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.