius' (inevitably flawed) ... Good Will Hunting, A Beautiful Mind ... it's as if there is a kind of romance in the depiction/representation of this activity that is utterly opaque to us mathematical mortals!

Music, mathematics and embodied knowledge.

For a musician looking at the relationship between mathematics and music is like, having lived in the world of shadows and reflections, to then turn around and examine the objects creating those shadows and reflections, and the light that connects the two worlds. When we compose, perform or listen to music, we are engaging with number and geometry on multiple levels, consciously and unconsciously. The mathematical ‘data’ in music is understood and interacted with as musical phenomena - from how we count metre or hear pitch to how we comprehend harmonic motion or structure a fugue - as musical gesture and form. The mathematical knowledge we acquire or apply in learning music – counting, calculating, transposing – is embodied knowledge that we approach from a musical perspective. It becomes intuitive to us as musicians - a part of the way we are ‘musical’ rather than the way we are ‘mathematical’.

If mathematics is embodied within musical phenomena then its transformation is via the body. Musical gesture and form must make sense physically, on a human scale, in order to be perceived as music (though the boundaries of this perception are continually being challenged and extended). The mathematics that is manifest in music has a relationship to the ways our body perceives the world: both in terms of immediate sonic phenomena – scale, harmony and duration – and structure on the level of musical gesture, phrase or sentence, as well as the architectural dimensions of form, proportion and symmetry.

I am interested to investigate the embodied knowledge I possess as a musician in terms of the mathematics that underpins it, in order to extend and intensify my understanding of music. Because of the essential connection through the body, interacting with mathematics ‘live’ through performance facilitates the transfer of knowledge on deeper somatic and sensory levels. Choreography and sculpture both serve to underline the vital link with the body and senses by building connections with the music and with each other as well as the mathematical content. In this way our access to embodied knowledge becomes multi-sensory and multidimensional.

Flute and Tango

Astor Piazzolla used flute with guitar tho the guitar is used like percussion?...
Heres the sheet music
http://www.scribd.com/doc/89087/Tango-Suite-Flute
and a snatch of the music played
http://mp3s.sheetmusicplus.com/soundclips/4789935_01.mp3

Making Tango

I’m interested in assembling a library of tango tastes, colours, residues. I was intrigued by the way Molloy was talking about the 'hum' in her head of fragments of tango words and melodies. I’d like to compile a lexicon, a dustpan of bits of rhythm, melodies, gestures and artifacts from tango. There is a sense in which Tango already revels in this degree of distillation and a language of suggestion.

overall architecture

Main Structure
A 'backbone' construction of dance and music will form the main thread of continuity upon which everything else will hang. This will be devised collaboratively during the two weeks’ development. Musicians and dancers will navigate a network of hexagons according to a labyrinthine scheme. Dancers will work with sound and musicians will be choreographed. Hexagons are spaces in which events take place. Events include movement patterning, rhythm/sound patterning, recitations/readings, improvisation, solos, duos, ensembles.

Singular events
Events that occur singularly, either within the continuum as it goes on, or interrupting it; or emerging/morphing from it; things that have been constructed/prepared separately then sewn in.

These are, e.g.:
Marcus events – speeches, games,? (within the flow? interruptions? happening from ‘outside’ looking in?);

the Crimson Hexagon – what will this be? (is it a ‘warp’ in time/space; things have heated up, become intensified;

focus shifts to film/camera/mirror world (in the flow?);

a pre-recorded sound event;

Musicians
The musicians so far include flautist Sarah Bennington and percussionist Scott Wilson, both very exciting young players who’ve recently graduated from The Guildhall.

I am characterising each musician (based on archetypes - not specific to the people):

flute – poet; virtuosic but subtle/delicate; sonic dancer of patterns/solos composed from syllables; exchanges flute for alto flute to become more tactile; flautist also doubles on voice and percussion; flute will need safe place(s) to reside when not being used

percussion - primordial figure with a certain mystique; keeper of the syllables, numbers, patterns; a 3D hexagon made for him that is membranes, shadows; some fixed percussion will need to be given its own space; some portable, hand held; also uses voice

Marcus
Marcus will be our mathematician-guide. We need to become clearer about the content and various modes of delivery. What are the main mathematical points or concepts? What is the main one of these? How are they delivered? To whom is he speaking? Use of other texts? Games? Motifs?

Text in general
This needs some thought and choice of sources (perhaps this is for our second meeting at The Hope)

Design
The main element of the design we will work with on this round is the blackboard floor. Kate and Carol are to discuss how this will work.

