View Full Version : Mathematical Composition/Improv Ideas

07-06-2002, 01:43 PM
Mathematical Exhaustion
This post is a simple demonstration of the possible sequences generated from three notes in groups of three.
123, 231, 312, 321, 213, 132

6 possibilities ( 3*2*1) or 3 Factorial

07-06-2002, 01:45 PM
I thought I would show a simple Melodic improvisation device known as a spin and give some permutations based on it.
Basically a spin has a motive that uses each note of a chord as its starting note and moves diatonically through the scale.
In this case I am using the chords Am G and F in the Key of A Natural Minor (Aeolian).
I am choosing Ascending spins (from each note) but descending through the chord tones.
The chosen inversions are Am in first inversion,G in second inversion, and F in root inversion. I chose these because the chord change is downward but I wanted the chord movement upward.
In the top stave the first tone of each group of three notes is a chord tone, these form the three previously mentioned inversions.
The next stave shows the same idea but with each group of three notes shifted left (with carry or wrap-around) by one position.

The obvious transforms of this are shift left by 1 and by 2,
retrograde (reverse) and retrograde shift left by 1 and by 2.

07-06-2002, 01:47 PM
Okay just to limit the space used, I put 3, 3 note groups of each type in each measure.
Now we could use a different type on each group of three if we want. We could also swap groups (shift the whole three note group left or right), or reverse the order of the groups.

6 permutations for each three note group.
6 permutations for each group of three.
So each measure has 36 possibilities for three measures
36 x 36 x 36 = 46656 just for this one three measure idea!

You could do spins that descend from each chord tone but ascend through the chord tone and repeat this to get another 46656!

07-06-2002, 01:49 PM
Move the group on the B string down 1 octave to be using an open voice form of the triads, same notes(down an octave in the mddle) sounds different.

07-08-2002, 08:48 AM
Hi Szulc,

I liked your post very much. I know that lots of ppl would oppose oh so strongly against such kind of approach to subtle substance as music.
Combinatorial calculus is the seventh string and the sixth finger while playing arpeggio.
Thanks for your post which inspired me to apply similar method to constructing sets of chord progressions given the melody line (alteration combinations, substitution variants, voice leading shapes etc.).
Math + Soul - what a beautiful combination sending shiver down my spine ;)


07-08-2002, 01:56 PM
I am glad some one read this and actually replied.

The idea here is to generate musical ideas in a formulaic/repeatable fashion, which can then be used as studies or exercises to help with your creativity and to help fill in the holes when your inspiration is low. It is also intended as a means of introduction to some simple improvisational techniques.
Math limits the possibilities and allows for a more focused look at exhaustion of ideas. Hopefully this way of thinking will have the impact of allowing students to manage and organize the creative process, giving some direction to following in the pursuit devloping a style of composition.

Bongo Boy
12-15-2002, 04:05 PM
Regarding some backgropund material that I relates to this sort of composition, please see:


12-17-2002, 05:08 AM
Hi Szulc.
Great posts and examples.
I've been sitting here for about twenty minutes playing them. Lacking the gift of verbal expression in the way Zatz posted in relationship to the seventh string and sixth finger, I can add in my own way;

Playing these examples is kinda like walking into a supermarket I've visited for years and find an isle I'd never been down before. I walk down it and see many new windows open up as I look at the shelves.

Some of the things I played from your examples fed my creative muse and kicked in the makin's for another song.
Before I get going that far though, I need to really understand all I know about this.
Thanks for sharing this with us.

Bongo, I checked out that link rather quickly, but I'll go back when I wear myself out on this improv idea.
Looks like an informative link.

12-17-2002, 05:24 AM
I hoped someone would find this thought provoking.

12-17-2002, 05:29 AM
Ya know, probably a lot more people look at this and try it than post a reply on it. By the # of view hits I'd say quite a few.
Even if only 20 % of the views did, I'm sure someone got something out of it besides the people who posted.

It'd be nice if more replied though.
Their ideas and imput could escalate something in someone elses mind.

12-20-2002, 05:29 AM
I would like to see the tab of your inspiration from this.

12-20-2002, 11:20 AM
I'll get it for you after the holidays szulc. Some of my family is here and more is coming. In the middle of the night is the only time I can find any peace.
I will do though.

08-08-2003, 01:55 AM
More Shread Ideas!