Speeds...

WARNING: MUSIC NERD INFO AHEAD

Ever since I discovered Elliott Carter's music I've been interested in the 'speed' of certain rhythms. What I am talking about is the rate at which a poly-rhythmic pulse moves across the regular 'crotchet' pulse.

For example: if you play dotted crotchets over crotchets you get the rhythm 2 over 3, 2 'hits' over your crotchet pulse, or 2/3. This poly-rhythm moves by at a rate of 0.67. That is, one and a half 'hits' for every 1 crotchet.

What I'm interested in is finding different poly-rhythms that are close in speed. Alternating between these gives the sense of speeding up and slowing down ever-so-slightly, without actually playing rubato. They're not easy to do, and even harder to do over a given structure like a tune, but hey, that's what practice is for.

So I finally got around to figuring out the numbers for most of the poly-rhythms I like using, and organised them from fastest (the rate of 'hits' is high) to slowest (the rate of 'hits' is low).

Above is the poly-rhythm, and below is the rate.

Table 1


7/2 5/2 7/3 7/4 5/3 3/2 7/5 4/3 5/4 7/6 1/1-------------------->

3.5 2.5 2.34 1.75 1.67 1.5 1.4 1.34 1.25 1.17 1



5/6 4/5 7/9 3/4 5/7 2/3 3/5 4/7 5/9 4/9 3/7

0.83 0.8 0.78 0.75 0.71 0.67 0.6 0.57 0.56 0.44 0.43


Obviously rhythm is not finite, and there are plenty of other rhythms I could add here to make this movement much smoother. I have just done it with the poly-rhythms I am most familiar with.

So if you're unsure on how to play these. If we have a poly-rhythm of x/y, x represents the divsion of the beat, and y represents the grouping of that division. So 5/7 is quintuplets grouped in lots of 7:

1 2 3 4 5, 1 2 3 4 5, 1 2 3 4 5, 1 2 3 4 5, 1 2 3 4 5, 1 2 3 4 5, 1 2 3 4 5

The highlighted numbers are you 'hits', the numbers 1-5 represent the 5 quintuplets in the pulse, and the number 1 represents the crotchet pulse.

Obviously in my table of speeds there are some rhythms that are so close the movement between them is almost imperceptible. From 4/9 to 3/7 there is only 0.01 difference, for instance.

Even if this seems un-realistic for your level of playing, you could examine the raltionships of speed from keeping your division of the beat the same, but changing the grouping.

Table 2

4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8 4/9 ------->etc

4 2 1.34 1 0.8 0.67 0.57 0.5 0.44


This pattern is much obviously much easier to play, as you don't have to change the division of the beat (going from septuplets grouped in 4 to quintuplets grouped in 3 is not very easy). Although I haven't worked it out mathematically, it looks like this way you get an exponential curve when graphing the relationship from one poly-rhythm to the next. This would obviously happen no matter what the division. So in 'Table 2', the rate of acceleration is increasing at an even rate, whereas in 'Table 1', I'm trying to get the acceleration to remain constant. The problem wth that is the number of poly-rhythms I'll need to get that to happen approached infinity.....oh well. I'm content now with my first efforts.
Now, to the practice room!

BTW.....

This is pretty good.....

Onwards!

Rather than write a 'best of 2009' blog like everyone else seems to around this time, I'm going to use this opportunity to talk about my plans for the next few years, namely in my development as a musician.
I love playing and listening to many different kinds of jazz/improvised music (Jazz from here-on in). Some of them I can come back to again and again, in both playing and listening. Some I need only a small fix. My point is, there are very few, comparatively, that I can come back to over and over again and never be sick of. This is by far more true of the jazz made in the last 20 years or so. I don't see this as a negative thing, as a slight on the music that has been made during this time, all it means to me is that I need to fill that void for myself. I need to create that music that I want to hear, to come back to over and over.
This music is rhythmic, it deals with phrases, it deals with texture in a polyphonic way.
It is not completely improvised (if that is even possible), but is based on a developed language amongst the band members, and hopefully, a whole community of players. It will probably have an element of formal composition, but these compositions will rarely dictate an entire, maybe not even the majority, of a piece. They are points of departure, that are not so contrived that they seem sonically separate from the act of spontaneous group composition. In fact, these compositions should be created using the exact same tools we use for improvising.
Lofty ideals maybe, but what else can I have when trying to create the music I want to hear?