Xenharmonic Wiki

159edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Aura (talk | contribs)
autopatrolled, emailconfirmed
6,010 edits
No edit summary
→Intervals: Moved table from Table of 159edo intervals with minor edits in the text above the table
Line 51: Line 51:


== Intervals ==
== Intervals ==
{{main|Table of 159edo Intervals}}
The following table assumes 17-limit patent val {{val|159 252 369 446 550 588 650}}.
 
Intervals highlighted in '''bold''' are prime harmonics or subharmonics. In addition, intervals that differ from assigned steps by more than 50%, multiples of such intervals, and intervals of odd limit higher than 1024, are not shown. Furthermore, when multiple well-known intervals for a given prime-limit share a step size, they may share a cell in the chart; conversely, a "?" in the chart means that no known interval meets the criteria for inclusion. Note that no 5-limit intervals can be represented by degrees other than multiples of 3, so those entries are left blank.
 
{| class="mw-collapsible mw-collapsed wikitable center-1"
|+ style=white-space:nowrap | Table of 159edo intervals
|-
! Step
! Cents
! 5 limit
! 7 limit
! 11 limit
! 13 limit
! 17 limit
|-
| 0
| 0
| colspan="5"| '''[[1/1]]'''
|-
| 1
| 7.5471698
|
| [[225/224]]
| [[243/242]]
| [[196/195]], [[351/350]]
| 256/255
|-
| 2
| 15.0943396
|
| ?
| [[121/120]], [[100/99]]
| [[144/143]]
| 120/119
|-
| 3
| 22.6415094
| [[81/80]]
| ?
| ?
| [[78/77]]
| 85/84
|-
| 4
| 30.1886792
|
| [[64/63]]
| [[56/55]], [[55/54]]
| ?
| [[52/51]]
|-
| 5
| 37.7358491
|
| ?
| [[45/44]]
| ?
| [[51/50]]
|-
| 6
| 45.2830189
| ?
| ?
| ?
| [[40/39]]
| 192/187
|-
| 7
| 52.8301887
|
| ?
| [[33/32]]
| ?
| [[34/33]]
|-
| 8
| 60.3773585
|
| [[28/27]]
| ?
| ?
| 88/85
|-
| 9
| 67.9245283
| [[25/24]]
| ?
| ?
| [[26/25]], [[27/26]]
| ?
|-
| 10
| 75.4716981
|
| ?
| ?
| ?
| 160/153
|-
| 11
| 83.0188679
|
| [[21/20]]
| [[22/21]]
| ?
| ?
|-
| 12
| 90.5660377
| [[256/243]], [[135/128]]
| ?
| ?
| ?
| ?
|-
| 13
| 98.1132075
|
| ?
| [[128/121]]
| [[55/52]]
| [[18/17]]
|-
| 14
| 105.6603774
|
| ?
| ?
| ?
| '''[[17/16]]'''
|-
| 15
| 113.2075472
| [[16/15]]
| ?
| ?
| ?
| ?
|-
| 16
| 120.7547170
|
| [[15/14]]
| 275/256
| ?
| ?
|-
| 17
| 128.3018868
|
| ?
| ?
| [[14/13]]
| 128/119
|-
| 18
| 135.8490566
| [[27/25]]
| ?
| ?
| [[13/12]]
| ?
|-
| 19
| 143.3962264
|
| ?
| [[88/81]]
| ?
| ?
|-
| 20
| 150.9433962
|
| ?
| [[12/11]]
| ?
| ?
|-
| 21
| 158.4905660
| ?
| ?
| ?
| [[128/117]]
| 561/512, 1024/935
|-
| 22
| 166.0377358
|
| ?
| [[11/10]]
| ?
| ?
|-
| 23
| 173.5849057
|
| 567/512
| 243/220
| ?
| 425/384
|-
| 24
| 181.1320755
| [[10/9]]
| ?
| 256/231
| ?
| ?
|-
| 25
| 188.6792458
|
| ?
| ?
| [[143/128]]
| 512/459
|-
| 26
| 196.2264151
|
| [[28/25]]
| ?
| ?
| ?
|-
| 27
| 203.7735849
| [[9/8]]
| ?
| ?
| ?
| ?
|-
| 28
| 211.3207547
|
| ?
| ?
| [[44/39]]
| 289/256
|-
| 29
| 218.8679245
|
| ?
| ?
| ?
| [[17/15]]
|-
| 30
| 226.4150943
| [[256/225]]
| ?
| [[154/135]]
| ?
| ?
