Porcupine intervals: Difference between revisions
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There's no accepted interval names for zarlino. Use ups and downs instead, which has real scores made in it. Formatting |
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{| class="wikitable right-3 center-5" | {| class="wikitable right-3 center-5" | ||
|- | |- | ||
! Name (ups and downs) | ! Name ([[Pergen|ups and downs]]) | ||
! Name (1L 6s (onyx)) | ! Name (1L 6s (onyx)) | ||
! Size* | ! Size* | ||
| Line 32: | Line 32: | ||
! colspan="6" | Seconds | ! colspan="6" | Seconds | ||
|- | |- | ||
| | | Upminor second (^m2) | ||
| Diminished second (d2) | | Diminished second (d2) | ||
| 101.6 | | 101.6 | ||
| Line 39: | Line 39: | ||
| | | | ||
|- | |- | ||
| | | Downmajor second (vM2) | ||
| Perfect second (P2) | | Perfect second (P2) | ||
| 162.7 | | 162.7 | ||
| Line 53: | Line 53: | ||
| | | | ||
|- | |- | ||
| | | Upmajor second (^M2) | ||
| Double-augmented second (AA2) | | Double-augmented second (AA2) | ||
| 284.9 | | 284.9 | ||
| Line 69: | Line 69: | ||
| Also "supermajor second" | | Also "supermajor second" | ||
|- | |- | ||
| | | Upminor third (^m3) | ||
| Minor third (m3) | | Minor third (m3) | ||
| 325.4 | | 325.4 | ||
| Line 76: | Line 76: | ||
| | | | ||
|- | |- | ||
| | | Downmajor third (vM3) | ||
| Major third (M3) | | Major third (M3) | ||
| 386.5 | | 386.5 | ||
| Line 106: | Line 106: | ||
| | | | ||
|- | |- | ||
| | | Upfourth (^4) | ||
| Major fourth (M4) | | Major fourth (M4) | ||
| 549.2 | | 549.2 | ||
| Line 113: | Line 113: | ||
| | | | ||
|- | |- | ||
| | | Downaugmented fourth (vA4) | ||
| Augmented fourth (A4) | | Augmented fourth (A4) | ||
| 610.3 | | 610.3 | ||
| Line 122: | Line 122: | ||
! colspan="6" | Fifths | ! colspan="6" | Fifths | ||
|- | |- | ||
| | | Updiminished fifth (^d5) | ||
| Diminished fifth (d5) | | Diminished fifth (d5) | ||
| 589.7 | | 589.7 | ||
| Line 159: | Line 159: | ||
| Also "supermajor fifth" | | Also "supermajor fifth" | ||
|- | |- | ||
| | | Upminor sixth (^m6) | ||
| Minor sixth (m6) | | Minor sixth (m6) | ||
| 813.5 | | 813.5 | ||
| Line 166: | Line 166: | ||
| | | | ||
|- | |- | ||
| | | Downmajor sixth (vM6) | ||
| Major sixth (M6) | | Major sixth (M6) | ||
| 874.6 | | 874.6 | ||
| Line 182: | Line 182: | ||
! colspan="6" | Sevenths | ! colspan="6" | Sevenths | ||
|- | |- | ||
| | | Downminor seventh (vm7) | ||
| Double-diminished seventh (dd7) | | Double-diminished seventh (dd7) | ||
| 915.1 | | 915.1 | ||
| Line 196: | Line 196: | ||
| | | | ||
|- | |- | ||
| | | Upminor seventh (^m7) | ||
| Perfect seventh (P7) | | Perfect seventh (P7) | ||
| 1037.3 | | 1037.3 | ||
| Line 203: | Line 203: | ||
| | | | ||
|- | |- | ||
| | | Downmajor seventh (vM7) | ||
| Augmented seventh (A7) | | Augmented seventh (A7) | ||
| 1098.4 | | 1098.4 | ||
Latest revision as of 07:26, 3 June 2025
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 (ups and downs) | Name (1L 6s (onyx)) | Size* | Ratio | Genspan | Comments |
|---|---|---|---|---|---|
| Unisons | |||||
| Perfect unison (P1) | Perfect unison (P1) | 0.0 | 1/1 | 0 | |
| Up unison (^1) | Augmented unison (A1) | 61.1 | 81/80~36/35~33/32~25/24 | -7 | Among other ratios |
| Seconds | |||||
| Upminor second (^m2) | Diminished second (d2) | 101.6 | 21/20~16/15 | 8 | |
| Downmajor second (vM2) | Perfect second (P2) | 162.7 | 12/11~11/10~10/9~35/32 | 1 | |
| Major second (M2) | Augmented second (A2) | 223.8 | 9/8~8/7 | -6 | |
| Upmajor second (^M2) | Double-augmented second (AA2) | 284.9 | Close to 13/11 | -13 | Also "subminor third" |
| Thirds | |||||
| Minor third (m3) | Diminished third (d3) | 264.3 | 7/6 | 9 | Also "supermajor second" |
| Upminor third (^m3) | Minor third (m3) | 325.4 | 6/5~11/9 | 2 | |
| Downmajor third (vM3) | Major third (M3) | 386.5 | 5/4 | -5 | |
| Major third (M3) | Augmented third (A3) | 447.6 | 9/7 (close to 13/10) | -12 | Also "subminor fourth" |
| Fourths | |||||
| Down fourth (v4) | Diminished fourth (d4) | 427.0 | 14/11 | 10 | Also "supermajor third" |
| Perfect fourth (P4) | Minor fourth (m4) | 488.1 | 4/3 | 3 | |
| Upfourth (^4) | Major fourth (M4) | 549.2 | 11/8 | -4 | |
| Downaugmented fourth (vA4) | Augmented fourth (A4) | 610.3 | 10/7 | -11 | Also "subminor fifth" |
| Fifths | |||||
| Updiminished fifth (^d5) | Diminished fifth (d5) | 589.7 | 7/5 | 11 | Also "supermajor fourth" |
| Down fifth (v5) | Minor fifth (m5) | 650.8 | 16/11 | 4 | |
| Perfect fifth (P5) | Major fifth (M5) | 711.9 | 3/2 | -3 | |
| Up fifth (^5) | Augmented fifth (A5) | 773.0 | 11/7 | -10 | Also "subminor sixth" |
| Sixths | |||||
| Minor sixth (m6) | Diminished sixth (d6) | 752.4 | 14/9 (close to 20/13) | 12 | Also "supermajor fifth" |
| Upminor sixth (^m6) | Minor sixth (m6) | 813.5 | 8/5 | 5 | |
| Downmajor sixth (vM6) | Major sixth (M6) | 874.6 | 5/3 | -2 | |
| Major sixth (M6) | Augmented sixth (A6) | 935.7 | 12/7 | -9 | Also "subminor seventh" |
| Sevenths | |||||
| Downminor seventh (vm7) | 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 | |
| Upminor seventh (^m7) | Perfect seventh (P7) | 1037.3 | 9/5~11/6 | -1 | |
| Downmajor seventh (vM7) | Augmented seventh (A7) | 1098.4 | 15/8 | -8 | |
| Octaves | |||||
| Down octave (v8) | Diminished octave (d8) | 1138.9 | 21/11~35/18~160/81 | 7 | |
| Perfect octave (P8) | Perfect octave (P8) | 1200.0 | 2/1 | 0 | |
| Up octave (^8) | 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¢.
