Porcupine: Difference between revisions
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{| class="wikitable center-all right-2 left-3 right-6 left-7" | {| class="wikitable center-all right-2 left-3 right-6 left-7" | ||
! colspan=" | ! colspan="5" | Up from the tonic, aka fourthward | ||
! colspan=" | ! colspan="5" | Down from the octave, aka fifthward | ||
|- | |- | ||
! # | ! # | ||
! Cents | ! Cents | ||
! Ratios | ! Ratios | ||
!Porcupine notation | |||
! Ups and downs<br>notation | ! Ups and downs<br>notation | ||
! # | ! # | ||
! Cents | ! Cents | ||
! Ratios | ! Ratios | ||
!Porcupine notation | |||
! Ups and downs<br>notation | ! Ups and downs<br>notation | ||
|- | |- | ||
| Line 40: | Line 42: | ||
| 0.0 | | 0.0 | ||
| '''1/1''' | | '''1/1''' | ||
|P1 | |||
| P1 | | P1 | ||
| 0 | | 0 | ||
| 1200.0 | | 1200.0 | ||
| '''2/1''' | | '''2/1''' | ||
|P8 | |||
| P8 | | P8 | ||
|- | |- | ||
| Line 49: | Line 53: | ||
| 162.8 | | 162.8 | ||
| 10/9, 11/10, 12/11 | | 10/9, 11/10, 12/11 | ||
|P2 | |||
| vM2 = ^^m2 | | vM2 = ^^m2 | ||
| -1 | | -1 | ||
| 1037.2 | | 1037.2 | ||
| 9/5, 11/6, 20/11 | | 9/5, 11/6, 20/11 | ||
|P7 | |||
| ^m7 = vvM7 | | ^m7 = vvM7 | ||
|- | |- | ||
| Line 58: | Line 64: | ||
| 325.6 | | 325.6 | ||
| 6/5, 11/9 | | 6/5, 11/9 | ||
|m3 | |||
| ^m3 = vvM3 | | ^m3 = vvM3 | ||
| -2 | | -2 | ||
| 874.4 | | 874.4 | ||
| 5/3, 18/11 | | 5/3, 18/11 | ||
|M6 | |||
| vM6 = ^^m6 | | vM6 = ^^m6 | ||
|- | |- | ||
| Line 67: | Line 75: | ||
| 488.4 | | 488.4 | ||
| 4/3 | | 4/3 | ||
|m4 | |||
| P4 | | P4 | ||
| -3 | | -3 | ||
| 711.6 | | 711.6 | ||
| '''3/2''' | | '''3/2''' | ||
|M5 | |||
| P5 | | P5 | ||
|- | |- | ||
| Line 76: | Line 86: | ||
| 651.3 | | 651.3 | ||
| 16/11, 22/15 | | 16/11, 22/15 | ||
|m5 | |||
| v5 = ^^d5 | | v5 = ^^d5 | ||
| -4 | | -4 | ||
| 548.7 | | 548.7 | ||
| '''11/8''', 15/11 | | '''11/8''', 15/11 | ||
|M4 | |||
| ^4 = vvA4 | | ^4 = vvA4 | ||
|- | |- | ||
| Line 85: | Line 97: | ||
| 814.1 | | 814.1 | ||
| 8/5 | | 8/5 | ||
|m6 | |||
| ^m6 = vvM6 | | ^m6 = vvM6 | ||
| -5 | | -5 | ||
| 385.9 | | 385.9 | ||
| '''5/4''' | | '''5/4''' | ||
|M3 | |||
| vM3 = ^^m3 | | vM3 = ^^m3 | ||
|- | |- | ||
| Line 94: | Line 108: | ||
| 976.9 | | 976.9 | ||
| '''7/4''', 16/9 | | '''7/4''', 16/9 | ||
|d7 | |||
| m7 | | m7 | ||
| -6 | | -6 | ||
| 223.1 | | 223.1 | ||
| 8/7, '''9/8''' | | 8/7, '''9/8''' | ||
|A2 | |||
| M2 | | M2 | ||
|- | |- | ||
| Line 103: | Line 119: | ||
| 1139.7 | | 1139.7 | ||
| 48/25, 160/81 | | 48/25, 160/81 | ||
|d8 | |||
| v8 = ^^d8 | | v8 = ^^d8 | ||
| -7 | | -7 | ||
| 60.3 | | 60.3 | ||
