31edo: Difference between revisions
→Intervals: split for a CLEAN interval table |
→Intervals: + a fairly undisputed interval category system for this specific edo |
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| Line 41: | Line 41: | ||
! # | ! # | ||
! Cents | ! Cents | ||
! Interval categories | |||
! Approximate ratios<ref group="note">{{sg|limit=23-limit}} Inconsistent intervals are in ''italics''.</ref> | ! Approximate ratios<ref group="note">{{sg|limit=23-limit}} Inconsistent intervals are in ''italics''.</ref> | ||
! [[Kite's ups and downs notation|Ups and downs notation]] | ! [[Kite's ups and downs notation|Ups and downs notation]] | ||
| Line 46: | Line 47: | ||
| 0 | | 0 | ||
| 0.0 | | 0.0 | ||
| Unison | |||
| [[1/1]] | | [[1/1]] | ||
| {{UDnote|step=0}} | | {{UDnote|step=0}} | ||
| Line 51: | Line 53: | ||
| 1 | | 1 | ||
| 38.7 | | 38.7 | ||
| Super-unison | |||
| [[45/44]], [[49/48]], [[46/45]], [[128/125]], [[36/35]] | | [[45/44]], [[49/48]], [[46/45]], [[128/125]], [[36/35]] | ||
| {{UDnote|step=1}} | | {{UDnote|step=1}} | ||
| Line 56: | Line 59: | ||
| 2 | | 2 | ||
| 77.4 | | 77.4 | ||
| Subminor second | |||
| [[25/24]], [[21/20]], [[22/21]], [[23/22]] | | [[25/24]], [[21/20]], [[22/21]], [[23/22]] | ||
| {{UDnote|step=2}} | | {{UDnote|step=2}} | ||
| Line 61: | Line 65: | ||
| 3 | | 3 | ||
| 116.1 | | 116.1 | ||
| Minor second | |||
| [[15/14]], [[16/15]] | | [[15/14]], [[16/15]] | ||
| {{UDnote|step=3}} | | {{UDnote|step=3}} | ||
| Line 66: | Line 71: | ||
| 4 | | 4 | ||
| 154.8 | | 154.8 | ||
| Neutral second | |||
| [[12/11]], [[11/10]], [[35/32]] | | [[12/11]], [[11/10]], [[35/32]] | ||
| {{UDnote|step=4}} | | {{UDnote|step=4}} | ||
| Line 71: | Line 77: | ||
| 5 | | 5 | ||
| 193.5 | | 193.5 | ||
| Major second | |||
| [[9/8]], [[10/9]], [[19/17]], [[28/25]] | | [[9/8]], [[10/9]], [[19/17]], [[28/25]] | ||
| {{UDnote|step=5}} | | {{UDnote|step=5}} | ||
| Line 76: | Line 83: | ||
| 6 | | 6 | ||
| 232.3 | | 232.3 | ||
| Supermajor second | |||
| [[8/7]], [[144/125]] | | [[8/7]], [[144/125]] | ||
| {{UDnote|step=6}} | | {{UDnote|step=6}} | ||
| Line 81: | Line 89: | ||
| 7 | | 7 | ||
| 271.0 | | 271.0 | ||
| Subminor third | |||
| [[7/6]], [[75/64]] | | [[7/6]], [[75/64]] | ||
| {{UDnote|step=7}} | | {{UDnote|step=7}} | ||
| Line 86: | Line 95: | ||
| 8 | | 8 | ||
| 309.7 | | 309.7 | ||
| Minor third | |||
| [[6/5]], ''[[13/11]]'', [[25/21]] | | [[6/5]], ''[[13/11]]'', [[25/21]] | ||
| {{UDnote|step=8}} | | {{UDnote|step=8}} | ||
