22edo tetrachords

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A chart of all possible 22edo tetrachords (28 altogether):

1-1-7 1-2-6 1-3-5 1-4-4 1-5-3 1-6-2 1-7-1
2-1-6 2-2-5 2-3-4 2-4-3 2-5-2 2-6-1
3-1-5 3-2-4 3-3-3 3-4-2 3-5-1
4-1-4 4-2-3 4-3-2 4-4-1
5-1-3 5-2-2 5-3-1
6-1-2 6-2-1
7-1-1

Tetrachord details:

tetrachord notation steps in cents interval names solfege notes
1-1-7 55 + 55 + 382 P1 d2 m2 P4 do di ra fa
1-2-6 55 + 109 + 327 P1 d2 N2 P4 do di ru fa
1-3-5 55 + 164 + 273 P1 d2 M2 P4 do di re fa
1-4-4 55 + 218 + 218 P1 d2 sm3 P4 do di ma fa found in Superpyth Phrygian
1-5-3 55 + 273 + 164 P1 d2 m3 P4 do di me fa
1-6-2 55 + 327 + 109 P1 d2 M3 P4 do di mi fa
1-7-1 55 + 382 + 55 P1 d2 SM3 P4 do di mo fa
2-1-6 109 + 55 + 327 P1 m2 N2 P4 do ra ru fa
2-2-5 109 + 109 + 273 P1 m2 M2 P4 do ra re fa
2-3-4 109 + 164 + 218 P1 m2 sm3 P4 do ra ma fa
2-4-3 109 + 218 +165 P1 m2 m3 P4 do ra me fa
2-5-2 109 + 273 + 109 P1 m2 M3 P4 do ra mi fa
2-6-1 109 + 327 + 55 P1 m2 SM3 P4 do ra mo fa
3-1-5 164 + 55 + 273 P1 N2 M2 P4 do ru re fa
3-2-4 164 + 109 + 218 P1 N2 sm3 P4 do ru ma fa
3-3-3 164 + 164 +164 P1 N2 m3 P4 do ru me fa perfectly even tetrachord, found in Porcupine temperament
3-4-2 164 + 218 + 109 P1 N2 M3 P4 do ru mi fa
3-5-1 164 + 273 + 55 P1 N2 SM3 P4 do ru mo fa
4-1-4 218 + 55 + 218 P1 M2 sm3 P4 do re ma fa found in Superpyth Minor (& Dorian)
4-2-3 218 + 109 + 164 P1 M2 m3 P4 do re me fa
4-3-2 218 + 164 + 109 P1 M2 M3 P4 do re mi fa
4-4-1 218 + 218 + 55 P1 M2 SM3 P4 do re mo fa found in Superpyth Major (& Mixolydian, & Lydian)
5-1-3 273 + 55 + 164 P1 sm3 m3 P4 do ma me fa
5-2-2 273 + 109 + 109 P1 sm3 M3 P4 do ma mi fa
5-3-1 273 + 164 + 55 P1 sm3 SM3 P4 do ma mo fa
6-1-2 327 + 55 + 109 P1 m3 M3 P4 do me mi fa
6-2-1 327 + 109 + 55 P1 m3 SM3 P4 do me mo fa
7-1-1 382 + 55 + 55 P1 M3 SM3 P4 do mi mo fa

Tetrachords in families:

sML MsL sLM MLs LsM LMs genus name(s) / notes
1-1-7 1-7-1 7-1-1 enharmonic close to Didymos's Enharmonic, 32/31 • 31/30 • 5/4.
1-2-6 2-1-6 1-6-2 2-6-1 6-1-2 6-2-1 chromatic
1-3-5 3-1-5 1-5-3 3-5-1 5-1-3 5-3-1 chromatic
2-2-5 2-5-2 5-2-2 chromatic
2-3-4 3-2-4 2-4-3 3-4-2 4-2-3 4-3-2 diatonic similar in function to JI tetrachord 16/15 • 9/8 • 10/9, but altered
1-1-4 1-4-1 4-1-1 diatonic SuperPyth
3-3-3 diatonic Porcupine

See also: 17edo tetrachords, Tricesimoprimal Tetrachordal Tesseract.