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.