User:PiotrGrochowski/Extra-Diatonic Intervals: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
add 43edo cents for convenience |
||
| Line 1: | Line 1: | ||
[[Extra-Diatonic Intervals]] tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like [[43edo]], [[74edo]] or [[105edo]]. To convert an interval unrelated to the circle of fifths, | [[Extra-Diatonic Intervals]] tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like [[43edo]], [[74edo]] or [[105edo]]. To convert an interval unrelated to the grosstone circle of fifths, such as superpyth intervals, select the closest 43edo interval. 13–limit ratios are based on [[grosstone]]. I might do another one based on [[50edo]] and meanpop instead... | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 10: | Line 8: | ||
|74edo steps | |74edo steps | ||
|105edo steps | |105edo steps | ||
|43edo cents | |||
|fifths | |fifths | ||
|13–limit ratios | |13–limit ratios | ||
|- | |- | ||
|unison | |unison | ||
|0 | |||
|0 | |0 | ||
|0 | |0 | ||
| Line 26: | Line 26: | ||
|2 | |2 | ||
|3 | |3 | ||
|27.907 | |||
| -12 | | -12 | ||
|36/35, 50/49, 56/55, 64/63 | |36/35, 50/49, 56/55, 64/63 | ||
| Line 34: | Line 35: | ||
|3 | |3 | ||
|4 | |4 | ||
|55.814 | |||
| +19 | | +19 | ||
|27/26, 33/32, 40/39, 49/48, 55/54 | |27/26, 33/32, 40/39, 49/48, 55/54 | ||
| Line 42: | Line 44: | ||
|5 | |5 | ||
|7 | |7 | ||
|83.721 | |||
| +7 | | +7 | ||
|21/20, 25/24, 28/27 | |21/20, 25/24, 28/27 | ||
| Line 50: | Line 53: | ||
|7 | |7 | ||
|10 | |10 | ||
|111.628 | |||
| -5 | | -5 | ||
|15/14, 16/15, 27/25, 35/33 | |15/14, 16/15, 27/25, 35/33 | ||
| Line 58: | Line 62: | ||
|9 | |9 | ||
|13 | |13 | ||
|139.535 | |||
| -17 | | -17 | ||
|12/11, 13/12, 54/49 | |12/11, 13/12, 54/49 | ||
| Line 66: | Line 71: | ||
|10 | |10 | ||
|14 | |14 | ||
|167.442 | |||
| +14 | | +14 | ||
|11/10, 49/45 | |11/10, 49/45 | ||
| Line 74: | Line 80: | ||
|12 | |12 | ||
|17 | |17 | ||
|195.349 | |||
| +2 | | +2 | ||
|9/8, 10/9, 28/25, 49/44, 55/49 | |9/8, 10/9, 28/25, 49/44, 55/49 | ||
|} | |} | ||
Revision as of 07:15, 1 October 2018
Extra-Diatonic Intervals tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like 43edo, 74edo or 105edo. To convert an interval unrelated to the grosstone circle of fifths, such as superpyth intervals, select the closest 43edo interval. 13–limit ratios are based on grosstone. I might do another one based on 50edo and meanpop instead...
| interval | 31edo steps | 43edo steps | 74edo steps | 105edo steps | 43edo cents | fifths | 13–limit ratios |
| unison | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 |
| comma unison | 1 | 1 | 2 | 3 | 27.907 | -12 | 36/35, 50/49, 56/55, 64/63 |
| low augmented unison | 1 | 2 | 3 | 4 | 55.814 | +19 | 27/26, 33/32, 40/39, 49/48, 55/54 |
| augmented unison | 2 | 3 | 5 | 7 | 83.721 | +7 | 21/20, 25/24, 28/27 |
| minor second | 3 | 4 | 7 | 10 | 111.628 | -5 | 15/14, 16/15, 27/25, 35/33 |
| lesser neutral second | 4 | 5 | 9 | 13 | 139.535 | -17 | 12/11, 13/12, 54/49 |
| greater neutral second | 4 | 6 | 10 | 14 | 167.442 | +14 | 11/10, 49/45 |
| major second | 5 | 7 | 12 | 17 | 195.349 | +2 | 9/8, 10/9, 28/25, 49/44, 55/49 |