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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]] and do not have numbers 70 or more. 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, round down if halfway. I might do another one based on [[50edo]] and meanpop too...
 
[[13-limit]] ratios are based on [[grosstone]] and are 69–integer–limit. They are valid to the amount of fifths, and need not necessarily convert to the same interval.
 
The base intervals come from the circle of fifths from -7 to 7 fifths: diminished octave, diminished fifth, minor second, minor sixth, minor third, minor seventh, fourth, unison, fifth, major second, major sixth, major third, major seventh, augmented fourth a d augmented unison. This is unlike Igliashon's [[Extra-Diatonic Intervals]], which only uses -5 to +5 fifths. The reasoning for the expanded range is that a chromatic scale is made of 6 augmented fourths and 6 diminished fifths, as well as 7 minor seconds and 5 augmented unisons. In the other hand, the diminished fourth at -8 fifths is considered a wolf major third in [[5-limit]], and a septimal major third in [[7-limit]], so this system names it a high major third instead.


{| class="wikitable"
{| class="wikitable"
|-
|-
|interval
|interval
|31edo steps
|[[31edo]] steps
|43edo steps
|[[43edo]] steps
|74edo steps
|[[74edo]] steps
|43edo cents
|43edo [[cent]]s
|fifths
|fifths
|13–limit ratios
|[[13-limit]] ratios
|-
|-
|unison
|unison
Line 25: Line 29:
|27.907
|27.907
| -12
| -12
|36/35, 50/49, 56/55, 64/63
|36/35, 45/44, 50/49, 56/55, 64/63
|-
|-
|low augmented unison
|low augmented unison
Line 41: Line 45:
|83.721
|83.721
| +7
| +7
|21/20, 25/24, 28/27
|21/20, 22/21, 25/24, 28/27
|-
|-
|minor second
|minor second
Line 162: Line 166:
| -1
| -1
|4/3, 27/20, 66/49
|4/3, 27/20, 66/49
|-
|high fourth
|14
|19
|33
|530.233
| -13
|15/11, 65/48
|-
|low augmented fourth
|14
|20
|34
|558.140
| +18
|11/8, 18/13, 49/36
|-
|augmented fourth
|15
|21
|36
|586.047
| +6
|7/5, 25/18, 45/32
|-
|diminished fifth
|16
|22
|38
|613.953
| -6
|10/7, 36/25, 63/44, 64/45
|-
|high diminished fifth
|17
|23
|40
|641.860
| -18
|13/9, 16/11
|-
|low fifth
|17
|24
|41
|669.767
| +13
|22/15
|-
|fifth
|18
|25
|43
|697.674
| +1
|3/2, 40/27, 49/33
|-
|high fifth
|19
|26
|45
|725.581
| -11
|32/21, 54/35
|-
|fifth–sixth
|19
|27
|46
|753.488
| +20
|20/13, 49/32, 55/36
|-
|low minor sixth
|20
|28
|48
|781.395
| +8
|11/7, 14/9, 25/16, 63/40
|-
|minor sixth
|21
|29
|50
|809.302
| -4
|8/5, 45/28
|-
|low neutral sixth
|22
|30
|52
|837.209
| -16
|13/8, 18/11
|-
|high neutral sixth
|22
|31
|53
|865.116
| +15
|33/20, 44/27, 49/30, 64/39
|-
|major sixth
|23
|32
|55
|893.023
| +3
|5/3, 27/16, 42/25
|-
|high major sixth
|24
|33
|57
|920.930
| -9
|12/7, 56/33
|-
|sixth–seventh
|25
|34
|59
|948.837
| -21
|26/15
|-
|low minor seventh
|25
|35
|60
|976.744
| +10
|7/4
|-
|minor seventh
|26
|36
|62
|1004.651
| -2
|9/5, 16/9, 25/14
|-
|low neutral seventh
|27
|37
|64
|1032.558
| -14
|20/11, 65/36
|-
|high neutral seventh
|27
|38
|65
|1060.465
| +17
|11/6, 24/13, 49/27
|-
|major seventh
|28
|39
|67
|1088.372
| +5
|15/8, 28/15, 50/27, 66/35
|-
|diminished octave
|29
|40
|69
|1116.279
| -7
|21/11, 27/14, 40/21, 48/25
|-
|high diminished octave
|30
|41
|71
|1144.186
| -19
|39/20, 52/27, 64/33
|-
|low octave
|30
|42
|72
|1172.093
| +12
|35/18, 49/25, 55/28, 63/32
|-
|octave
|31
|43
|74
|1200
| 0
|2/1
|}
|}
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