31edo: Difference between revisions
→Intervals: sort intervals by complexity |
→Intervals: - complex ratios. + some absolutely critical but missing ones |
||
| Line 42: | Line 42: | ||
! Cents | ! Cents | ||
! Interval categories | ! Interval categories | ||
! Approximate ratios<ref group="note"> | ! 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]] | ! [[Kite's ups and downs notation|Ups and downs notation]] | ||
|- | |- | ||
| Line 54: | Line 54: | ||
| 38.7 | | 38.7 | ||
| Super-unison | | Super-unison | ||
| [[36/35]], [[45/44]], [[ | | [[36/35]], [[45/44]], [[49/48]], [[50/49]], [[64/63]] | ||
| {{UDnote|step=1}} | | {{UDnote|step=1}} | ||
|- | |- | ||
| Line 60: | Line 60: | ||
| 77.4 | | 77.4 | ||
| Subminor second | | Subminor second | ||
| [[21/20]], [[22/21]], [[23/22]], [[25/24]] | | [[21/20]], [[22/21]], [[23/22]], [[25/24]], [[28/27]] | ||
| {{UDnote|step=2}} | | {{UDnote|step=2}} | ||
|- | |- | ||
| Line 66: | Line 66: | ||
| 116.1 | | 116.1 | ||
| Minor second | | Minor second | ||
| [[15/14]], [[16/15]] | | [[14/13]], [[15/14]], [[16/15]] | ||
| {{UDnote|step=3}} | | {{UDnote|step=3}} | ||
|- | |- | ||
| Line 72: | Line 72: | ||
| 154.8 | | 154.8 | ||
| Neutral second | | Neutral second | ||
| [[11/10]], [[12/11]], [[ | | [[11/10]], [[12/11]], [[13/12]] | ||
| {{UDnote|step=4}} | | {{UDnote|step=4}} | ||
|- | |- | ||
| Line 84: | Line 84: | ||
| 232.3 | | 232.3 | ||
| Supermajor second | | Supermajor second | ||
| [[8/7 | | [[8/7]] | ||
| {{UDnote|step=6}} | | {{UDnote|step=6}} | ||
|- | |- | ||
| Line 90: | Line 90: | ||
| 271.0 | | 271.0 | ||
| Subminor third | | Subminor third | ||
| [[7/6 | | [[7/6]] | ||
| {{UDnote|step=7}} | | {{UDnote|step=7}} | ||
|- | |- | ||
| Line 102: | Line 102: | ||
| 348.4 | | 348.4 | ||
| Neutral third | | Neutral third | ||
| [[11/9]], [[16/13 | | [[11/9]], [[16/13]] | ||
| {{UDnote|step=9}} | | {{UDnote|step=9}} | ||
|- | |- | ||
| Line 120: | Line 120: | ||
| 464.5 | | 464.5 | ||
| Subfourth | | Subfourth | ||
| [[13/10]], [[17/13]], [[21/16 | | [[13/10]], [[17/13]], [[21/16]] | ||
| {{UDnote|step=12}} | | {{UDnote|step=12}} | ||
|- | |- | ||
| Line 132: | Line 132: | ||
| 541.9 | | 541.9 | ||
| Superfourth | | Superfourth | ||
| [[11/8]], [[15/11]], [[26/19 | | [[11/8]], [[15/11]], [[26/19]], ''[[18/13]]'' | ||
| {{UDnote|step=14}} | | {{UDnote|step=14}} | ||
|- | |- | ||
| Line 150: | Line 150: | ||
| 658.1 | | 658.1 | ||
| Subfifth | | Subfifth | ||
| [[16/11]], [[19/13]], [[22/15 | | [[16/11]], [[19/13]], [[22/15]], ''[[13/9]]'' | ||
| {{UDnote|step=17}} | | {{UDnote|step=17}} | ||
|- | |- | ||
| Line 162: | Line 162: | ||
| 735.5 | | 735.5 | ||
| Superfifth | | Superfifth | ||
| [[20/13]], [[26/17]], [[32/21 | | [[20/13]], [[26/17]], [[32/21]] | ||
| {{UDnote|step=19}} | | {{UDnote|step=19}} | ||
|- | |- | ||
| Line 180: | Line 180: | ||
| 851.6 | | 851.6 | ||
| Neutral sixth | | Neutral sixth | ||
| [[13/8]], [[18/11 | | [[13/8]], [[18/11]] | ||
| {{UDnote|step=22}} | | {{UDnote|step=22}} | ||
|- | |- | ||
| Line 186: | Line 186: | ||
| 890.3 | | 890.3 | ||
| Major sixth | | Major sixth | ||
| [[5/3]], [[42/25]] | | [[5/3]], [[42/25]], ''[[22/13]]'' | ||
| {{UDnote|step=23}} | | {{UDnote|step=23}} | ||
|- | |- | ||
| Line 192: | Line 192: | ||
| 929.0 | | 929.0 | ||
| Supermajor sixth | | Supermajor sixth | ||
| [[12/7 | | [[12/7]] | ||
| {{UDnote|step=24}} | | {{UDnote|step=24}} | ||
|- | |- | ||
| Line 198: | Line 198: | ||
| 967.7 | | 967.7 | ||
| Subminor seventh | | Subminor seventh | ||
| [[7/4 | | [[7/4]] | ||
| {{UDnote|step=25}} | | {{UDnote|step=25}} | ||
|- | |- | ||
| Line 210: | Line 210: | ||
| 1045.2 | | 1045.2 | ||
| Neutral seventh | | Neutral seventh | ||
| [[11/6]], [[20/11]], [[ | | [[11/6]], [[20/11]], [[24/13]] | ||
| {{UDnote|step=27}} | | {{UDnote|step=27}} | ||
|- | |- | ||
| Line 216: | Line 216: | ||
| 1083.9 | | 1083.9 | ||
| Major seventh | | Major seventh | ||
| [[15/8]], [[28/15]] | | [[13/7]], [[15/8]], [[28/15]] | ||
| {{UDnote|step=28}} | | {{UDnote|step=28}} | ||
|- | |- | ||
| Line 222: | Line 222: | ||
| 1122.6 | | 1122.6 | ||
| Supermajor seventh | | Supermajor seventh | ||
| [[21/11]], [[40/21]], [[44/23]], [[48/25]] | | [[21/11]], [[27/14]], [[40/21]], [[44/23]], [[48/25]] | ||
| {{UDnote|step=29}} | | {{UDnote|step=29}} | ||
|- | |- | ||
| Line 228: | Line 228: | ||
| 1161.3 | | 1161.3 | ||
| Sub-octave | | Sub-octave | ||
| [[35/18]], [[ | | [[35/18]], [[49/25]], [[63/32]], [[88/45]], [[96/49]] | ||
| {{UDnote|step=30}} | | {{UDnote|step=30}} | ||
|- | |- | ||