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So how to make permutation music..? - Featuring Doepfer A-150-8 VC Octal Switch

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Axis 8

00:00 Intro
6:42 The Permutation Test
8:11 Explanation of the patch
18:53 Octal Switch inputs and trigger setup

Here's a brief explanation (and hopefully, very accessible) of how to calculate the number of unique combinations when you combine any number of different things (in our case, notes, samples, modulation sources, audio in general):

Note! I will use notes in the explanation, but it can be anything, really..
With two unique notes, denoted N1 and N2, you'll have two unique sequences (generally called combinations):
N1 N2
or
N2 N1

With three unique notes, N1, N2 and N3, you'll have this pattern of sequences:
Seq 1: N1 N2 N3
Seq 2: N1 N3 N2
Seq 3: N2 N1 N3
Seq 4: N2 N3 N1
Seq 5: N3 N1 N2
Seq 6: N3 N2 N1

Hence 6 unique sequences whatever 3 unique notes you choose. Notice that the changes are subtle, e.g. just one note changing place is the difference between sequence no. 1 and no. 3.

How to calculate the number of combinations? If you look closely at the last example you'll notice a pattern:
Step 1: 3 different notes to start with (ie N1, N2 and N3). Pick one.
Step 2: 2 different notes remaining to choose from. Pick one.
Step 3: 1 remaining note.
Consequently we have 3 x 2 x 1 = 6 unique combinations.

With 4 different notes, and using the same thinking as above, the number of unique sequences is: 4 x 3 x 2 x 1 = 24.

By extension, 5 unique notes give: 5 x 4 x 3 x 2 x 1 = 120 unique combinations.
How about 8 unique notes? 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40 320 unique combinations!
(Absurd: 16 unique notes: 20 922 789 888 000 combinations, ie more than 20 trillion unique sequences.)

Interestingly, since the variation between the sequences will be subtle confer the example above with 3 unique notes a pertinent question arises: What set of notes to choose in order to make the unique string of subtle sequence changes as compulsive and entertaining as possbile..?

posted by frekjagl