Communicative Musicality and Entropy

An activity which I've done a few times now is to invite people to simulate conversation in music using my Roli Seaboard. The result sounds a bit like the Clangers, but people enjoy it (and I get something much more expressive out of them than I would if I tried to get them to vocalise "talk"). What's interesting is that it's obvious when its done well - the musical conversation has a kind of coherence about it - which raises a fundamental question about the coherence of any shared "musicking" between people, and the prosody of language.

This coherence is, I think, a fractal structure, and another aspect of this analysis is to consider how the fractal might emerge. Any musical communication involves an "emergent alphabet" of utterances, which invites the suggestion that a fractal must express the emergence of this alphabet. The emergent alphabet issue also presents a problem when trying to apply analytical techniques like information theory to music: information theory relies on the fact that the alphabet is known at the outset, so it knows what to count. If the alphabet is emergent, it doesn't know what to count until (possibly) the end. However, it is a possibility that an alphabet at time t1 has a similar structure in terms of entropy as a larger alphabet at t2. This is where the fractal likely resides.

The critical question is at what point is it necessary to expand the alphabet? This is closely related to the question as to "at what point is a new concept introduced into a learning conversation?" My answer to this draws on the relations between entropies of basic elements.

Consider that a "basic" alphabet in sound contains four elements: pitch, rhythm, intervals and volume. They can be A, B, C, D. Over time, the entropies for each of these values can be calculated, and at different times the entropy for each  will either increase or decrease. For example, a note which is sung typically has an "attack" - which is an increase in volume, and hence an increase in the entropy of volume. It may then have a "sustain" period where the volume is constant: that gives a entropy closer to zero. Finally the note is released, which results in a rapid decrease in volume to nothing, which is also an increase in entropy. Every dimension is like this, having a period of increase and decrease, so for each of A, B, C, D there is a corresponding A*, B*, C*, D* for its inverse. This means that AA*, BB* CC*, etc are all effectively zero. In drawing the attack and decay of a note and encoding  an increase in entropy as 1, and a decrease as 0, we might see:

A   A*
1    0
0    1
0    1
1    0

Sometimes it may seem that the entropy of A oscillates very quickly with the entropy of A* (e.g. vibrato), or even that it is difficult over a period of time to determine whether on average there is an increase or a decrease: both seem to be simultaneously present. If we draw this then we might see:

A   A*
1    0
1    0
0    1
1    1
1    0
0    1
1    0
1    0

taken over a longer period of time, we would basically see:

A   A*
1    1
1    1
1    1

This means that the AA* pair is complete and in total is zero. The question is whether this is the trigger for the production of a new element in the alphabet. I think it is. Intuitively, what is described is the point at which a gesture or idea is thoroughly familiar to the point of being boring, and this requires something new. It is a way of describing the satiety of the alphabet.

Now what happens in communicative musicality? When two people are in musical conversation, there is in each person a different idea of what the alphabet might be. So person x might articulate an alphabet which is A,A*,B,B* and person y might articulate an alphabet which is A, A*, C, C*. The conversation articulates a combined alphabet: A, A*, B, B*, C, C*, AC, AC*. At what point does this alphabet become sated, where each element is 1?

In a conversation that "doesn't work", what will happen is that the communication breaks down. This means that the utterance of one person is not met by a corresponding utterance by the other. Equally, the other person might simply keep on repeating the same behaviour (the same alphabet) irrespective of the attempts of the other person to elicit a different response. Both these situations result in restrictions to the growth of the alphabet.

But when it does work, there is adaptation in the utterances of both parties, which eventually results in an expanded alphabet that is shared between the people.