Re: [tuning] Digest Number 748

> From: "Mats �ljare" <oljare@hotmail.com>
> Subject: Rhytmic primes
>
> I�ve been wondering recently if there is a direct parallel between prime
> ratios in pitches and in rhythm.

The way I have been thinking of this lately is more in the polyrhythm
sense. The 'accepted and cool' polyrythms of African music and its
derivatives (Haitian and Cuban Yoruba inspired religious drumming and
jazz drumming, for instance) are generally 3:2, 6:4 perhaps 4:3. Often
WITHIN the 4 and 3 there will be duple and triple subdivisions as well,
but typically one doesn't find higher primes.

There are a few observations.

Rhythm 'chords' are much simpler than harmonic chords.

In most musics, rhythmic motion is analogous to 'drone' oriented
music (it is rare to see music where the tempo is multiplied by
4/3 for two measures, whereas in Western music one can see the
harmony make such a transition).

Prime limit seems to be more important than odd limit (i.e., '9's are
more common than '5's and '7's)

There may be some interesting observations regarding 'tuning' perception,
is 7:4 in rhythm perceived as an 'out of tune' 8:4? (Perhaps, if a jazz
drummer does this, it might be inthe context of playing 'behind the beat').

The point you bring up is a grouping aspect. I don't think grouping is
an analogue to tuning, as per my thoughts above. I also don't see the
difficulty with large groupings, although how the players approach it
is important. It may pay to find the paper 'the magic number 7 plus or
minus 2'. If there is a heirarchical level at which the grouping is
'2's and '3's and the structure of the heirarchy is '7 plus or minus 2',
then I think it can be held onto.

However, what may be valid in your analoque is that at some level, maybe
a 17 beat form, maybe 29, things start turning into a random mixture of
'2's and '3's unless a further heirarchical level is found.

An analogy to tuning can be made at the level of these long forms,
and that is between polymetric thinking and to 'punning' in a
temperment. For instance, a 33 beat form may be phrased
8 5 7 5 8 or 11 11 11 (and others of course).
In a recent tune of mine, the basic phrase structure is

5 * [ 3 * 4/4 ] (AABA'A') ----------> A
2 * [ 3 * 3/4 + 1 * 4/4 ] (DD') ------> B
1 * [ 3 * 4/4 ] A ------------\
2 * [ 2 * 4/4 ] A'' ------------\---> A'

Since it's a jazz tune, you improvise over the form. From an improv point
of view, you might phrase the "three bars of 4/4" section as "4 bars of
3/4". If we relate it to harmony, we're really only playing with the
'timbre' of the the rhythmic chord, making it a bit more strident. A
more relaxed approach (but harder to hold onto) is to improvise 3
phrases of 20 beats each during the 'big A' section.

These games are common in most rhythmic musics.

Bob Valentine