| Line 91: | Line 101: | ||
| 9 | | 9 | ||
| 348.4 | | 348.4 | ||
| Neutral third | |||
| [[11/9]], [[27/22]], [[16/13]], [[60/49]], [[49/40]] | | [[11/9]], [[27/22]], [[16/13]], [[60/49]], [[49/40]] | ||
| {{UDnote|step=9}} | | {{UDnote|step=9}} | ||
| Line 96: | Line 107: | ||
| 10 | | 10 | ||
| 387.1 | | 387.1 | ||
| Major third | |||
| [[5/4]] | | [[5/4]] | ||
| {{UDnote|step=10}} | | {{UDnote|step=10}} | ||
| Line 101: | Line 113: | ||
| 11 | | 11 | ||
| 425.8 | | 425.8 | ||
| Supermajor third | |||
| [[9/7]], [[14/11]], [[23/18]], [[32/25]] | | [[9/7]], [[14/11]], [[23/18]], [[32/25]] | ||
| {{UDnote|step=11}} | | {{UDnote|step=11}} | ||
| Line 106: | Line 119: | ||
| 12 | | 12 | ||
| 464.5 | | 464.5 | ||
| Subfourth | |||
| [[21/16]], [[64/49]], [[13/10]], [[17/13]], [[125/96]] | | [[21/16]], [[64/49]], [[13/10]], [[17/13]], [[125/96]] | ||
| {{UDnote|step=12}} | | {{UDnote|step=12}} | ||
| Line 111: | Line 125: | ||
| 13 | | 13 | ||
| 503.2 | | 503.2 | ||
| Perfect fourth | |||
| [[4/3]] | | [[4/3]] | ||
| {{UDnote|step=13}} | | {{UDnote|step=13}} | ||
| Line 116: | Line 131: | ||
| 14 | | 14 | ||
| 541.9 | | 541.9 | ||
| Superfourth | |||
| [[175/128]], [[11/8]], [[15/11]], ''[[18/13]]'', [[26/19]] | | [[175/128]], [[11/8]], [[15/11]], ''[[18/13]]'', [[26/19]] | ||
| {{UDnote|step=14}} | | {{UDnote|step=14}} | ||
| Line 121: | Line 137: | ||
| 15 | | 15 | ||
| 580.6 | | 580.6 | ||
| Augmented fourth | |||
| [[7/5]], [[45/32]], [[25/18]] | | [[7/5]], [[45/32]], [[25/18]] | ||
| {{UDnote|step=15}} | | {{UDnote|step=15}} | ||
| Line 126: | Line 143: | ||
| 16 | | 16 | ||
| 619.4 | | 619.4 | ||
| Diminished fifth | |||
| [[10/7]], [[64/45]], [[36/25]] | | [[10/7]], [[64/45]], [[36/25]] | ||
| {{UDnote|step=16}} | | {{UDnote|step=16}} | ||
| Line 131: | Line 149: | ||
| 17 | | 17 | ||
| 658.1 | | 658.1 | ||
| Subfifth | |||
| [[256/175]], ''[[13/9]]'', [[16/11]], [[22/15]], [[19/13]] | | [[256/175]], ''[[13/9]]'', [[16/11]], [[22/15]], [[19/13]] | ||
| {{UDnote|step=17}} | | {{UDnote|step=17}} | ||
| Line 136: | Line 155: | ||
| 18 | | 18 | ||
| 696.8 | | 696.8 | ||
| Perfect fifth | |||
| [[3/2]] | | [[3/2]] | ||
| {{UDnote|step=18}} | | {{UDnote|step=18}} | ||
| Line 141: | Line 161: | ||
| 19 | | 19 | ||
| 735.5 | | 735.5 | ||
| Superfifth | |||
| [[32/21]], [[49/32]], [[20/13]], [[26/17]], [[192/125]] | | [[32/21]], [[49/32]], [[20/13]], [[26/17]], [[192/125]] | ||
| {{UDnote|step=19}} | | {{UDnote|step=19}} | ||
| Line 146: | Line 167: | ||
