Porcupine intervals
These are the intervals found in porcupine temperament.
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 (zarlino) | Name (heptatonic MOS) | Size* | Ratio | Genspan | Comments |
|---|---|---|---|---|---|
| Unisons | |||||
| Perfect unison (P1) | Perfect unison (P1) | 0.0 | 1/1 | 0 | |
| Augmented unison (A1) | Augmented unison (A1) | 61.1 | 81/80~36/35~33/32~25/24 | -7 | And other ratios, of course |
| Seconds | |||||
| Minor second (m2) | Diminished second (d2) | 101.6 | 21/20~16/15 | 8 | |
| Neutral second (n2) | Perfect second (P2) | 162.7 | 12/11~11/10~10/9~35/32 | 1 | Rather than "minor 2nd" |
| Major second (M2) | Augmented second (A2) | 223.8 | 9/8~8/7 | -6 | Rather than "major 2nd" |
| Augmented second (A2) | Double-augmented second (AA2) | 284.9 | Close to 13/11 | -13 | Also "subminor third" |
| Thirds | |||||
| Wolf third (w3) | Diminished third (d3) | 264.3 | 7/6 | 9 | Also "supermajor second" |
| Minor third (m3) | Minor third (m3) | 325.4 | 6/5~11/9 | 2 | |
| Major third (M3) | Major third (M3) | 386.5 | 5/4 | -5 | |
| Augmented third (A3) | Augmented third (A3) | 447.6 | 9/7 (close to 13/10) | -12 | Also "subminor fourth" |
| Fourths | |||||
| Diminished fourth (d4) | Diminished fourth (d4) | 427.0 | 14/11 | 10 | Also "supermajor third" |
| Perfect fourth (P4) | Minor fourth (m4) | 488.1 | 4/3 | 3 | Rather than "perfect fourth" |
| Wolf fourth (w4) | Major fourth (M4) | 549.2 | 11/8 | -4 | |
| Augmented fourth (A4) | Augmented fourth (A4) | 610.3 | 10/7 | -11 | Also "subminor fifth" |
| Fifths | |||||
| Diminished fifth (d5) | Diminished fifth (d5) | 589.7 | 7/5 | 11 | Also "supermajor fourth" |
| Wolf fifth (w5) | Minor fifth (m5) | 650.8 | 16/11 | 4 | |
| Perfect fifth (P5) | Major fifth (M5) | 711.9 | 3/2 | -3 | Rather than "perfect fifth" |
| Augmented fifth (A5) | Augmented fifth (A5) | 773.0 | 11/7 | -10 | Also "subminor sixth" |
| Sixths | |||||
| Diminished sixth (d6) | Diminished sixth (d6) | 752.4 | 14/9 (close to 20/13) | 12 | Also "supermajor fifth" |
| Minor sixth (m6) | Minor sixth (m6) | 813.5 | 8/5 | 5 | |
| Major sixth (M6) | Major sixth (M6) | 874.6 | 5/3 | -2 | |
| Wolf sixth (W6) | Augmented sixth (A6) | 935.7 | 12/7 | -9 | Also "subminor seventh" |
| Sevenths | |||||
| Diminished seventh (d7) | Double-diminished seventh (dd7) | 915.1 | Close to 22/13 | 13 | Also "supermajor sixth" |
| Minor seventh (m7) | Diminished seventh (d7) | 976.2 | 7/4~16/9 | 6 | Rather than "minor 7th" |
| Neutral seventh (n7) | Perfect seventh (P7) | 1037.3 | 9/5~11/6 | -1 | Rather than "major 7th" |
| Major seventh (M7) | Augmented seventh (A7) | 1098.4 | 15/8 | -8 | |
| Octaves | |||||
| Diminished octave (d8) | Diminished octave (d8) | 1138.9 | 21/11~35/18~160/81 | 7 | |
| Perfect octave (P8) | Perfect octave (P8) | 1200.0 | 2/1 | 0 | |
| Augmented octave (A8) | Augmented octave (A8) | 1261.1 | 81/40~45/22~33/16~25/12 | -7 | |
- In cents, 11-limit POTE tuning of porcupine, where the generator is ~162.7¢.
