31edo: Difference between revisions
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→Intervals: added interval names to the main table |
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! Interval categories | ! Interval categories | ||
! Approximate ratios<ref group="note">As a 13-limit temperament, with additional ratios of 17, 19, and 23. Inconsistent intervals are in ''italics''.</ref> | ! Approximate ratios<ref group="note">As a 13-limit temperament, with additional ratios of 17, 19, and 23. Inconsistent intervals are in ''italics''.</ref> | ||
! [[Kite's ups and downs notation|Ups and downs notation]] | ! colspan="2" |[[Kite's ups and downs notation|Ups and downs notation]] | ||
([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and vd2) | |||
|- | |- | ||
| 0 | | 0 | ||
| Line 64: | Line 65: | ||
| Unison | | Unison | ||
| [[1/1]] | | [[1/1]] | ||
|P1 | |||
| {{UDnote|step=0}} | | {{UDnote|step=0}} | ||
|- | |- | ||
| Line 70: | Line 72: | ||
| Super-unison | | Super-unison | ||
| [[36/35]], [[45/44]], [[49/48]], [[50/49]], [[64/63]], [[128/125]] | | [[36/35]], [[45/44]], [[49/48]], [[50/49]], [[64/63]], [[128/125]] | ||
|^1, d2 | |||
| {{UDnote|step=1}} | | {{UDnote|step=1}} | ||
|- | |- | ||
| Line 76: | Line 79: | ||
| Subminor second | | Subminor second | ||
| [[21/20]], [[22/21]], [[23/22]], [[25/24]], [[28/27]] | | [[21/20]], [[22/21]], [[23/22]], [[25/24]], [[28/27]] | ||
|A1, vm2 | |||
| {{UDnote|step=2}} | | {{UDnote|step=2}} | ||
|- | |- | ||
| Line 82: | Line 86: | ||
| Minor second | | Minor second | ||
| [[14/13]], [[15/14]], [[16/15]] | | [[14/13]], [[15/14]], [[16/15]] | ||
|m2 | |||
| {{UDnote|step=3}} | | {{UDnote|step=3}} | ||
|- | |- | ||
| Line 88: | Line 93: | ||
| Neutral second | | Neutral second | ||
| [[11/10]], [[12/11]], [[13/12]], [[35/32]] | | [[11/10]], [[12/11]], [[13/12]], [[35/32]] | ||
|~2 | |||
| {{UDnote|step=4}} | | {{UDnote|step=4}} | ||
|- | |- | ||
| Line 94: | Line 100: | ||
| Major second | | Major second | ||
| [[9/8]], [[10/9]], [[19/17]], [[28/25]] | | [[9/8]], [[10/9]], [[19/17]], [[28/25]] | ||
|M2 | |||
| {{UDnote|step=5}} | | {{UDnote|step=5}} | ||
|- | |- | ||
| Line 100: | Line 107: | ||
| Supermajor second | | Supermajor second | ||
| [[8/7]] | | [[8/7]] | ||
|^M2 | |||
| {{UDnote|step=6}} | | {{UDnote|step=6}} | ||
|- | |- | ||
| Line 106: | Line 114: | ||
| Subminor third | | Subminor third | ||
| [[7/6]] | | [[7/6]] | ||
|vm3 | |||
| {{UDnote|step=7}} | | {{UDnote|step=7}} | ||
|- | |- | ||
| Line 112: | Line 121: | ||
| Minor third | | Minor third | ||
| [[6/5]], [[25/21]], ''[[13/11]]'' | | [[6/5]], [[25/21]], ''[[13/11]]'' | ||
|m3 | |||
| {{UDnote|step=8}} | | {{UDnote|step=8}} | ||
|- | |- | ||
| Line 118: | Line 128: | ||
| Neutral third | | Neutral third | ||
| [[11/9]], [[16/13]] | | [[11/9]], [[16/13]] | ||
|~3 | |||
| {{UDnote|step=9}} | | {{UDnote|step=9}} | ||
|- | |- | ||
| Line 124: | Line 135: | ||
| Major third | | Major third | ||
| [[5/4]] | | [[5/4]] | ||
|M3 | |||
| {{UDnote|step=10}} | | {{UDnote|step=10}} | ||
|- | |- | ||
| Line 130: | Line 142: | ||
| Supermajor third | | Supermajor third | ||
| [[9/7]], [[14/11]], [[23/18]], [[32/25]] | | [[9/7]], [[14/11]], [[23/18]], [[32/25]] | ||
|^M3 | |||
| {{UDnote|step=11}} | | {{UDnote|step=11}} | ||
|- | |- | ||
| Line 136: | Line 149: | ||
| Subfourth | | Subfourth | ||
| [[13/10]], [[17/13]], [[21/16]] | | [[13/10]], [[17/13]], [[21/16]] | ||
|v4 | |||
| {{UDnote|step=12}} | | {{UDnote|step=12}} | ||
|- | |- | ||
| Line 142: | Line 156: | ||
| Perfect fourth | | Perfect fourth | ||
| [[4/3]] | | [[4/3]] | ||
|P4 | |||
| {{UDnote|step=13}} | | {{UDnote|step=13}} | ||
|- | |- | ||
| Line 148: | Line 163: | ||
| Superfourth | | Superfourth | ||
