User:CritDeathX/Sam's Permutations

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Wait, why am I trying to be funny in these headings? (reasoning)

So, Inthar had decided to make the idea of dipentatonic scales, and I had the idea of maybe slamming some cool permutation thingies onto these things.

For context, a dipentatonic scale is "a 10-note scale where every other note gives an MOS pentatonic scale generated by a diatonic-sized fifth (between the 7edo fifth and the 5edo fifth) of a fixed size." What I plan to do is to find all the different pentatonics within these 10-note scales and give light directions as to where this can go.

The Actual Thing

The Sources

  • 0-3-5-9-11-14-16-19-22-25-27
  • 0-3-5-9-11-14-16-20-22-25-27
  • 0-3-5-8-11-14-16-19-22-24-27
  • 0-3-5-8-11-14-16-19-22-25-27

If you couldn't tell, all of these scales are in 27EDO.

The Pentatonic Permutations

x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x
x x x x x

The best part about this specific way of making the graph is that you can slap two different dipentatonic scales into either of these and combine them to get interesting scales.

For example, taking the 38th row for the 2nd scale and the 24th row for the 3rd scale & combining them, we get a nonatonic scale. Taking the 19th row for the 1st scale and the 56th row for the 4th scale and combining them gives you another nonatonic scale. Pretty neat! (though the 2nd scale could probably do better with a different mode, but hey)

The Dipentatonic Permutations

Now, this is where we do something akin to Wilson's Marwa Permutations. We're going to have four different graphs for this, since I imagine each scale has a different chain of the generic interval. I will also be using the ^v notation for 27EDO.

I'll admit, I'm not gonna list out all the premutations for each of these scales, cause I'm kinda lazy, so enjoy what I have for now.

1; fifth

5 vv5 5 ^b5 vv5 vv5 5 ^b5 5
5 5 vv5 ^b5 vv5 vv5 5 ^b5 5
5 5 ^b5 vv5 vv5 vv5 5 ^b5 5
5 5 ^b5 vv5 vv5 5 vv5 ^b5 5
5 5 ^b5 vv5 vv5 5 ^b5 vv5 5
vv5 5 5 ^b5 vv5 vv5 5 ^b5 5
5 vv5 5 vv5 ^b5 vv5 5 ^b5 5
5 vv5 5 vv5 vv5 ^b5 5 ^b5 5
5 vv5 5 vv5 vv5 5 ^b5 ^b5 5
^b5 5 vv5 5 vv5 vv5 5 ^b5 5
5 ^b5 vv5 5 vv5 vv5 5 ^b5 5
5 vv5 ^b5 5 vv5 vv5 5 ^b5 5
5 vv5 5 ^b5 vv5 5 vv5 ^b5 5
5 vv5 5 ^b5 vv5 5 ^b5 vv5 5
vv5 5 vv5 5 ^b5 vv5 5 ^b5 5
5 vv5 vv5 5 ^b5 vv5 5 ^b5 5
5 vv5 5 vv5 ^b5 vv5 5 ^b5 5
^b5 5 vv5 5 ^b5 vv5 vv5 5 5
5 ^b5 vv5 5 ^b5 vv5 vv5 5 5
5 vv5 ^b5 5 ^b5 vv5 vv5 5 5
5 vv5 5 ^b5 ^b5 vv5 vv5 5 5
5 vv5 5 ^b5 vv5 ^b5 vv5 5 5
5 vv5 5 ^b5 vv5 vv5 ^b5 5 5

2;

3;

4;