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Table of 159edo Intervals: Difference between revisions

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intro with link to 159edo
Remove words on italics since there's no such instances. Remove "?" in 5-limit entries for degrees other than multiples of 3 since that's impossible
Line 1: Line 1:
This '''table of [[159edo]] intervals''' assumes 17-limit patent val <159 252 369 446 550 588 650|. Intervals highlighted in '''bold''' are prime harmonics or subharmonics, while other well-known intervals will likely have links to their respective pages. In addition, intervals that differ from the nearest step by more than 3.5 cents will be in ''italics'', while intervals that differ from assigned steps by a rate of 50% or more, multiples of such intervals, or else, intervals that have an odd limit higher than 1024, will not be included in the chart at all. 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.
This '''table of [[159edo]] intervals''' assumes 17-limit patent val {{val|159 252 369 446 550 588 650}}.  
{| class="wikitable"
 
Intervals highlighted in '''bold''' are prime harmonics or subharmonics, while other well-known intervals will likely have links to their respective pages. 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="wikitable center-1"
|-
|-
!| Step
! Step
!| Cents
! Cents
!| 5 limit
! 5 limit
!| 7 limit
! 7 limit
!| 11 limit
! 11 limit
!| 13 limit
! 13 limit
!| 17 limit
! 17 limit
|-
|-
| 0
| 0
Line 16: Line 19:
| 1
| 1
| 7.5471698
| 7.5471698
| ?
|  
| [[225/224]]
| [[225/224]]
| [[243/242]]
| [[243/242]]
Line 24: Line 27:
| 2
| 2
| 15.0943396
| 15.0943396
| ?
|  
| ?
| ?
| [[121/120]], [[100/99]]
| [[121/120]], [[100/99]]
Line 40: Line 43:
| 4
| 4
| 30.1886792
| 30.1886792
| ?
|  
| [[64/63]]
| [[64/63]]
| [[56/55]], [[55/54]]
| [[56/55]], [[55/54]]
Line 48: Line 51:
| 5
| 5
| 37.7358491
| 37.7358491
| ?
|  
| ?
| ?
| [[45/44]]
| [[45/44]]
Line 64: Line 67:
| 7
| 7
| 52.8301887
| 52.8301887
| ?
|  
| ?
| ?
| [[33/32]]
| [[33/32]]
Line 72: Line 75:
| 8
| 8
| 60.3773585
| 60.3773585
| ?
|  
| [[28/27]]
| [[28/27]]
| ?
| ?
Line 88: Line 91:
| 10
| 10
| 75.4716981
| 75.4716981
| ?
|  
| ?
| ?
| ?
| ?
Line 96: Line 99:
| 11
| 11
| 83.0188679
| 83.0188679
| ?
|  
| [[21/20]]
| [[21/20]]
| [[22/21]]
| [[22/21]]
Line 112: Line 115:
| 13
| 13
| 98.1132075
| 98.1132075
| ?
|  
| ?
| ?
| [[128/121]]
| [[128/121]]
Line 120: Line 123:
| 14
| 14
| 105.6603774
| 105.6603774
| ?
|  
| ?
| ?
| ?
| ?
Line 136: Line 139:
| 16
| 16
| 120.7547170
| 120.7547170
| ?
|  
| [[15/14]]
| [[15/14]]
| 275/256
| 275/256
Line 144: Line 147:
| 17
| 17
| 128.3018868
| 128.3018868
| ?
|  
| ?
| ?
| ?
| ?
Line 160: Line 163:
| 19
| 19
| 143.3962264
| 143.3962264
| ?
|  
| ?
| ?
| [[88/81]]
| [[88/81]]
Line 168: Line 171:
| 20
| 20
| 150.9433962
| 150.9433962
| ?
|  
| ?
| ?
| [[12/11]]
| [[12/11]]
Line 184: Line 187:
| 22
| 22
| 166.0377358
| 166.0377358
| ?
|  
| ?
| ?
| [[11/10]]
| [[11/10]]
Line 192: Line 195:
| 23
| 23
| 173.5849057
| 173.5849057
| ?
|  
| 567/512
| 567/512
| 243/220
| 243/220
Line 208: Line 211:
| 25
| 25
| 188.6792458
| 188.6792458
| ?
|  
| ?
| ?
| ?
| ?
