permutations

Lately I've been examining how very little musical material can generate vast amounts of music. Think about all the tonal music that basically elaborates a I - V - I relationship.

To get some of this flavor let's take 3 notes (a, b, and c) and put them into sixteenth note "slots". Let's also stipulate -- at first -- that we can only duplicate one note (i.e. we have to use all of the tones). Here's what we start to get:

aabc abca bcaa
aacb acba cbaa
abac acab
baca caba
baac caab

bbac bacb acbb
bbca bcab cabb
babc bcba
abcb cbab
abbc cbba

ccab cabc abcc
ccba cbac bacc
cacb cbca
acbc bcac
accb cbba

So here we get 36 different little motives from 3 notes distributed over 4 note-slots. We could augment our rule to allow the duplication of 2 notes (thereby not using all three notes). Here's a little of what we get:

aabb abba bbaa
abab baba

aacc acca...

bbcc bccb...

That's 15 more motives or cells. Also let's allow a triplication of notes:

aaab abaa baaa
bbba babb abbb
bbbc bcbb cbbb
cccb cbcc bccc
ccca cacc accc
aaac acaa caaa

There's 18. And lastly let's allow a quadruplication:

aaaa bbbb cccc

which adds 3 more cells. All in all this totals 72 different motive-cells.

And this is just a surface scratching. We could further define some rules for our rhythms: take for example
aaaa.
This could be 4 sixteenth notes, but we could also combine them into larger units, such as:
one 16th and a dotted eighth,
one 16th, an eightn and a 16th,
a dotted eighth and a sixteenth,
2 eighth notes,
one quarter note.

Obviously our cell-motives will increase dramatically when this "rule" is applied across the board.

Why so possibly obsessive about this sort of thing? Well in improvisation and composition we're always looking for ways to make what we do more organic. Just this most basic surface examination shows that there is A LOT of material waiting to be made out of very little building blocks (similar to how electrons, protons and neutrons combine to form over a hundred different elements). Anyway if you're ever bored or just un-inspired take up this sort of exercise and see where it leads you.