Xenharmonic Wiki

31edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
→Intervals: split for a CLEAN interval table
→Intervals: + a fairly undisputed interval category system for this specific edo
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}}
Retrieved from "https://en.xen.wiki/w/31edo"