Line 216: Line 219:
| 26
| 26
| 196.2264151
| 196.2264151
| ?
|  
| [[28/25]]
| [[28/25]]
| ?
| ?
Line 232: Line 235:
| 28
| 28
| 211.3207547
| 211.3207547
| ?
|  
| ?
| ?
| ?
| ?
Line 240: Line 243:
| 29
| 29
| 218.8679245
| 218.8679245
| ?
|  
| ?
| ?
| ?
| ?
Line 256: Line 259:
| 31
| 31
| 233.9622642
| 233.9622642
| ?
|  
| '''[[8/7]]'''
| '''[[8/7]]'''
| [[55/48]]
| [[55/48]]
Line 264: Line 267:
| 32
| 32
| 241.5094340
| 241.5094340
| ?
|  
| ?
| ?
| 1024/891
| 1024/891
Line 280: Line 283:
| 34
| 34
| 256.6037736
| 256.6037736
| ?
|  
| ?
| ?
| 297/256
| 297/256
Line 288: Line 291:
| 35
| 35
| 264.1509434
| 264.1509434
| ?
|  
| [[7/6]]
| [[7/6]]
| [[64/55]]
| [[64/55]]
Line 304: Line 307:
| 37
| 37
| 279.2452830
| 279.2452830
| ?
|  
| ?
| ?
| ?
| ?
Line 312: Line 315:
| 38
| 38
| 286.7924528
| 286.7924528
| ?
|  
| ?
| ?
| [[33/28]]
| [[33/28]]
Line 328: Line 331:
| 40
| 40
| 301.8867925
| 301.8867925
| ?
|  
| [[25/21]]
| [[25/21]]
| ?
| ?
Line 336: Line 339:
| 41
| 41
| 309.4339622
| 309.4339622
| ?
|  
| ?
| ?
| ?
| ?
Line 352: Line 355:
| 43
| 43
| 324.5283019
| 324.5283019
| ?
|  
| ?
| ?
| ?
| ?
Line 360: Line 363:
| 44
| 44
| 332.0754717
| 332.0754717
| ?
|  
| ?
| ?
| ?
| ?
Line 376: Line 379:
| 46
| 46
| 347.1698113
| 347.1698113
| ?
|  
| ?  
| ?  
| [[11/9]]
| [[11/9]]
Line 384: Line 387:
| 47
| 47
| 354.7169811
| 354.7169811
| ?
|  
| ?
| ?
| [[27/22]]
| [[27/22]]
Line 400: Line 403:
| 49
| 49
| 369.8113208
| 369.8113208
| ?
|  
| ?
| ?
| ?
| ?
Line 408: Line 411:
| 50
| 50
| 377.3584906
| 377.3584906
| ?
|  
| ?
| ?
| 1024/825
| 1024/825
Line 424: Line 427:
| 52
| 52
| 392.4528302
| 392.4528302
| ?
|  
| ?
| ?
| ?
| ?
Line 432: Line 435:
| 53
| 53
| 400
| 400
| ?
|  
| [[63/50]]
| [[63/50]]
| ?
| ?
Line 448: Line 451:
| 55
| 55
| 415.0943396
| 415.0943396
| ?
|  
| ?
| ?
| [[14/11]]
| [[14/11]]
Line 456: Line 459:
| 56
| 56
| 422.6415094
| 422.6415094
| ?
|  
| ?
| ?
| ?
| ?
