Bipentatonic scale: Difference between revisions

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Dipentatonic scales can be classified by their fifth size and the separation between the two chains of fifths. This article surveys dipentatonic scales you can get in various edos with relatively good fifths. Dipentatonic scales tend to work better with sharper fifths, because it's easier to interleave a minor third of one pentatonic inside a major third of the second pentatonic.

==10edo==

==Sharp-fifth edos==

===10edo===

The trivial case.

==15edo==

===15edo===

Up to modal rotation, blackwood[10] is the only dipentatonic scale in 15edo.

==17edo==

===17edo===

The following are, up to modal rotation, a complete list of 17edo dipentatonic scales.

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*0-2-3-5-7-9-10-12-14-15-17: separation by 12\17 (~13/8) (neutral thirds MOS)

==22edo==

===22edo===

The following are, up to modal rotation, a complete list of 22edo dipentatonic scales.

The following are, up to modal rotation, a complete list of 22edo dipentatonic scales. The first three or so are similar to corresponding 12edo pajara scales.

*0-2-4-7-9-11-13-15-18-20-22: separation by 11\22 (pajara MOS)

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*0-3-4-8-9-12-13-17-18-21-22: separation by 21\22 (superpyth subset)

==27edo==

===27edo===

The following are, up to modal rotation, a complete list of 27edo dipentatonic scales with no step of size 1\27. (I'm excluding 1\27 because it's near maximum dissonance.)

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*0-3-5-8-11-14-16-19-22-24-27: separation by 19\27 (~13/8) (neutral thirds MOS)

*0-3-5-8-11-14-16-19-22-25-27: separation by 3\27 (~13/12) (neutral thirds MODMOS)

===29edo===

==Flat-fifth edos==

For edos with fifths flatter than 12edo, let's loosen the definition of a dipentatonic a bit: the pentatonics don't have to be every other note.

...

===19edo===

===26edo===

===31edo===

[[Category:Scales]]

@@ Line 3: / Line 3: @@
 Dipentatonic scales can be classified by their fifth size and the separation between the two chains of fifths. This article surveys dipentatonic scales you can get in various edos with relatively good fifths. Dipentatonic scales tend to work better with sharper fifths, because it's easier to interleave a minor third of one pentatonic inside a major third of the second pentatonic.
-==10edo==
+==Sharp-fifth edos==
+===10edo===
 The trivial case.
-==15edo==
+===15edo===
 Up to modal rotation, blackwood[10] is the only dipentatonic scale in 15edo.
-==17edo==
+===17edo===
 The following are, up to modal rotation, a complete list of 17edo dipentatonic scales.
@@ Line 15: / Line 16: @@
 *0-2-3-5-7-9-10-12-14-15-17: separation by 12\17 (~13/8) (neutral thirds MOS)
-==22edo==
+===22edo===
-The following are, up to modal rotation, a complete list of 22edo dipentatonic scales.
+The following are, up to modal rotation, a complete list of 22edo dipentatonic scales. The first three or so are similar to corresponding 12edo pajara scales.
 *0-2-4-7-9-11-13-15-18-20-22: separation by 11\22 (pajara MOS)
@@ Line 27: / Line 28: @@
 *0-3-4-8-9-12-13-17-18-21-22: separation by 21\22 (superpyth subset)
-==27edo==
+===27edo===
 The following are, up to modal rotation, a complete list of 27edo dipentatonic scales with no step of size 1\27. (I'm excluding 1\27 because it's near maximum dissonance.)
@@ Line 34: / Line 35: @@
 *0-3-5-8-11-14-16-19-22-24-27: separation by 19\27 (~13/8) (neutral thirds MOS)
 *0-3-5-8-11-14-16-19-22-25-27: separation by 3\27 (~13/12) (neutral thirds MODMOS)
+===29edo===
+==Flat-fifth edos==
+For edos with fifths flatter than 12edo, let's loosen the definition of a dipentatonic a bit: the pentatonics don't have to be every other note.
+...
+===19edo===
+===26edo===
+===31edo===
 [[Category:Scales]]