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→Intervals: improve table; omit 63 as oversharp and and include 49 and 53 as fitting; omitted complex inconsistent interval pair 75/53 and 106/53 resulting from inclusion of 53, as 75's inclusion is mainly convenient; add some notable 13-limit commas manually
Line 17: Line 17:


== 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=47,no=[5,17,19,25,27,37,41],add=[63,73,75,87,89,91,93],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.


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 47-odd-limit add-63 add-73 add-75 add-87 add-89 add-91 add-93 interpretation, tuned to the strengths of [[63edo]]. Note that because of the cancellation of factors, some odd harmonics of 5 (the more relevant ones) are present, specifically {{nowrap|75/3 {{=}} 25}}, {{nowrap|45/3 {{=}} 15}}, and {{nowrap|45/9 {{=}} 5}}.
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.


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.
Line 29: Line 29:
! Degree
! Degree
! Cents
! Cents
! Approximate ratios<ref group="note">{{sg|limit=2.3.5.7.11.13.23.29.31.43.47.73.89-subgroup (no-17's no-19's no-37's no-41's 47-limit add-73 add-89)}} Note that due to the error on 5, only low-complexity intervals involving 5 are included here.</ref>
! Approximate ratios<ref group="note">{{sg|limit=2.3.5.7.11.13.23.29.31.43.47.53.73.89-subgroup (no-17's no-19's no-37's no-41's 47-limit add-73 add-89 add-105)}} Note that due to the error on 5, only low-complexity intervals involving 5 are included here.</ref>
|-
|-
| 0
| 0
Line 37: Line 37:
| 1
| 1
| 19.05
| 19.05
| 94/93, 93/92, [[92/91]], [[91/90]], 90/89, 89/88, 88/87, 87/86, 73/72, [[64/63]]
| 106/105, [[105/104]], 94/93, 93/92, [[92/91]], [[91/90]], 90/89, 89/88, 88/87, 87/86, 73/72, [[65/64]], [[64/63]]
|-
|-
| 2
| 2
| 38.1
| 38.1
| ''63/62'', 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, 75/73
|-
|-
| 3
| 3
Line 49: Line 49:
| 4
| 4
| 76.19
| 76.19
| [[26/25]], 73/70, [[24/23]], 47/45, 93/89, [[23/22]], 91/87, 45/43, [[22/21]]
| [[26/25]], 49/47, 73/70, [[24/23]], 47/45, 93/89, [[23/22]], 91/87, 45/43, [[22/21]]
|-
|-
| 5
| 5
| 95.24
| 95.24
| ''[[21/20]]'', [[96/91]], 94/89, 93/88, 92/87, 91/86, 89/84, [[35/33]]
| 98/93, [[96/91]], 94/89, 56/53, 93/88, 92/87, 91/86, 89/84, [[35/33]], [[52/49]]
|-
|-
| 6
| 6
| 114.29
| 114.29
| 33/31, [[16/15]], 47/44, 78/73, 31/29, 46/43, [[15/14]]
| 33/31, [[49/46]], [[16/15]], 47/44, 78/73, 31/29, 46/43, [[15/14]]
|-
|-
| 7
| 7
| 133.33
| 133.33
| [[14/13]], 96/89, 94/87, 93/86, [[13/12]]
| [[14/13]], 96/89, 94/87, 93/86, 53/49, [[13/12]]
|-
|-
| 8
| 8
| 152.38
| 152.38