Video
During rehearsals/development Kate will capture video and stills of aspects of the working process as well as each of us talking about the nature of space in our particular medium. This video will be important for the website and DVD but can it also be used as an additional public engagement element in the form of a documentary that’s shown at the start, as a montage or other kind of presentation, separate from the flow of the piece?

triangularity

Picking up on Marcus' mention of '1,2,3,lots...' and triangles, I woke up thinking about the triangularity we will have with our 3 dancers and 3 musicians. Three is the minimum number with which to produce a meaningful dimensionality of sound in an ensemble but with three you can start to approach a sense of 'lots'.

Put the two ensembles together and we have...lots, and with Marcus that makes... more lots. Then with mirrors and projection...lots and lots...

Amongst the ways I want to deploy the three musicians, one is to place them spaced apart on three sides of the periphery of the space, essentially forming a 'triangle'(but perhaps conceived more as a 'circle'), to get a sense of a dynamic spatialisation of the sound. Syllables flying across the space. The challenge in scoring this is that the performers need to have some independent means of rhythmic organisation if they are to produce a tight rhythmic structure without being conducted. I would also like to do this vocally, with all the performers: in this case using each performer's pulse rate to achieve multiple tempi - a real sense of lots can be achieved this way.

At the other extreme, I want to place them close together and facing in, to perform a variety of 'games' that signify dice-throwing in different ways. One of these is permutations of three points. Another is a kind of 'paper-scissors-rock' idea that produces endlessly permutating chords. These will be potentially infinite. They will just start and stop spontaneously. We can play with ways to vary and mutate them.

Other ways of conceptualising and organising 'three': two musicians, one dancer. Two dancers, one musician. Marcus on trumpet makes four musicians.

Infinity Dance of Carols made me think of Whirling Dervish

Remembered seeing Whirling Dervish in Cairo apparently Dervish means Doorway

As explained by Sufis:

At the beginning of the Sema, by holding his arms crosswise, the semazen appears to represent the number one, thus testifying to God's unity. While whirling, his arms are open: his right arm is directed to the sky, ready to receive God's beneficence; his left hand, upon which his eyes are fastened, is turned toward the earth.

Quoting From Marcus
"In the essays in my addition of Labyrinths there is an essay by Borges dedicated to The Fearful Sphere of Pascal. It traces back how the sphere has been an important symbol for many philosophers. Parmenides: The divine being is like the mass of a well-rounded sphere whose force is constant from the centre in any direction. The music of the spheres. Kepler's model of the universe as interconnected spheres."

phasing and infinity

Have just listened - finally - to Marcus' first programme for R3 in October, in which he mentions tabla and particularly the idea of phasing cycles as well as referring to Reich and Messiaen.

With Indian music, the dissonance and 'play' in the rhythm is felt because the basic taal cycle has a strongly fixed identity and we are always waiting - though that's not what we are necessarily aware of consciously - for the downbeat of the cycles to coincide. The phasing is usually played out over a small-scale period of a few cycles - always kept within a human scale. This keeps the sense of muscularity in the rhythm and there's never the sense of a mechanistic playing out of a process. John Ball talks about the sense of a balance between stronger and weaker phases of energy in the taal cycle and about the 'space' that the taal makes in which to improvise and play with patterns. There is a sense in which this playing could go on infinitely but it was interesting when I asked John about this that he said there's a point at which you become bored and you never want to reach the stage of exhausting the possibilities. In this way we keep an 'infinity of possibilites' in front of us.

The phasing in Reich by contrast can often take a whole piece to play itself out. The phasing of identical patterns, one of which gets slightly adjusted so the two slip further apart on each repetition, leads to an appealing blurring in the surface of the music; the downbeat becomes completely obscured and the end is usually understood by the realignment of the entire cycle rather than reaching the individual 'point' of a common downbeat. Quite often the patterning (and therefore the entire piece) is understood within the first couple of cycles and it becomes a mechanical process that has to be played out. There is, of course, a halfway point when the two patterns are moving back into alignment after reaching the stage of being furthest out of phase. It is music constructed from straight-forward symmetries. Our mind perhaps reaches a perception of infinity with this music because of the long-term scale of the phasing which goes beyond something we can hold in our head.

The phasing in the piano part of Messiaen's Liturgie is far more abstract and long-term so that one will never hear an alignment; the pulse and tonality are in any case sufficiently obscured that you'd be unlikely to recognise it if it did come along. In this way it is used to signify eternal, divine infinity (and it might as well be infinite).