| 20 | | 20 | ||
| 774.2 | | 774.2 | ||
| Subminor sixth | |||
| [[14/9]], [[11/7]], [[25/16]] | | [[14/9]], [[11/7]], [[25/16]] | ||
| {{UDnote|step=20}} | | {{UDnote|step=20}} | ||
| Line 151: | Line 173: | ||
| 21 | | 21 | ||
| 812.9 | | 812.9 | ||
| Minor sixth | |||
| [[8/5]] | | [[8/5]] | ||
| {{UDnote|step=21}} | | {{UDnote|step=21}} | ||
| Line 156: | Line 179: | ||
| 22 | | 22 | ||
| 851.6 | | 851.6 | ||
| Neutral sixth | |||
| [[18/11]], [[44/27]], [[13/8]], [[49/30]], [[80/49]] | | [[18/11]], [[44/27]], [[13/8]], [[49/30]], [[80/49]] | ||
| {{UDnote|step=22}} | | {{UDnote|step=22}} | ||
| Line 161: | Line 185: | ||
| 23 | | 23 | ||
| 890.3 | | 890.3 | ||
| Major sixth | |||
| [[5/3]], [[42/25]] | | [[5/3]], [[42/25]] | ||
| {{UDnote|step=23}} | | {{UDnote|step=23}} | ||
| Line 166: | Line 191: | ||
| 24 | | 24 | ||
| 929.0 | | 929.0 | ||
| Supermajor sixth | |||
| [[12/7]], [[128/75]] | | [[12/7]], [[128/75]] | ||
| {{UDnote|step=24}} | | {{UDnote|step=24}} | ||
| Line 171: | Line 197: | ||
| 25 | | 25 | ||
| 967.7 | | 967.7 | ||
| Subminor seventh | |||
| [[7/4]], [[125/72]] | | [[7/4]], [[125/72]] | ||
| {{UDnote|step=25}} | | {{UDnote|step=25}} | ||
| Line 176: | Line 203: | ||
| 26 | | 26 | ||
| 1006.5 | | 1006.5 | ||
| Minor seventh | |||
| [[16/9]], [[9/5]], [[34/19]], [[25/14]] | | [[16/9]], [[9/5]], [[34/19]], [[25/14]] | ||
| {{UDnote|step=26}} | | {{UDnote|step=26}} | ||
| Line 181: | Line 209: | ||
| 27 | | 27 | ||
| 1045.2 | | 1045.2 | ||
| Neutral seventh | |||
| [[11/6]], [[20/11]], [[64/35]] | | [[11/6]], [[20/11]], [[64/35]] | ||
| {{UDnote|step=27}} | | {{UDnote|step=27}} | ||
| Line 186: | Line 215: | ||
| 28 | | 28 | ||
| 1083.9 | | 1083.9 | ||
| Major seventh | |||
| [[28/15]], [[15/8]] | | [[28/15]], [[15/8]] | ||
| {{UDnote|step=28}} | | {{UDnote|step=28}} | ||
| Line 191: | Line 221: | ||
| 29 | | 29 | ||
| 1122.6 | | 1122.6 | ||
| Supermajor seventh | |||
| [[48/25]], [[40/21]], [[21/11]], [[44/23]] | | [[48/25]], [[40/21]], [[21/11]], [[44/23]] | ||
| {{UDnote|step=29}} | | {{UDnote|step=29}} | ||
| Line 196: | Line 227: | ||
| 30 | | 30 | ||
| 1161.3 | | 1161.3 | ||
| Sub-octave | |||
| [[88/45]], [[96/49]], [[45/23]], [[125/64]], [[35/18]] | | [[88/45]], [[96/49]], [[45/23]], [[125/64]], [[35/18]] | ||
| {{UDnote|step=30}} | | {{UDnote|step=30}} | ||
| Line 201: | Line 233: | ||
| 31 | | 31 | ||
| 1200.0 | | 1200.0 | ||
| Octave | |||
| [[2/1]] | | [[2/1]] | ||
| {{UDnote|step=31}} | | {{UDnote|step=31}} | ||