| 63/58, [[12/11]], 47/43, [[35/32]], [[23/21]]
| [[49/45]], [[12/11]], 47/43, [[35/32]], 58/53, [[23/21]]
|-
|-
| 9
| 9
| 171.43
| 171.43
| [[11/10]], 43/39, 32/29, 73/66, 52/47, 31/28, ''[[10/9]]''
| [[11/10]], 98/89, 43/39, 32/29, 53/48, 116/105, 73/66, 52/47, 31/28
|-
|-
| 10
| 10
| 190.48
| 190.48
| [[39/35]], 29/26, 48/43, 104/93, 47/42
| [[49/44]], [[39/35]], 29/26, 48/43, 105/94, 104/93, 47/42
|-
|-
| 11
| 11
| 209.52
| 209.52
| ''[[28/25]]'', [[9/8]], [[44/39]], 35/31, [[26/23]], ''[[25/22]]''
| ''[[28/25]]'', [[9/8]], 98/87, 53/47, [[44/39]], 35/31, [[26/23]], 60/53, ''[[25/22]]''
|-
|-
| 12
| 12
| 228.57
| 228.57
| 33/29, 73/64, 89/78, [[8/7]]
| 33/29, 49/43, 106/93, 73/64, 89/78, [[105/92]], [[8/7]]
|-
|-
| 13
| 13
| 247.62
| 247.62
| ''86/75'', 84/73, [[15/13]], [[52/45]], 73/63
| ''86/75'', 84/73, 53/46, [[15/13]], [[52/45]]
|-
|-
| 14
| 14
| 266.67
| 266.67
| ''29/25'', 36/31, [[7/6]], 104/89, [[75/64]]
| ''29/25'', 36/31, 106/91, [[7/6]], 104/89, 62/53, [[75/64]]
|-
|-
| 15
| 15
| 285.71
| 285.71
| [[88/75]], 73/62, 86/73, [[33/28]], [[46/39]], [[13/11]], ''[[25/21]]''
| [[88/75]], 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, 56/47, 87/73, 31/26, 43/36, 104/87
| 89/75, 106/89, 56/47, 87/73, 31/26, [[105/88]], 43/36, 104/87
|-
|-
| 17
| 17
| 323.81
| 323.81
| [[6/5]], 112/93, 47/39, 88/73, 35/29, 29/24, 52/43, 75/62
| [[6/5]], 112/93, 53/44, 47/39, 88/73, 35/29, 64/53, 29/24, 52/43, 75/62
|-
|-
| 18
| 18
| 342.86
| 342.86
| ''[[63/52]]'', [[91/75]], 73/60, [[28/23]], [[39/32]], 89/73, [[11/9]]
| [[91/75]], 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]], 90/73, 58/47, 89/72, [[26/21]]
| [[92/75]], 43/35, [[16/13]], 53/43, 90/73, 58/47, 89/72, [[26/21]]
|-
|-
| 20
| 20
| 380.95
| 380.95
| 31/25, 36/29, 87/70, [[56/45]], 91/73, 116/93, [[5/4]]
| 31/25, 36/29, 87/70, [[56/45]], 66/53, 91/73, 116/93, [[5/4]]
|-
|-
| 21
| 21
| 400.0
| 400.0
| 94/75, [[44/35]], 39/31, 112/89, 73/58, 92/73, 29/23, [[91/72]]
| 94/75, [[49/39]], [[44/35]], 39/31, 112/89, 73/58, 92/73, 29/23, 53/42, [[91/72]], 62/49
|-
|-
| 22
| 22
Line 129: Line 129:
| 24
| 24
| 457.14
| 457.14
| [[13/10]], 56/43, 43/33, 116/89, 73/56, [[30/23]], 47/36
| [[13/10]], 56/43, 43/33, 116/89, 73/56, [[30/23]], 47/36, [[64/49]]
|-
|-
| 25
| 25
| 476.19
| 476.19
| [[21/16]], [[46/35]], 96/73, 29/22, [[120/91]], 62/47
| ''[[98/75]]'', [[21/16]], [[46/35]], 96/73, 29/22, [[120/91]], 62/47, 70/53
|-
|-
| 26
| 26
Line 141: Line 141:
| 27
| 27
| 514.29
| 514.29
| 63/47, 47/35, 43/32, 39/29, [[35/26]], 31/23, 120/89, 89/66, 58/43
| 98/73, 47/35, 43/32, 39/29, [[35/26]], [[66/49]], 31/23, 120/89, 89/66, 58/43
|-
|-
| 28
| 28
| 533.33
| 533.33
