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63edo: Difference between revisions

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Godtone (talk | contribs)
autopatrolled, emailconfirmed
2,289 edits
manually remove intervals of 75 as always being too damaged for their complexity, as evidenced by always appearing at the extreme ends of the spectrum of interpretations, if not as the most extreme entry then as the second-most, next to a vastly simpler interval that can justify the damage
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== Intervals ==
== Intervals ==
The following table was created using [[User:Godtone#My python 3 code|Godtone's code]] with the command <code><nowiki>interpret_edo(63,ol=53,no=[5,17,19,25,27,37,41,51],add=[73,75,87,89,91,93,105],dec="''",wiki=23)</nowiki></code> (run in a Python 3 interactive console) plus manual correction of the order of some inconsistent intervals.
The following table was created using [[User:Godtone#My python 3 code|Godtone's code]] with the command <code><nowiki>interpret_edo(63,ol=53,no=[5,17,19,25,27,37,41,51],add=[73,75,87,89,91,93,105],dec="''",wiki=23)</nowiki></code> (run in a Python 3 interactive console) plus manual correction of the order of some inconsistent intervals and removal of unsimplified intervals of 75.


As the command indicates, it is a(n accurate) no-5's* no-17's no-19's no-25's no-27's no-37's no-41's 49-odd-limit add-53 add-63 add-73 add-75 add-87 add-89 add-91 add-93 add-105 interpretation, tuned to the strengths of [[63edo]]. * Note that because of the cancellation of factors, some odd harmonics of 5 (the simpler/more relevant ones) are present, EG {{nowrap|75/3 {{=}} 25}}, {{nowrap|45/3 {{=}} 15}}, {{nowrap|105/75 {{=}} 7/5}}, {{nowrap| 75/35/2 {{=}} 15/14}}, and {{nowrap|45/9 {{=}} 5}}, so it isn't really "no-5's", just has a de-emphasized focus.
As the command and description indicates, it is a(n accurate) "no-5's"* no-17's no-19's no-25's no-27's no-37's no-41's 49-odd-limit add-53 add-63 add-73 add-87 add-89 add-91 add-93 add-105 interpretation, tuned to the strengths of [[63edo]]. * Note that because of the cancellation of factors, some odd harmonics of 5 (the simpler/more relevant ones) are present, EG {{nowrap|75/3 {{=}} 25}}, {{nowrap|45/3 {{=}} 15}}, {{nowrap|105/75 {{=}} 7/5}}, {{nowrap| 75/35/2 {{=}} 15/14}}, and {{nowrap|45/9 {{=}} 5}}, so it isn't really "no-5's", just has a de-emphasized focus.