|-
| 31
| 233.9622642
|
| '''[[8/7]]'''
| [[55/48]]
| ?
| ?
|-
| 32
| 241.5094340
|
| ?
| 1024/891
| ?
| ?
|-
| 33
| 249.0566038
| ?
| ?
| ?
| [[15/13]]
| ?
|-
| 34
| 256.6037736
|
| ?
| 297/256
| ?
| ?
|-
| 35
| 264.1509434
|
| [[7/6]]
| [[64/55]]
| ?
| ?
|-
| 36
| 271.6981132
| [[75/64]]
| ?
| ?
| ?
| ?
|-
| 37
| 279.2452830
|
| ?
| ?
| ?
| [[20/17]]
|-
| 38
| 286.7924528
|
| ?
| [[33/28]]
| [[13/11]]
| 85/72
|-
| 39
| 294.3396226
| [[32/27]]
| ?
| ?
| ?
| ?
|-
| 40
| 301.8867925
|
| [[25/21]]
| 144/121
| ?
| ?
|-
| 41
| 309.4339622
|
| ?
| ?
| 512/429
| 153/128
|-
| 42
| 316.9811321
| [[6/5]]
| ?
| [[77/64]]
| ?
| ?
|-
| 43
| 324.5283019
|
| [[135/112]]
| ?
| ?
| 512/425
|-
| 44
| 332.0754717
|
| ?
| [[40/33]], [[121/100]]
| ?
| 144/119, 165/136
|-
| 45
| 339.6226415
| ?
| ?
| ?
| [[39/32]]
| [[17/14]]
|-
| 46
| 347.1698113
|
| ?
| [[11/9]]
| ?
| ?
|-
| 47
| 354.7169811
|
| ?
| [[27/22]]
| ?
| ?
|-
| 48
| 362.2641509
| ?
| ?
| ?
| '''[[16/13]]'''
| [[21/17]]
|-
| 49
| 369.8113208
|
| ?
| ?
| ?
| 68/55
|-
| 50
| 377.3584906
|
| [[56/45]]
| 1024/825
| ?
| ?
|-
| 51
| 384.9056604
| '''[[5/4]]'''
| ?
| [[96/77]]
| ?
| ?
|-
| 52
| 392.4528302
|
| ?
| ?
| ?
| [[64/51]]
|-
| 53
| 400
|
| [[63/50]]
| [[121/96]]
| ?
| ?
|-
| 54
| 407.5471698
| [[81/64]]
| ?
| ?
| ?
| ?
|-
| 55
| 415.0943396
|
| ?
| [[14/11]]
| [[33/26]]
| 108/85
|-
| 56
| 422.6415094
|
| ?
| ?
| 143/112
| 51/40
|-
| 57
| 430.1886792
| [[32/25]]
| ?
| ?
| ?
| ?
|-
| 58
| 437.7358491
|
| [[9/7]]
| [[165/128]]
| ?
| ?
|-
| 59
| 445.2830189
|
| ?
| [[128/99]]
| ?
| [[22/17]]
|-
| 60
| 452.8301887
| ?
| ?
| ?
| [[13/10]]
| ?
|-
| 61
| 460.3773585
|
| ?
| 176/135
| ?
| ?
|-
| 62
| 467.9245283
|
| [[21/16]]
| [[55/42]], [[72/55]]
| ?
| [[17/13]]
|-
| 63
| 475.4716981
| 320/243, 675/512
| ?
| ?
| ?
| ?
|-
| 64
| 483.0188679
|
| ?
| [[33/25]]
| ?
| [[45/34]]
|-
| 65
| 490.5660377
|
| ?
| ?
| ?
| [[85/64]]
|-
| 66
| 498.1132075
| '''[[4/3]]'''
| ?
| ?
| ?
| ?
|-
| 67
| 505.6603774
|
| [[75/56]]
| [[162/121]]
| ?
| ?
|-
| 68
| 513.2075472
|
| ?
| [[121/90]]
| ?
| ?
|-
| 69
| 520.7547170
| [[27/20]]
| ?
| ?
| [[104/77]]
| ?
|-
| 70
| 528.3018868
|
| ?
| [[110/81]]
| ?
| ?
|-
| 71
| 535.8490566
|
| ?
| [[15/11]]
| ?
| ?
|-
| 72
| 543.3962264
| ?
| ?
| ?
| 160/117
| 256/187
|-
| 73
| 550.9433962
|
| ?
| '''[[11/8]]'''
| ?
| ?
|-
| 74
| 558.4905660
|
| [[112/81]]
| ?