Line 472: Line 475:
| 58
| 58
| 437.7358491
| 437.7358491
| ?
|  
| [[9/7]]
| [[9/7]]
| [[165/128]]
| [[165/128]]
Line 480: Line 483:
| 59
| 59
| 445.2830189
| 445.2830189
| ?
|  
| ?
| ?
| [[128/99]]
| [[128/99]]
Line 496: Line 499:
| 61
| 61
| 460.3773585
| 460.3773585
| ?
|  
| ?
| ?
| 176/135
| 176/135
Line 504: Line 507:
| 62
| 62
| 467.9245283
| 467.9245283
| ?
|  
| [[21/16]]
| [[21/16]]
| ?
| ?
Line 520: Line 523:
| 64
| 64
| 483.0188679
| 483.0188679
| ?
|  
| ?
| ?
| [[33/25]]
| [[33/25]]
Line 528: Line 531:
| 65
| 65
| 490.5660377
| 490.5660377
| ?
|  
| ?
| ?
| ?
| ?
Line 544: Line 547:
| 67
| 67
| 505.6603774
| 505.6603774
| ?
|  
| [[75/56]]
| [[75/56]]
| ?
| ?
Line 552: Line 555:
| 68
| 68
| 513.2075472
| 513.2075472
| ?
|  
| ?
| ?
| [[121/90]]
| [[121/90]]
Line 568: Line 571:
| 70
| 70
| 528.3018868
| 528.3018868
| ?
|  
| ?
| ?
| [[110/81]]
| [[110/81]]
Line 576: Line 579:
| 71
| 71
| 535.8490566
| 535.8490566
| ?
|  
| ?
| ?
| [[15/11]]
| [[15/11]]
Line 592: Line 595:
| 73
| 73
| 550.9433962
| 550.9433962
| ?
|  
| ?
| ?
| '''[[11/8]]'''
| '''[[11/8]]'''
Line 600: Line 603:
| 74
| 74
| 558.4905660
| 558.4905660
| ?
|  
| [[112/81]]
| [[112/81]]
| ?
| ?
Line 616: Line 619:
| 76
| 76
| 573.5849057
| 573.5849057
| ?
|  
| ?
| ?
| ?
| ?
Line 624: Line 627:
| 77
| 77
| 581.1320755
| 581.1320755
| ?
|  
| [[7/5]]
| [[7/5]]
| ?
| ?
Line 640: Line 643:
| 79
| 79
| 596.2264151
| 596.2264151
| ?
|  
| ?
| ?
| ?
| ?
Line 648: Line 651:
| 80
| 80
| 603.7735849
| 603.7735849
| ?
|  
| ?
| ?
| ?
| ?
Line 664: Line 667:
| 82
| 82
| 618.8679245
| 618.8679245
| ?
|  
| [[10/7]]
| [[10/7]]
| ?
| ?
Line 672: Line 675:
| 83
| 83
| 626.4150943
| 626.4150943
| ?
|  
| ?
| ?
| ?
| ?
Line 688: Line 691:
| 85
| 85
| 641.5094340
| 641.5094340
| ?
|  
| [[81/56]]
| [[81/56]]
| ?
| ?
Line 696: Line 699:
| 86
| 86
| 649.0566038
| 649.0566038
| ?
|  
| ?
| ?
| '''[[16/11]]'''
| '''[[16/11]]'''
Line 712: Line 715:
| 88
| 88
| 664.1509434
| 664.1509434
| ?
|  
| ?
| ?
| [[22/15]]
| [[22/15]]
Line 720: Line 723:
| 89
| 89
| 671.6981132
| 671.6981132
| ?
|  
| ?
| ?
| [[81/55]]
| [[81/55]]
Line 736: Line 739:
| 91
| 91
| 686.7924528
| 686.7924528
| ?
|  
| ?
| ?
| [[180/121]]
| [[180/121]]
Line 744: Line 747:
| 92
| 92
| 694.3396226
| 694.3396226
| ?
|  
| [[112/75]]
| [[112/75]]
| ?
| ?
