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| Line 16: |
Line 16: |
| * 5L 3M 2s, LMLsLMLsLM | | * 5L 3M 2s, LMLsLMLsLM |
| * 5L 4M 1s, LMLMLMLMLs | | * 5L 4M 1s, LMLMLMLMLs |
| <!--
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| ==Sharp-fifth edos==
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| ===10edo===
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| The trivial case.
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| ===15edo===
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| Up to modal rotation, blackwood[10] is the only dipentatonic scale in 15edo.
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| ===17edo===
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| The following are, up to modal rotation, a complete list of 17edo dipentatonic scales.
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|
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| *0-2-3-6-7-9-10-13-14-16-17: separation by 16\17
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| *0-2-3-6-7-9-10-12-14-16-17: separation by 9\17 (~13/9)
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| *0-2-3-5-7-9-10-12-14-16-17: separation by 2\17 (~13/12) (neutral thirds MODMOS)
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| *0-2-3-5-7-9-10-12-14-15-17: separation by 12\17 (~13/8) (neutral thirds MOS)
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|
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| ===22edo===
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| 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.
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| *0-2-4-7-9-11-13-15-18-20-22: separation by 11\22 (pajara MOS)
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| *0-2-4-7-9-11-13-16-18-20-22: separation by 20\22 (~15/8) (pajara MODMOS)
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| (above is complete list with no 1\22)
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| *0-3-4-7-9-11-13-16-18-20-22: separation by 7\22 (~5/4) (pajara MODMOS)
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| *0-3-4-7-9-12-13-16-18-20-22: separation by 16\22
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| *0-3-4-7-9-12-13-16-18-21-22: separation by 3\22
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| *0-3-4-8-9-12-13-16-18-21-22: separation by 12\22
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| *0-3-4-8-9-12-13-17-18-21-22: separation by 21\22 (superpyth subset)
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|
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| ===27edo===
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| 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.) Similar scales are available in other edos that support [http://x31eq.com/cgi-bin/rt.cgi?limit=2_3_5_7_13&ets=10_27&tuning=po this temperament], such as [[37edo]].
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| *3242323332: separation by 14\27 (~13/9) (more 5-limit harmony, with one 4:5:6:9:13; no wolf fifths)
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| *3242324232: separation by 25\27 (~15/8) (more 5-limit harmony, with one 4:5:6:7:9:13; though there's a flat "wolf fifth" it doesn't occur as the same interval class as a regular fifth.)
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| *3233323323: separation by 19\27 (~13/8) (neutral thirds MOS)
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| *3233323332: separation by 3\27 (~13/12) (neutral thirds MODMOS)
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|
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| ===29edo===
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| ==Flat-fifth edos==
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| 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.
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|
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| ...
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| ===19edo===
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| ===26edo===
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| ===31edo===
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| -->
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|
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| == Just dipentatonic scales == | | == Just dipentatonic scales == |
| Every other note of a just dipentatonic scale gives a Pythagorean pentatonic. Dipentatonic scales that are also [[SN scales|3-SN scales]] can be constructed by placing the same interval above or below each step of a pentatonic scale. This interval defines the scale, and the logic behind the listing below. | | Every other note of a just dipentatonic scale gives a Pythagorean pentatonic. Dipentatonic scales that are also [[SN scales|3-SN scales]] can be constructed by placing the same interval above or below each step of a pentatonic scale. This interval defines the scale, and the logic behind the listing below. |