User:PiotrGrochowski/Extra-Diatonic Intervals: Difference between revisions
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ditch the 105edo column, it produces an uneven 3–1 step scale that may be inconsistent |
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| Line 7: | Line 7: | ||
|43edo steps | |43edo steps | ||
|74edo steps | |74edo steps | ||
|43edo cents | |43edo cents | ||
|fifths | |fifths | ||
| Line 13: | Line 12: | ||
|- | |- | ||
|unison | |unison | ||
|0 | |0 | ||
|0 | |0 | ||
| Line 25: | Line 23: | ||
|1 | |1 | ||
|2 | |2 | ||
|27.907 | |27.907 | ||
| -12 | | -12 | ||
| Line 34: | Line 31: | ||
|2 | |2 | ||
|3 | |3 | ||
|55.814 | |55.814 | ||
| +19 | | +19 | ||
| Line 43: | Line 39: | ||
|3 | |3 | ||
|5 | |5 | ||
|83.721 | |83.721 | ||
| +7 | | +7 | ||
| Line 52: | Line 47: | ||
|4 | |4 | ||
|7 | |7 | ||
|111.628 | |111.628 | ||
| -5 | | -5 | ||
| Line 61: | Line 55: | ||
|5 | |5 | ||
|9 | |9 | ||
|139.535 | |139.535 | ||
| -17 | | -17 | ||
| Line 70: | Line 63: | ||
|6 | |6 | ||
|10 | |10 | ||
|167.442 | |167.442 | ||
| +14 | | +14 | ||
| Line 79: | Line 71: | ||
|7 | |7 | ||
|12 | |12 | ||
|195.349 | |195.349 | ||
| +2 | | +2 | ||
| Line 88: | Line 79: | ||
|8 | |8 | ||
|14 | |14 | ||
|223.256 | |223.256 | ||
| -10 | | -10 | ||
| Line 97: | Line 87: | ||
|9 | |9 | ||
|15 | |15 | ||
|251.163 | |251.163 | ||
| +21 | | +21 | ||
| Line 106: | Line 95: | ||
|10 | |10 | ||
|17 | |17 | ||
|279.070 | |279.070 | ||
| +9 | | +9 | ||
| Line 115: | Line 103: | ||
|11 | |11 | ||
|19 | |19 | ||
|306.977 | |306.977 | ||
| -3 | | -3 | ||
| Line 124: | Line 111: | ||
|12 | |12 | ||
|21 | |21 | ||
|334.884 | |334.884 | ||
| -15 | | -15 | ||
|27/22, 39/32, 40/33, 60/49, 65/54 | |27/22, 39/32, 40/33, 60/49, 65/54 | ||
|- | |||
|high neutral third | |||
|9 | |||
| | |||
|} | |} | ||
Revision as of 17:36, 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 to a name, select the closest 43edo interval. 13–limit ratios are based on grosstone. I might do another one based on 50edo and meanpop too...
| interval | 31edo steps | 43edo steps | 74edo steps | 43edo cents | fifths | 13–limit ratios |
| unison | 0 | 0 | 0 | 0 | 0 | 1/1 |
| comma unison | 1 | 1 | 2 | 27.907 | -12 | 36/35, 50/49, 56/55, 64/63 |
| low augmented unison | 1 | 2 | 3 | 55.814 | +19 | 27/26, 33/32, 40/39, 49/48, 55/54 |
| augmented unison | 2 | 3 | 5 | 83.721 | +7 | 21/20, 25/24, 28/27 |
| minor second | 3 | 4 | 7 | 111.628 | -5 | 15/14, 16/15, 27/25, 35/33 |
| low neutral second | 4 | 5 | 9 | 139.535 | -17 | 12/11, 13/12, 54/49 |
| high neutral second | 4 | 6 | 10 | 167.442 | +14 | 11/10, 49/45 |
| major second | 5 | 7 | 12 | 195.349 | +2 | 9/8, 10/9, 28/25, 49/44, 55/49 |
| high major second | 6 | 8 | 14 | 223.256 | -10 | 8/7 |
| second–third | 6 | 9 | 15 | 251.163 | +21 | 15/13, 55/48 |
| low minor third | 7 | 10 | 17 | 279.070 | +9 | 7/6, 33/28 |
| minor third | 8 | 11 | 19 | 306.977 | -3 | 6/5, 25/21, 32/27 |
| low neutral third | 9 | 12 | 21 | 334.884 | -15 | 27/22, 39/32, 40/33, 60/49, 65/54 |
| high neutral third | 9 |