Line 760: Line 763:
| 94
| 94
| 709.4339622
| 709.4339622
| ?
|  
| ?
| ?
| ?
| ?
Line 768: Line 771:
| 95
| 95
| 716.9811321
| 716.9811321
| ?
|  
| ?
| ?
| [[50/33]]
| [[50/33]]
Line 784: Line 787:
| 97
| 97
| 732.0754717
| 732.0754717
| ?
|  
| [[32/21]]
| [[32/21]]
| ?
| ?
Line 792: Line 795:
| 98
| 98
| 739.6226415
| 739.6226415
| ?
|  
| ?
| ?
| 135/88
| 135/88
Line 808: Line 811:
| 100
| 100
| 754.7169811
| 754.7169811
| ?
|  
| ?
| ?
| [[99/64]]
| [[99/64]]
Line 816: Line 819:
| 101
| 101
| 762.2641509
| 762.2641509
| ?
|  
| [[14/9]]
| [[14/9]]
| [[256/165]]
| [[256/165]]
Line 832: Line 835:
| 103
| 103
| 777.3584906
| 777.3584906
| ?
|  
| ?
| ?
| ?
| ?
Line 840: Line 843:
| 104
| 104
| 784.9056604
| 784.9056604
| ?
|  
| ?
| ?
| [[11/7]]
| [[11/7]]
Line 856: Line 859:
| 106
| 106
| 800
| 800
| ?
|  
| [[100/63]]
| [[100/63]]
| ?
| ?
Line 864: Line 867:
| 107
| 107
| 807.5471698
| 807.5471698
| ?
|  
| ?
| ?
| ?
| ?
Line 880: Line 883:
| 109
| 109
| 822.6415094
| 822.6415094
| ?
|  
| ?
| ?
| 825/512
| 825/512
Line 888: Line 891:
| 110
| 110
| 830.1886792
| 830.1886792
| ?
|  
| ?
| ?
| ?
| ?
Line 904: Line 907:
| 112
| 112
| 845.2830189
| 845.2830189
| ?
|  
| ?
| ?
| [[44/27]]
| [[44/27]]
Line 912: Line 915:
| 113
| 113
| 852.8301887
| 852.8301887
|
| ?
| ?
| ?
| [[18/11]]
| [[18/11]]
| ?
| ?
| ?  
| ?
|-
|-
| 114
| 114
Line 928: Line 931:
| 115
| 115
| 867.9245283
| 867.9245283
| ?
|  
| ?
| ?
| ?
| ?
Line 936: Line 939:
| 116
| 116
| 875.4716981
| 875.4716981
| ?
|  
| ?
| ?
| ?
| ?
Line 952: Line 955:
| 118
| 118
| 890.5660377
| 890.5660377
| ?
|  
| ?
| ?
| ?
| ?
Line 960: Line 963:
| 119
| 119
| 898.1132075
| 898.1132075
| ?
|  
| [[42/25]]
| [[42/25]]
| ?
| ?
Line 976: Line 979:
| 121
| 121
| 913.2075472
| 913.2075472
| ?
|  
| ?
| ?
| [[56/33]]
| [[56/33]]
Line 984: Line 987:
| 122
| 122
| 920.7547170
| 920.7547170
| ?
|  
| ?
| ?
| ?
| ?
Line 1,000: Line 1,003:
| 124
| 124
| 935.8490566
| 935.8490566
| ?
|  
| [[12/7]]
| [[12/7]]
| [[55/32]]
| [[55/32]]
Line 1,008: Line 1,011:
| 125
| 125
| 943.3962264
| 943.3962264
| ?
|  
| ?
| ?
| 512/297
| 512/297
Line 1,024: Line 1,027:
| 127
| 127
| 958.4905660
| 958.4905660
| ?
|  
| ?
| ?
| 891/512
| 891/512
Line 1,032: Line 1,035:
| 128
| 128
| 966.0377358
| 966.0377358
| ?
|  
| '''[[7/4]]'''
| '''[[7/4]]'''
| [[96/55]]
| [[96/55]]
Line 1,048: Line 1,051:
| 130
| 130
| 981.1320755
| 981.1320755
| ?
|  
| ?
| ?
| ?
| ?