| [[11/8]], [[15/11]], [[26/19]], ''[[18/13]]'', [[48/35]] | | [[11/8]], [[15/11]], [[26/19]], ''[[18/13]]'', [[48/35]] | ||
|^4, ~4 | |||
| {{UDnote|step=14}} | | {{UDnote|step=14}} | ||
|- | |- | ||
| Line 154: | Line 170: | ||
| Augmented fourth | | Augmented fourth | ||
| [[7/5]], [[25/18]], [[45/32]] | | [[7/5]], [[25/18]], [[45/32]] | ||
|A4, vd5 | |||
| {{UDnote|step=15}} | | {{UDnote|step=15}} | ||
|- | |- | ||
| Line 160: | Line 177: | ||
| Diminished fifth | | Diminished fifth | ||
| [[10/7]], [[36/25]], [[64/45]] | | [[10/7]], [[36/25]], [[64/45]] | ||
|^A4, d5 | |||
| {{UDnote|step=16}} | | {{UDnote|step=16}} | ||
|- | |- | ||
| Line 166: | Line 184: | ||
| Subfifth | | Subfifth | ||
| [[16/11]], [[19/13]], [[22/15]], ''[[13/9]]'', [[35/24]] | | [[16/11]], [[19/13]], [[22/15]], ''[[13/9]]'', [[35/24]] | ||
|v5, ~5 | |||
| {{UDnote|step=17}} | | {{UDnote|step=17}} | ||
|- | |- | ||
| Line 172: | Line 191: | ||
| Perfect fifth | | Perfect fifth | ||
| [[3/2]] | | [[3/2]] | ||
|P5 | |||
| {{UDnote|step=18}} | | {{UDnote|step=18}} | ||
|- | |- | ||
| Line 178: | Line 198: | ||
| Superfifth | | Superfifth | ||
| [[20/13]], [[26/17]], [[32/21]] | | [[20/13]], [[26/17]], [[32/21]] | ||
|^5 | |||
| {{UDnote|step=19}} | | {{UDnote|step=19}} | ||
|- | |- | ||
| Line 184: | Line 205: | ||
| Subminor sixth | | Subminor sixth | ||
| [[11/7]], [[14/9]], [[25/16]] | | [[11/7]], [[14/9]], [[25/16]] | ||
|vm6 | |||
| {{UDnote|step=20}} | | {{UDnote|step=20}} | ||
|- | |- | ||
| Line 190: | Line 212: | ||
| Minor sixth | | Minor sixth | ||
| [[8/5]] | | [[8/5]] | ||
|m6 | |||
| {{UDnote|step=21}} | | {{UDnote|step=21}} | ||
|- | |- | ||
| Line 196: | Line 219: | ||
| Neutral sixth | | Neutral sixth | ||
| [[13/8]], [[18/11]] | | [[13/8]], [[18/11]] | ||
|~6 | |||
| {{UDnote|step=22}} | | {{UDnote|step=22}} | ||
|- | |- | ||
| Line 202: | Line 226: | ||
| Major sixth | | Major sixth | ||
| [[5/3]], [[42/25]], ''[[22/13]]'' | | [[5/3]], [[42/25]], ''[[22/13]]'' | ||
|M6 | |||
| {{UDnote|step=23}} | | {{UDnote|step=23}} | ||
|- | |- | ||
| Line 208: | Line 233: | ||
| Supermajor sixth | | Supermajor sixth | ||
| [[12/7]] | | [[12/7]] | ||
|^M6 | |||
| {{UDnote|step=24}} | | {{UDnote|step=24}} | ||
|- | |- | ||
| Line 214: | Line 240: | ||
| Subminor seventh | | Subminor seventh | ||
| [[7/4]] | | [[7/4]] | ||
|vm7 | |||
| {{UDnote|step=25}} | | {{UDnote|step=25}} | ||
|- | |- | ||
| Line 220: | Line 247: | ||
| Minor seventh | | Minor seventh | ||
| [[9/5]], [[16/9]], [[25/14]], [[34/19]] | | [[9/5]], [[16/9]], [[25/14]], [[34/19]] | ||
|m7 | |||
| {{UDnote|step=26}} | | {{UDnote|step=26}} | ||
|- | |- | ||
| Line 226: | Line 254: | ||
| Neutral seventh | | Neutral seventh | ||
| [[11/6]], [[20/11]], [[24/13]], [[64/35]] | | [[11/6]], [[20/11]], [[24/13]], [[64/35]] | ||
|~7 | |||
| {{UDnote|step=27}} | | {{UDnote|step=27}} | ||
|- | |- | ||
| Line 232: | Line 261: | ||
| Major seventh | | Major seventh | ||
| [[13/7]], [[15/8]], [[28/15]] | | [[13/7]], [[15/8]], [[28/15]] | ||
|M7 | |||
| {{UDnote|step=28}} | | {{UDnote|step=28}} | ||
|- | |- | ||
| Line 238: | Line 268: | ||
| Supermajor seventh | | Supermajor seventh | ||
| [[21/11]], [[27/14]], [[40/21]], [[44/23]], [[48/25]] | | [[21/11]], [[27/14]], [[40/21]], [[44/23]], [[48/25]] | ||
|^M7 | |||
| {{UDnote|step=29}} | | {{UDnote|step=29}} | ||
|- | |- | ||
| Line 244: | Line 275: | ||
| Sub-octave | | Sub-octave | ||
| [[35/18]], [[49/25]], [[63/32]], [[88/45]], [[96/49]], [[125/64]] | | [[35/18]], [[49/25]], [[63/32]], [[88/45]], [[96/49]], [[125/64]] | ||
|v8 | |||
| {{UDnote|step=30}} | | {{UDnote|step=30}} | ||
|- | |- | ||
| Line 250: | Line 282: | ||
| Octave | | Octave | ||
| [[2/1]] | | [[2/1]] | ||
|P8 | |||
| {{UDnote|step=31}} | | {{UDnote|step=31}} | ||
|} | |} | ||