User:CritDeathX/Sam's Permutations: Difference between revisions

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For example, taking the 38th row for the 2nd scale and the 24th row for the 3rd scale & combining them, we get [https://sevish.com/scaleworkshop/?name=&data=3%5C27%0A8%5C27%0A11%5C27%0A14%5C27%0A16%5C27%0A19%5C27%0A24%5C27%0A25%5C27%0A27%5C27&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ a nonatonic scale].  Taking the 19th row for the 1st scale and the 56th row for the 4th scale and combining them gives you [https://sevish.com/scaleworkshop/?name=&data=3%5C27%0A5%5C27%0A8%5C27%0A9%5C27%0A11%5C27%0A14%5C27%0A16%5C27%0A22%5C27%0A27%5C27&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ another nonatonic scale]. Pretty neat! (though the 2nd scale could probably do better with a different mode, but hey)
For example, taking the 38th row for the 2nd scale and the 24th row for the 3rd scale & combining them, we get [https://sevish.com/scaleworkshop/?name=&data=3%5C27%0A8%5C27%0A11%5C27%0A14%5C27%0A16%5C27%0A19%5C27%0A24%5C27%0A25%5C27%0A27%5C27&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ a nonatonic scale].  Taking the 19th row for the 1st scale and the 56th row for the 4th scale and combining them gives you [https://sevish.com/scaleworkshop/?name=&data=3%5C27%0A5%5C27%0A8%5C27%0A9%5C27%0A11%5C27%0A14%5C27%0A16%5C27%0A22%5C27%0A27%5C27&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ another nonatonic scale]. Pretty neat! (though the 2nd scale could probably do better with a different mode, but hey)


You can already imagine about the modes of these pentatonic scales, including all the scales that could be made from combining them and the modes within. I don't know how many scales you can make from this, but I can only imagine its a lot. I imagine a bigger graph can be made for finding the modes of each of the dipentatonic scales to possibly find more pentatonics from it. I might actually do that soon.
== The Dipentatonic Permutations ==
Now, this is where we do something akin to [[Erv Wilson|Wilson]]'s [http://anaphoria.com/xen9mar.pdf 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.


Its crazy what simple things can do to a scale.
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 ===
{| class="wikitable"
|''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; ===
{| class="wikitable"
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|}
 
=== 3; ===
{| class="wikitable"
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|}
 
=== 4; ===
{| class="wikitable"
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|}

Latest revision as of 16:21, 29 July 2020

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;

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