Line 1,056: Line 1,059:
| 131
| 131
| 988.6792458
| 988.6792458
| ?
|  
| ?
| ?
| ?
| ?
Line 1,072: Line 1,075:
| 133
| 133
| 1003.7735849
| 1003.7735849
| ?
|  
| [[25/14]]
| [[25/14]]
| ?
| ?
Line 1,080: Line 1,083:
| 134
| 134
| 1011.3207547
| 1011.3207547
| ?
|  
| ?
| ?
| ?
| ?
Line 1,096: Line 1,099:
| 136
| 136
| 1026.4150943
| 1026.4150943
| ?
|  
| 1024/567
| 1024/567
| 440/243
| 440/243
Line 1,104: Line 1,107:
| 137
| 137
| 1033.9622642
| 1033.9622642
| ?
|  
| ?
| ?
| [[20/11]]
| [[20/11]]
Line 1,120: Line 1,123:
| 139
| 139
| 1049.0566038
| 1049.0566038
| ?
|  
| ?
| ?
| [[11/6]]
| [[11/6]]
Line 1,128: Line 1,131:
| 140
| 140
| 1056.6037736
| 1056.6037736
| ?
|  
| ?
| ?
| [[81/44]]
| [[81/44]]
Line 1,144: Line 1,147:
| 142
| 142
| 1071.6981132
| 1071.6981132
| ?
|  
| ?
| ?
| ?
| ?
Line 1,152: Line 1,155:
| 143
| 143
| 1079.2452830
| 1079.2452830
| ?
|  
| [[28/15]]
| [[28/15]]
| 512/275
| 512/275
Line 1,168: Line 1,171:
| 145
| 145
| 1094.3396226
| 1094.3396226
| ?
|  
| ?
| ?
| ?
| ?
Line 1,176: Line 1,179:
| 146
| 146
| 1101.8867925
| 1101.8867925
| ?
|  
| ?
| ?
| [[121/64]]
| [[121/64]]
Line 1,192: Line 1,195:
| 148
| 148
| 1116.9811321
| 1116.9811321
| ?
|  
| [[40/21]]
| [[40/21]]
| [[21/11]]
| [[21/11]]
Line 1,200: Line 1,203:
| 149
| 149
| 1124.5283019
| 1124.5283019
| ?
|  
| ?
| ?
| ?
| ?
Line 1,216: Line 1,219:
| 151
| 151
| 1139.6226415
| 1139.6226415
| ?
|  
| [[27/14]]
| [[27/14]]
| ?
| ?
Line 1,224: Line 1,227:
| 152
| 152
| 1147.1698113
| 1147.1698113
| ?
|  
| ?
| ?
| [[64/33]]
| [[64/33]]
Line 1,240: Line 1,243:
| 154
| 154
| 1162.2641509
| 1162.2641509
| ?
|  
| ?
| ?
| [[88/45]]
| [[88/45]]
Line 1,248: Line 1,251:
| 155
| 155
| 1169.8113208
| 1169.8113208
| ?
|  
| [[63/32]]
| [[63/32]]
| [[55/28]], [[108/55]]
| [[55/28]], [[108/55]]
Line 1,264: Line 1,267:
| 157
| 157
| 1184.9056604
| 1184.9056604
| ?
|  
| ?
| ?
| [[240/121]], [[99/50]]
| [[240/121]], [[99/50]]
Line 1,272: Line 1,275:
| 158
| 158
| 1192.4528302
| 1192.4528302
| ?
|  
| [[448/225]]
| [[448/225]]
| [[484/243]]
| [[484/243]]
Retrieved from "https://en.xen.wiki/w/Table_of_159edo_Intervals"