User:PiotrGrochowski/Extra-Diatonic Intervals: Difference between revisions

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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 unrelated to the circle of fifths, normalize it to 43edo steps, then round. 13–limit ratios are based on [[grosstone]].
[[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, normalize it to 43edo steps, then round. 13–limit ratios are based on [[grosstone]]. I might do another one based on [[50edo]] and meanpop instead...


{| class="wikitable"
{| class="wikitable"
Line 27: Line 27:
|36/35, 50/49, 56/55, 64/63
|36/35, 50/49, 56/55, 64/63
|-
|-
|audible unison
|low augmented unison
|1
|1
|2
|2
Line 49: Line 49:
|10
|10
| -5
| -5
|9/8, 10/9, 28/25, 49/44, 55/49
|
|-
|-
|neutral second low
|lesser neutral second
|4
|4
|5
|5
Line 58: Line 58:
| -17
| -17
|12/11
|12/11
|-
|greater neutral second
|4
|6
|10
|14
| +14
|11/10
|-
|major second
|5
|7
|12
|17
| +2
|9/8, 10/9, 28/25, 49/44, 55/49
|}
|}

Revision as of 06:43, 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 circle of fifths, normalize it to 43edo steps, then round. 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 fifths 13–limit ratios
unison 0 0 0 0 0 1/1
comma unison 1 1 2 3 -12 36/35, 50/49, 56/55, 64/63
low augmented unison 1 2 3 4 +19 27/26, 33/32, 40/39, 49/48, 55/54
augmented unison 2 3 5 7 +7 21/20, 25/24, 28/27
minor second 3 4 7 10 -5
lesser neutral second 4 5 9 13 -17 12/11
greater neutral second 4 6 10 14 +14 11/10
major second 5 7 12 17 +2 9/8, 10/9, 28/25, 49/44, 55/49
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