Porcupine intervals
This is one possible naming and organization system for intervals of porcupine temperament. It's based on the porcupine[7] scale, or equivalently on the val <7 11 16|.
In 22edo, all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.
In 15edo, on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a minor fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.
| Name | Size* | Ratio | genspan | Comments |
|---|---|---|---|---|
| Unisons | ||||
| Perfect unison (P1) | 0 | 1/1 | 0 | |
| Augmented unison (A1) | 61.1 | 81/80~36/35~33/32~25/24 | -7 | And other ratios, of course |
| Seconds | ||||
| Diminished second (d2) | 101.6 | 21/20~16/15 | 8 | |
| Perfect second (P2) | 162.7 | 12/11~11/10~10/9~35/32 | 1 | Rather than "minor 2nd" |
| Augmented second (A2) | 223.8 | 9/8~8/7 | -6 | Rather than "major 2nd" |
| Double-augmented second (AA2) | 284.9 | Close to 13/11 | -13 | Also "subminor third" |
| Thirds | ||||
| Diminished third (d3) | 264.3 | 7/6 | 9 | Also "supermajor second" |
| Minor third (m3) | 325.4 | 6/5~11/9 | 2 | Coincidentally familiar |
| Major third (M3) | 386.5 | 5/4 | -5 | Coincidentally familiar |
| Augmented third (A3) | 447.6 | 9/7 (close to 13/10) | -12 | Also "subminor fourth" |
| Fourths | ||||
| Diminished fourth (d4) | 427.0 | 14/11 | 10 | Also "supermajor third" |
| Minor fourth (m4) | 488.1 | 4/3 | 3 | Rather than "perfect fourth" |
| Major fourth (M4) | 549.2 | 11/8 | -4 | |
| Augmented fourth (A4) | 610.3 | 10/7 | -11 | Also "subminor fifth" |
| Fifths | ||||
| Diminished fifth (d5) | 589.7 | 7/5 | 11 | Also "supermajor fourth" |
| Minor fifth (m5) | 650.8 | 16/11 | 4 | |
| Major fifth (M5) | 711.9 | 3/2 | -3 | Rather than "perfect fifth" |
| Augmented fifth (A5) | 773.0 | 11/7 | -10 | Also "subminor sixth" |
| Sixths | ||||
| Diminished sixth (d6) | 752.4 | 14/9 (close to 20/13) | 12 | Also "supermajor fifth" |
| Minor sixth (m6) | 813.5 | 8/5 | 5 | Coincidentally familiar |
| Major sixth (M6) | 874.6 | 5/3 | -2 | Coincidentally familiar |
| Augmented sixth (A6) | 935.7 | 12/7 | -9 | Also "subminor seventh" |
| Sevenths | ||||
| Double-diminished seventh (dd7) | 915.1 | Close to 22/13 | 13 | Also "supermajor sixth" |
| Diminished seventh (d7) | 976.2 | 7/4~16/9 | 6 | Rather than "minor 7th" |
| Perfect seventh (P7) | 1037.3 | 9/5~11/6 | -1 | Rather than "major 7th" |
| Augmented seventh (A7) | 1098.4 | 15/8 | -8 | |
| Octaves | ||||
| Diminished octave (d8) | 1138.9 | 21/11~35/18~160/81 | 7 | |
| Perfect octave (P8) | 1200 | 2/1 | 0 | |
| Augmented octave (A8) | 1261.1 | 81/40~45/22~33/16~25/12 | -7 | |
- In POTE 11-limit porcupine, where the generator is ~162.7¢.
See also: Porcupine Notation