| ?
| ?
|-
| 75
| 566.0377358
| [[25/18]]
| ?
| ?
| [[18/13]]
| ?
|-
| 76
| 573.5849057
|
| ?
| ?
| ?
| 357/256
|-
| 77
| 581.1320755
|
| [[7/5]]
| ?
| ?
| ?
|-
| 78
| 588.6792458
| [[1024/729]], [[45/32]]
| ?
| ?
| ?
| ?
|-
| 79
| 596.2264151
|
| ?
| ?
| ?
| [[24/17]]
|-
| 80
| 603.7735849
|
| ?
| ?
| ?
| [[17/12]]
|-
| 81
| 611.3207547
| [[729/512]], [[64/45]]
| ?
| ?
| ?
| ?
|-
| 82
| 618.8679245
|
| [[10/7]]
| ?
| ?
| ?
|-
| 83
| 626.4150943
|
| ?
| ?
| ?
| 512/357
|-
| 84
| 633.9622642
| [[36/25]]
| ?
| ?
| [[13/9]]
| ?
|-
| 85
| 641.5094340
|
| [[81/56]]
| ?
| ?
| ?
|-
| 86
| 649.0566038
|
| ?
| '''[[16/11]]'''
| ?
| ?
|-
| 87
| 656.6037736
| ?
| ?
| ?
| 117/80
| 187/128
|-
| 88
| 664.1509434
|
| ?
| [[22/15]]
| ?
| ?
|-
| 89
| 671.6981132
|
| ?
| [[81/55]]
| ?
| ?
|-
| 90
| 679.2452830
| [[40/27]]
| ?
| ?
| [[77/52]]
| ?
|-
| 91
| 686.7924528
|
| ?
| [[180/121]]
| ?
| ?
|-
| 92
| 694.3396226
|
| [[112/75]]
| [[121/81]]
| ?
| ?
|-
| 93
| 701.8867925
| '''[[3/2]]'''
| ?
| ?
| ?
| ?
|-
| 94
| 709.4339622
|
| ?
| ?
| ?
| [[128/85]]
|-
| 95
| 716.9811321
|
| ?
| [[50/33]]
| ?
| [[68/45]]
|-
| 96
| 724.5283019
| 243/160, 1024/675
| ?
| ?
| ?
| ?
|-
| 97
| 732.0754717
|
| [[32/21]]
| [[84/55]], [[55/36]]
| ?
| [[26/17]]
|-
| 98
| 739.6226415
|
| ?
| 135/88
| ?
| ?
|-
| 99
| 747.1698113
| ?
| ?
| ?
| [[20/13]]
| ?
|-
| 100
| 754.7169811
|
| ?
| [[99/64]]
| ?
| [[17/11]]
|-
| 101
| 762.2641509
|
| [[14/9]]
| [[256/165]]
| ?
| ?
|-
| 102
| 769.8113208
| [[25/16]]
| ?
| ?
| ?
| ?
|-
| 103
| 777.3584906
|
| ?
| ?
| 224/143
| 80/51
|-
| 104
| 784.9056604
|
| ?
| [[11/7]]
| [[52/33]]
| 85/54
|-
| 105
| 792.4528302
| [[128/81]]
| ?
| ?
| ?
| ?
|-
| 106
| 800
|
| [[100/63]]
| [[192/121]]
| ?
| ?
|-
| 107
| 807.5471698
|
| ?
| ?
| ?
| [[51/32]]
|-
| 108
| 815.0943396
| '''[[8/5]]'''
| ?
| [[77/48]]
| ?
| ?
|-
| 109
| 822.6415094
|
| [[45/28]]
| 825/512
| ?
| ?
|-
| 110
| 830.1886792
|
| ?
| ?
| ?
| 55/34
|-
| 111
| 837.7358491
| ?
| ?
| ?
| '''[[13/8]]'''
| [[34/21]]
|-
| 112
| 845.2830189
|
| ?
| [[44/27]]
| ?
| ?
|-
| 113
| 852.8301887
|
| ?
| [[18/11]]
| ?
| ?
|-
| 114
| 860.3773585
| ?
| ?
| ?
| [[64/39]]
| [[28/17]]
|-
| 115
| 867.9245283
|
| ?
| [[33/20]], [[200/121]]
| ?
| 119/72, 272/165
|-
| 116
| 875.4716981
|
| [[224/135]]
| ?
| ?
| 425/256
|-
| 117
| 883.0188679
| [[5/3]]
| ?
| [[128/77]]
| ?
| ?