| 25/24, 81/80 | | 25/24, 81/80 | ||
|A1 | |||
| ^1 = vvA1 | | ^1 = vvA1 | ||
|- | |- | ||
| Line 112: | Line 130: | ||
| 102.5 | | 102.5 | ||
| 16/15, 21/20 | | 16/15, 21/20 | ||
|d2 | |||
| ^m2 = vvM2 | | ^m2 = vvM2 | ||
| -8 | | -8 | ||
| 1097.5 | | 1097.5 | ||
| 15/8, 40/21 | | 15/8, 40/21 | ||
|A7 | |||
| vM7 = ^^m7 | | vM7 = ^^m7 | ||
|- | |- | ||
| Line 121: | Line 141: | ||
| 265.3 | | 265.3 | ||
| 7/6 | | 7/6 | ||
|d3 | |||
| m3 | | m3 | ||
| -9 | | -9 | ||
| 934.7 | | 934.7 | ||
| 12/7 | | 12/7 | ||
|A6 | |||
| M6 | | M6 | ||
|- | |- | ||
| Line 130: | Line 152: | ||
| 428.2 | | 428.2 | ||
| 14/11 | | 14/11 | ||
|d4 | |||
| v4 = ^^d4 | | v4 = ^^d4 | ||
| -10 | | -10 | ||
| 771.8 | | 771.8 | ||
| 11/7 | | 11/7 | ||
|A5 | |||
| ^5 = vvA5 | | ^5 = vvA5 | ||
|- | |- | ||
| Line 139: | Line 163: | ||
| 591.0 | | 591.0 | ||
| 7/5 | | 7/5 | ||
|d5 | |||
| ^d5 = vv5 | | ^d5 = vv5 | ||
| -11 | | -11 | ||
| 609.0 | | 609.0 | ||
| 10/7 | | 10/7 | ||
|A4 | |||
| vA4 = ^^4 | | vA4 = ^^4 | ||
|- | |- | ||
| Line 148: | Line 174: | ||
| 753.8 | | 753.8 | ||
| 14/9 | | 14/9 | ||
|d6 | |||
| m6 | | m6 | ||
| -12 | | -12 | ||
| 446.2 | | 446.2 | ||
| 9/7 | | 9/7 | ||
|A3 | |||
| M3 | | M3 | ||
|} | |} | ||
| Line 169: | Line 197: | ||
|} | |} | ||
The [[11/9]] interval, usually considered a "neutral third", is in porcupine identical to the [[6/5]] "minor third". An interval in the neutral third range is not found for a long time (until 17 generators up), and as a result that interval varies drastically depending on the tuning. This also means that the [[27/20]] "acute fourth" of the JI diatonic scale is equivalent to [[11/8]] (rather than becoming 4/3 as in meantone). | The [[11/9]] interval, usually considered a "neutral third", is in porcupine identical to the [[6/5]] "minor third", due to the extreme flatness of 10/9. An interval in the neutral third range is not found for a long time (until 17 generators up), and as a result that interval varies drastically depending on the tuning. This also means that the [[27/20]] "acute fourth" of the JI diatonic scale is equivalent to [[11/8]] (rather than becoming 4/3 as in meantone). | ||
The interval representing both [[25/24]] and [[81/80]] can be found in this interval chain at -7 steps, and ranges from about 45 to 80 cents depending on the tuning. | The interval representing both [[25/24]] and [[81/80]] can be found in this interval chain at -7 steps, and ranges from about 45 to 80 cents depending on the tuning. This can be considered the "chroma" of porcupine temperament. | ||
== Chords == | == Chords == | ||