Intervals are listed in order of size, so that one can know their relative order at a glance and deem the value of the interpretation for a harmonic context, and [[23-limit]] intervals are highlighted for navigability as [[13-limit]] intervals are more likely to already have pages, and as we are excluding primes 17 and 19, we are only adding prime 23 to the 13-limit.
Intervals are listed in order of size, so that one can know their relative order at a glance and deem the value of the interpretation for a harmonic context, and [[23-limit]] intervals are highlighted for navigability as [[13-limit]] intervals are more likely to already have pages, and as we are excluding primes 17 and 19, we are only adding prime 23 to the 13-limit.
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| 2
| 2
| 38.1
| 38.1
| ''[[66/65]]'', 53/52, [[49/48]], 48/47, 47/46, 93/91, [[46/45]], 91/89, [[45/44]], 89/87, 44/43, 43/42, 75/73
| ''[[66/65]]'', 53/52, [[49/48]], 48/47, 47/46, 93/91, [[46/45]], 91/89, [[45/44]], 89/87, 44/43, 43/42
|-
|-
| 3
| 3
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| 13
| 13
| 247.62
| 247.62
| ''86/75'', 84/73, 53/46, [[15/13]], [[52/45]]
| 84/73, 53/46, [[15/13]], [[52/45]]
|-
|-
| 14
| 14
| 266.67
| 266.67
| ''29/25'', 36/31, 106/91, [[7/6]], 104/89, 62/53, [[75/64]]
| ''29/25'', 36/31, 106/91, [[7/6]], 104/89, 62/53
|-
|-
| 15
| 15
| 285.71
| 285.71
| [[88/75]], 73/62, 53/45, 86/73, [[33/28]], [[46/39]], 105/89, 124/105, [[13/11]], 58/49
| 73/62, 53/45, 86/73, [[33/28]], [[46/39]], 105/89, 124/105, [[13/11]], 58/49
|-
|-
| 16
| 16
| 304.76
| 304.76
| 89/75, 106/89, 56/47, 87/73, 31/26, [[105/88]], 43/36, 104/87
| 106/89, 56/47, 87/73, 31/26, [[105/88]], 43/36, 104/87
|-
|-
| 17
| 17
| 323.81
| 323.81
| [[6/5]], 112/93, 53/44, 47/39, 88/73, 35/29, 64/53, 29/24, 52/43, 75/62
| [[6/5]], 112/93, 53/44, 47/39, 88/73, 35/29, 64/53, 29/24, 52/43
|-
|-
| 18
| 18
| 342.86
| 342.86
| [[91/75]], 73/60, [[28/23]], 106/87, [[39/32]], [[128/105]], 89/73, 105/86, [[11/9]], [[60/49]]
| 73/60, [[28/23]], 106/87, [[39/32]], [[128/105]], 89/73, 105/86, [[11/9]], [[60/49]]
|-
|-
| 19
| 19
| 361.9
| 361.9
| [[92/75]], 43/35, [[16/13]], 53/43, 90/73, 58/47, 89/72, [[26/21]]
| 43/35, [[16/13]], 53/43, 90/73, 58/47, 89/72, [[26/21]]
|-
|-
| 20
| 20
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| 21
| 21
| 400.0
| 400.0
| 94/75, [[49/39]], [[44/35]], 39/31, 112/89, 73/58, 92/73, 29/23, 53/42, [[91/72]], 62/49
| [[49/39]], [[44/35]], 39/31, 112/89, 73/58, 92/73, 29/23, 53/42, [[91/72]], 62/49
|-
|-
| 22
| 22
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| 23
| 23
| 438.1
| 438.1
| ''[[32/25]]'', [[9/7]], 112/87, 94/73, 58/45, 40/31, 31/24, 75/58
| ''[[32/25]]'', [[9/7]], 112/87, 94/73, 58/45, 40/31, 31/24
|-
|-
| 24
| 24
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| 25
| 25
| 476.19
| 476.19
| ''[[98/75]]'', [[21/16]], [[46/35]], 96/73, 29/22, [[120/91]], 62/47, 70/53
| [[21/16]], [[46/35]], 96/73, 29/22, [[120/91]], 62/47, 70/53
|-
|-
| 26
| 26
| 495.24
| 495.24
| 93/70, [[4/3]], ''[[75/56]]''
| 93/70, [[4/3]]
|-
|-
| 27
| 27
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| 30
| 30
| 571.43
| 571.43
| [[18/13]], [[104/75]], 43/31, 146/105, 89/64, [[32/23]], [[39/28]], 124/89, [[46/33]], 60/43
| [[18/13]], 43/31, 146/105, 89/64, [[32/23]], [[39/28]], 124/89, [[46/33]], 60/43
|-
|-
| 31
| 31
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| 33
| 33
| 628.57
| 628.57
| 43/30, [[33/23]], 89/62, [[56/39]], [[23/16]], 128/89, 105/73, 62/43, [[75/52]], [[13/9]]
| 43/30, [[33/23]], 89/62, [[56/39]], [[23/16]], 128/89, 105/73, 62/43, [[13/9]]
|-
|-
| 34
| 34
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| 37
| 37
| 704.76
| 704.76
| ''[[112/75]]'', [[3/2]], 140/93
| [[3/2]], 140/93
|-
|-
| 38
| 38
| 723.81
| 723.81
| 53/35, 47/31, [[91/60]], 44/29, 73/48, [[35/23]], [[32/21]], ''[[75/49]]''
| 53/35, 47/31, [[91/60]], 44/29, 73/48, [[35/23]], [[32/21]]
|-
|-
| 39
| 39
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| 40
| 40
| 761.9
| 761.9
| 116/75, 48/31, 31/20, 45/29, 73/47, 87/56, [[14/9]], ''[[25/16]]''
| 48/31, 31/20, 45/29, 73/47, 87/56, [[14/9]], ''[[25/16]]''
|-
|-
| 41
| 41
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| 42
| 42
| 800.0
| 800.0
| 49/31, [[144/91]], 84/53, 46/29, 73/46, 116/73, 89/56, 62/39, [[35/22]], [[78/49]], 75/47
| 49/31, [[144/91]], 84/53, 46/29, 73/46, 116/73, 89/56, 62/39, [[35/22]], [[78/49]]
|-
|-
| 43
| 43
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| 44
| 44
| 838.1
| 838.1
| [[21/13]], 144/89, 47/29, 73/45, 86/53, [[13/8]], 70/43, [[75/46]]
| [[21/13]], 144/89, 47/29, 73/45, 86/53, [[13/8]], 70/43
|-
|-
| 45
| 45
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| 46
| 46
| 876.19
| 876.19
| 124/75, 43/26, 48/29, 53/32, 58/35, 73/44, 78/47, 88/53, 93/56, [[5/3]]
| 43/26, 48/29, 53/32, 58/35, 73/44, 78/47, 88/53, 93/56, [[5/3]]
|-
|-
| 47
| 47
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| 48
| 48
| 914.29
| 914.29
| 49/29, [[22/13]], 105/62, 178/105, [[39/23]], [[56/33]], 73/43, 90/53, 124/73, [[75/44]]
| 49/29, [[22/13]], 105/62, 178/105, [[39/23]], [[56/33]], 73/43, 90/53, 124/73
|-
|-
| 49
| 49
| 933.33
| 933.33
| [[128/75]], 53/31, 89/52, [[12/7]], 91/53, 31/18, ''50/29''
| 53/31, 89/52, [[12/7]], 91/53, 31/18, ''50/29''
|-
|-
| 50
| 50
| 952.38
| 952.38
| [[45/26]], [[26/15]], 92/53, 73/42, ''75/43''
| [[45/26]], [[26/15]], 92/53, 73/42
|-
|-
| 51
| 51
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| 61
| 61
| 1161.9
| 1161.9
| 146/75, 84/43, 43/22, 174/89, [[88/45]], 178/91, [[45/23]], 182/93, 92/47, 47/24, [[96/49]], 104/53
| 84/43, 43/22, 174/89, [[88/45]], 178/91, [[45/23]], 182/93, 92/47, 47/24, [[96/49]], 104/53
|-
|-
| 62
| 62
| 1180.95
| 1180.95
| [[63/32]], 2/([[65/64]]), 144/73, 172/87, 87/44, 176/89, 89/45, [[180/91]], [[91/46]], 184/93, 93/47, [[208/105]], 105/53
| [[63/32]], 144/73, 172/87, 87/44, 176/89, 89/45, [[180/91]], [[91/46]], 184/93, 93/47, [[208/105]], 105/53
|-
|-
| 63
| 63
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