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
complete up to fourth, add info about fractions and make "comma unison" consistent by renaming it to "high unison"
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[[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...
[[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]] and do not have numbers 70 or more. I might do another one based on [[50edo]] and meanpop too...


{| class="wikitable"
{| class="wikitable"
Line 19: Line 19:
|1/1
|1/1
|-
|-
|comma unison
|high unison
|1
|1
|1
|1
Line 117: Line 117:
|high neutral third
|high neutral third
|9
|9
|
|13
|22
|362.791
| +16
|11/9, 16/13, 49/40
|-
|major third
|10
|14
|24
|390.698
| +4
|5/4, 56/45, 63/50
|-
|high major third
|11
|15
|26
|418.605
| -8
|9/7, 14/11, 32/25
|-
|third–fourth
|12
|16
|28
|446.512
| -20
|13/10, 64/49
|-
|low fourth
|12
|17
|29
|474.419
| +11
|21/16, 35/27, 55/42
|-
|fourth
|13
|18
|31
|502.326
| -1
|4/3, 27/20, 66/49
|}
|}

Revision as of 18:00, 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 and do not have numbers 70 or more. 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
high 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 13 22 362.791 +16 11/9, 16/13, 49/40
major third 10 14 24 390.698 +4 5/4, 56/45, 63/50
high major third 11 15 26 418.605 -8 9/7, 14/11, 32/25
third–fourth 12 16 28 446.512 -20 13/10, 64/49
low fourth 12 17 29 474.419 +11 21/16, 35/27, 55/42
fourth 13 18 31 502.326 -1 4/3, 27/20, 66/49
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