I think it would be a very interesting point of dialogue to talk about the methods we use in our different art forms to signify infinity. I have used 'unfinished' phasing in a way that is similar, though on a much shorter-scale, to the Messiaen to signify infinity (an example is in the string hocketing in The Structure of Memory). But there are also a number of other devices that I use, that I've begun to realise are about infinity. Almost every piece on the new CD makes some kind of allusion to infinity. Kate and I were also talking about blurring of images as one way visual art can use to create this. Now we've learned through Borges and Marcus about the various different kinds of mathematical infinity this becomes very interesting to consider.

virtuosic syllabing

I've been composing flute music, working at a high-energy virtuosic solo of 2-3 mins that I want to be one of the 'spotlit' moments of the hexagonal counterpoint. The basic method of construction is around the idea of 'letters' that permutate. The letters in this case are rhythmic patterns/cells each framed within one beat (so when they are strung together it is on the grid of a consistent pulse; however the rhythms mostly are syncopated so you hardly ever hear a downbeat, obscuring the sense of a consistent pulse).

I am aiming for a sense of permutation, circling, with a continual stream of 'letters'. I want to work with different kinds of streams, different kinds of 'random' from those that are information rich to those that might consist of 3 letters like the book with "MCV" repeated over and over...perhaps. (I am still looking to explore the decimal fractions idea that Marcus has introduced, perhaps within this context; I think of them as little seed pods).

How to set up the algorithm so it produces the right kind of music has been the challenge - that is the challenge of working algorithmically. I've moved away from the notion of pitch (note names) as 'letters' as it places too much importance on pitch and leads to a bland, characterless result.

I have mapped the rhythmic 'letters' to the numbers 1-8 (so instead of 22 there are just 8) and I am using the decimal places of pi to dictate the order (so a random 'permutation'). 9 at the moment is a space, and I like the spaces, but 0 is also a space (there aren't so many zeros early on) and the choice is whether to differentiate them as spaces (e.g. 'comma' and 'full stop') or to use zero as something else, perhaps as a kind of switch for something in the system to change. The digits of pi imitate randomness and are apparently infinite; it signifies the circle and the impossibility of circumference (and perhaps the impossibility of the circumference of the sphere that is the library/universe).

When I arrived at the rhythmic 'letters' (really 'syllables') I started off by using a short pitch series that cycled through strict permutations, each pitch assigned to one rhythmic attack so the distribution depended on the number of attacks in each rhythmic syllable; the drawback with this kind of pitch system for me is that the intervallic consistency (intervals, or the tune, remain constant while the pitch changes as you start one element later each time, transposing from the new starting point) and sense of a closed system starts to limit the music once you've gone around the cycle. For several years now I've used pseudo-random numbers up to 24 (i.e. giving the quarter tonal-chromatic complement) to generate pitch (water mountain was the first piece) and I then craft that 'found material' into phrases, pieces. That doesn't mean the pitch in my music is 'random' but that I don't start with pitch/notes at the centre of the universe I am creating. Likewise with this piece, I think the process of working with 'letters' has made me really consider what might be a 'letter', or 'grain' or unit of composition in my music. So I've switched to generating the pitch with random numbers, distributing them as they come across the attacks of the rhythms, to produce the raw material.

By adding pitch to the rhythms in this way you end up with an endless variety of differently-shaped 'syllables', despite the consistency of the rhythms, and the next layer of composing is to arrange the registration of the notes (i.e. which octave to put them in) and perhaps rearrange the ordering of the pitches or even change them occasionally, file them and sand them down in terms of the way they 'speak' on the instrument and to make them practical to perform. It's almost impossible to compose and interact with material in this way without hearing a 'line' emerging (like looking at a Pollock drip painting and seeing shapes) and the longer you work with the material the more likely it is to result in a process of selection, re-ordering or complete transformation; as well as recycling material inverted or transformed some other way.

Today I'm working with the idea of weaving in a second strand to the main flute line as described above, like weaving in another dimension, so that the flute is at times playing 2 lines, making it pretty busy. My plan is that gradually the second line takes over; the second line (at present) is faster, more erratic and continuous (perhaps there is a signification of infinity here), constructed from a different set of numbers: this time filtered random numbers so that at first it's sparse but later becomes more dense; pitch taken from the first line and inverted, etc. so that it is a kind of dirty mirror of the first. Anyway, let's see how that goes.