| 42/31, 87/64, 64/47, 124/91, [[15/11]], 86/63
| 42/31, 72/53, 53/39, 87/64, [[49/36]], 64/47, 124/91, [[15/11]]
|-
|-
| 29
| 29
| 552.38
| 552.38
| [[63/46]], [[48/35]], [[11/8]], 128/93, 62/45, [[91/66]], 40/29, 29/21
| [[48/35]], [[11/8]], 128/93, 73/53, 62/45, [[91/66]], 40/29, 29/21
|-
|-
| 30
| 30
| 571.43
| 571.43
| [[18/13]], [[104/75]], 43/31, 89/64, [[32/23]], [[39/28]], 124/89, [[46/33]], 60/43, [[88/63]]
| [[18/13]], [[104/75]], 43/31, 146/105, 89/64, [[32/23]], [[39/28]], 124/89, [[46/33]], 60/43
|-
|-
| 31
| 31
| 590.48
| 590.48
| [[7/5]], 87/62, 73/52, 66/47, [[45/32]], [[128/91]], 31/22, 89/63
| [[7/5]], 87/62, 73/52, 66/47, [[45/32]], [[128/91]], 31/22
|-
|-
| 32
| 32
| 609.52
| 609.52
| 126/89, 44/31, [[91/64]], [[64/45]], 47/33, 104/73, 124/87, [[10/7]]
| 44/31, [[91/64]], [[64/45]], 47/33, 104/73, 124/87, [[10/7]]
|-
|-
| 33
| 33
| 628.57
| 628.57
| [[63/44]], 43/30, [[33/23]], 89/62, [[56/39]], [[23/16]], 128/89, 62/43, [[75/52]], [[13/9]]
| 43/30, [[33/23]], 89/62, [[56/39]], [[23/16]], 128/89, 105/73, 62/43, [[75/52]], [[13/9]]
|-
|-
| 34
| 34
| 647.62
| 647.62
| 42/29, 29/20, [[132/91]], 45/31, 93/64, [[16/11]], [[35/24]], [[92/63]]
| 42/29, 29/20, [[132/91]], 45/31, 106/73, 93/64, [[16/11]], [[35/24]]
|-
|-
| 35
| 35
| 666.67
| 666.67
| 63/43, [[22/15]], 91/62, 47/32, 128/87, 31/21
| [[22/15]], 91/62, 47/32, [[72/49]], 128/87, 78/53, 53/36, 31/21
|-
|-
| 36
| 36
| 685.71
| 685.71
| 43/29, 132/89, 89/60, 46/31, [[52/35]], 58/39, 64/43, 70/47, 94/63
| 43/29, 132/89, 89/60, 46/31, [[49/33]], [[52/35]], 58/39, 64/43, 70/47, 73/49
|-
|-
| 37
| 37
Line 185: Line 185:
| 38
| 38
| 723.81
| 723.81
| 47/31, [[91/60]], 44/29, 73/48, [[35/23]], [[32/21]]
| 53/35, 47/31, [[91/60]], 44/29, 73/48, [[35/23]], [[32/21]], ''[[75/49]]''
|-
|-
| 39
| 39
| 742.86
| 742.86
| 72/47, [[23/15]], 112/73, 89/58, 66/43, 43/28, [[20/13]]
| [[49/32]], 72/47, [[23/15]], 112/73, 89/58, 66/43, 43/28, [[20/13]]
|-
|-
| 40
| 40
Line 201: Line 201:
| 42
| 42
| 800.0
| 800.0
| [[144/91]], 46/29, 73/46, 116/73, 89/56, 62/39, [[35/22]], 75/47
| 49/31, [[144/91]], 84/53, 46/29, 73/46, 116/73, 89/56, 62/39, [[35/22]], [[78/49]], 75/47
|-
|-
| 43
| 43
| 819.05
| 819.05
| [[8/5]], 93/58, 146/91, [[45/28]], 140/87, 29/18, 50/31
| [[8/5]], 93/58, 146/91, 53/33, [[45/28]], 140/87, 29/18, 50/31
|-
|-
| 44
| 44
| 838.1
| 838.1
| [[21/13]], 144/89, 47/29, 73/45, [[13/8]], 70/43, [[75/46]]
| [[21/13]], 144/89, 47/29, 73/45, 86/53, [[13/8]], 70/43, [[75/46]]
|-
|-
| 45
| 45
| 857.14
| 857.14
| [[18/11]], 146/89, [[64/39]], [[23/14]], 120/73, [[150/91]], ''[[104/63]]''
| [[49/30]], [[18/11]], 172/105, 146/89, [[105/64]], [[64/39]], 87/53, [[23/14]], 120/73, [[150/91]]