|-
| 118
| 890.5660377
|
| ?
| ?
| 429/256
| 256/153
|-
| 119
| 898.1132075
|
| [[42/25]]
| 121/72
| ?
| ?
|-
| 120
| 905.6603774
| [[27/16]]
| ?
| ?
| ?
| ?
|-
| 121
| 913.2075472
|
| ?
| [[56/33]]
| [[22/13]]
| 144/85
|-
| 122
| 920.7547170
|
| ?
| ?
| ?
| [[17/10]]
|-
| 123
| 928.3018868
| [[128/75]]
| ?
| ?
| ?
| ?
|-
| 124
| 935.8490566
|
| [[12/7]]
| [[55/32]]
| ?
| ?
|-
| 125
| 943.3962264
|
| ?
| 512/297
| ?
| ?
|-
| 126
| 950.9433962
| ?
| ?
| ?
| [[26/15]]
| ?
|-
| 127
| 958.4905660
|
| ?
| 891/512
| ?
| ?
|-
| 128
| 966.0377358
|
| '''[[7/4]]'''
| [[96/55]]
| ?
| ?
|-
| 129
| 973.5849057
| [[225/128]]
| ?
| [[135/77]]
| ?
| ?
|-
| 130
| 981.1320755
|
| ?
| ?
| ?
| [[30/17]]
|-
| 131
| 988.6792458
|
| ?
| ?
| [[39/22]]
| 512/289
|-
| 132
| 996.2264151
| [[16/9]]
| ?
| ?
| ?
| ?
|-
| 133
| 1003.7735849
|
| [[25/14]]
| ?
| ?
| ?
|-
| 134
| 1011.3207547
|
| ?
| ?
| [[256/143]]
| 459/256
|-
| 135
| 1018.8679245
| [[9/5]]
| ?
| 231/128
| ?
| ?
|-
| 136
| 1026.4150943
|
| 1024/567
| 440/243
| ?
| 768/425
|-
| 137
| 1033.9622642
|
| ?
| [[20/11]]
| ?
| ?
|-
| 138
| 1041.5094340
| ?
| ?
| ?
| [[117/64]]
| 1024/561, 935/512
|-
| 139
| 1049.0566038
|
| ?
| [[11/6]]
| ?
| ?
|-
| 140
| 1056.6037736
|
| ?
| [[81/44]]
| ?
| ?
|-
| 141
| 1064.1509434
| [[50/27]]
| ?
| ?
| [[24/13]]
| ?
|-
| 142
| 1071.6981132
|
| ?
| ?
| [[13/7]]
| 119/64
|-
| 143
| 1079.2452830
|
| [[28/15]]
| 512/275
| ?
| ?
|-
| 144
| 1086.7924528
| [[15/8]]
| ?
| ?
| ?
| ?
|-
| 145
| 1094.3396226
|
| ?
| ?
| ?
| '''[[32/17]]'''
|-
| 146
| 1101.8867925
|
| ?
| [[121/64]]
| [[104/55]]
| [[17/9]]
|-
| 147
| 1109.4339622
| [[243/128]], [[256/135]]
| ?
| ?
| ?
| ?
|-
| 148
| 1116.9811321
|
| [[40/21]]
| [[21/11]]
| ?
| ?
|-
| 149
| 1124.5283019
|
| ?
| ?
| ?
| 153/80
|-
| 150
| 1132.0754717
| [[48/25]]
| ?
| ?
| [[25/13]], [[52/27]]
| ?
|-
| 151
| 1139.6226415
|
| [[27/14]]
| ?
| ?
| 85/44
|-
| 152
| 1147.1698113
|
| ?
| [[64/33]]
| ?
| [[33/17]]
|-
| 153
| 1154.7169811
| ?
| ?
| ?
| [[39/20]]
| 187/96
|-
| 154
| 1162.2641509
|
| ?
| [[88/45]]
| ?
| [[100/51]]
|-
| 155
| 1169.8113208
|
| [[63/32]]
| [[55/28]], [[108/55]]
| ?
| [[51/26]]
|-
| 156
| 1177.3584906
| [[160/81]]
| ?
| ?
| [[77/39]]
| 168/85
|-
| 157
| 1184.9056604
|
| ?
| [[240/121]], [[99/50]]
| [[143/72]]
| 119/60
|-
| 158
| 1192.4528302
|
| [[448/225]]
| [[484/243]]
| [[195/98]], [[700/351]]
| 255/128
|-
| 159
| 1200
| colspan="5"| '''[[2/1]]'''
|-
|}


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/159edo"