|-
|-
| 46
| 46
| 876.19
| 876.19
| 124/75, 43/26, 48/29, 58/35, 73/44, 78/47, 93/56, [[5/3]]
| 124/75, 43/26, 48/29, 53/32, 58/35, 73/44, 78/47, 88/53, 93/56, [[5/3]]
|-
|-
| 47
| 47
| 895.24
| 895.24
| 87/52, 72/43, 52/31, 146/87, 47/28, 150/89
| 87/52, 72/43, [[176/105]], 52/31, 146/87, 47/28, 89/53, 150/89
|-
|-
| 48
| 48
| 914.29
| 914.29
| ''[[42/25]]'', [[22/13]], [[39/23]], [[56/33]], 73/43, 124/73, [[75/44]]
| 49/29, [[22/13]], 105/62, 178/105, [[39/23]], [[56/33]], 73/43, 90/53, 124/73, [[75/44]]
|-
|-
| 49
| 49
| 933.33
| 933.33
| [[128/75]], 89/52, [[12/7]], 31/18, ''50/29''
| [[128/75]], 53/31, 89/52, [[12/7]], 91/53, 31/18, ''50/29''
|-
|-
| 50
| 50
| 952.38
| 952.38
| 126/73, [[45/26]], [[26/15]], 73/42, ''75/43''
| [[45/26]], [[26/15]], 92/53, 73/42, ''75/43''
|-
|-
| 51
| 51
| 971.43
| 971.43
| [[7/4]], 156/89, 128/73, 58/33
| [[7/4]], [[184/105]], 156/89, 128/73, 93/53, 86/49, 58/33
|-
|-
| 52
| 52
| 990.48
| 990.48
| ''[[44/25]]'', [[23/13]], 62/35, [[39/22]], [[16/9]], ''[[25/14]]''
| ''[[44/25]]'', 53/30, [[23/13]], 62/35, [[39/22]], 94/53, 87/49, [[16/9]], ''[[25/14]]''
|-
|-
| 53
| 53
| 1009.52
| 1009.52
| 84/47, 93/52, 43/24, 52/29, [[70/39]]
| 84/47, 93/52, 188/105, 43/24, 52/29, [[70/39]], [[88/49]]
|-
|-
| 54
| 54
| 1028.57
| 1028.57
| ''[[9/5]]'', 56/31, 47/26, 132/73, 29/16, 78/43, [[20/11]]
| 56/31, 47/26, 132/73, 105/58, 96/53, 29/16, 78/43, 89/49, [[20/11]]
|-
|-
| 55
| 55
| 1047.62
| 1047.62
| [[42/23]], [[64/35]], 86/47, [[11/6]], 116/63
| [[42/23]], 53/29, [[64/35]], 86/47, [[11/6]], [[90/49]]
|-
|-
| 56
| 56
| 1066.67
| 1066.67
| [[24/13]], 172/93, 87/47, 89/48, [[13/7]]
| [[24/13]], 98/53, 172/93, 87/47, 89/48, [[13/7]]
|-
|-
| 57
| 57
| 1085.71
| 1085.71
| [[28/15]], 43/23, 58/31, 73/39, 88/47, [[15/8]], 62/33
| [[28/15]], 43/23, 58/31, 73/39, 88/47, [[15/8]], [[92/49]], 62/33
|-
|-
| 58
| 58
| 1104.76
| 1104.76
| [[66/35]], 168/89, 172/91, 87/46, 176/93, 89/47, [[91/48]], ''[[40/21]]''
| [[49/26]], [[66/35]], 168/89, 172/91, 87/46, 176/93, 53/28, 89/47, [[91/48]], 93/49
|-
|-
| 59
| 59
| 1123.81
| 1123.81
| [[21/11]], 86/45, 174/91, [[44/23]], 178/93, 90/47, [[23/12]], 140/73, [[25/13]]
| [[21/11]], 86/45, 174/91, [[44/23]], 178/93, 90/47, [[23/12]], 140/73, 94/49, [[25/13]]
|-
|-
| 60
| 60
Line 277: Line 277:
| 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, ''124/63''
| 146/75, 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]], 144/73, 172/87, 87/44, 176/89, 89/45, [[180/91]], [[91/46]], 184/93, 93/47
| [[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
| 63
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