Table of 159edo Intervals: Difference between revisions

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This table 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.
#REDIRECT [[159edo#Intervals]]
{| class="wikitable"
|-
!| 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
| 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]]
|729/704
| ?
| ?
|-
| 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]]
| ?
| [[18/17]]
|-
| 14
| 105.6603774
| ?
| ?
| ?
| ?
| '''[[17/16]]'''
|-
| 15
| 113.2075472
| [[16/15]]
| ?
| ?
| ?
| ?
|-
| 16
| 120.7547170
| ?
| [[15/14]]
| ?
| ?
| ?
|-
| 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
| ?
| ?
| ?
| ?
| 289/256
|-
| 29
| 218.8679245
| ?
| ?
| ?
| ?
| [[17/15]]
|-
| 30
| 226.4150943
| [[256/225]]
| ?
| ?
| ?
| ?
|-
| 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]]
| ?
| ?
| ?
|-
| 41
| 309.4339622
| ?
| ?
| ?
| 512/429
| 153/128
|-
| 42
| 316.9811321
| [[6/5]]
| ?
| [[77/64]]
| ?
| ?
|-
| 43
| 324.5283019
| ?
| ?
| ?
| ?
| 512/425
|-
| 44
| 332.0754717
| ?
| ?
| ?
| ?
| 144/119, 165/136
|-
| 45
| 339.6226415
| ?
| ?
| ?
| [[39/32]]
| ?
|-
| 46
| 347.1698113
| ?
| ?
| [[11/9]]
| ?
| ?
|-
| 47
| 354.7169811
| ?
| ?
| [[27/22]]
| ?
| ?
|-
| 48
| 362.2641509
| ?
| ?
| ?
| '''[[16/13]]'''
| ?
|-
| 49
| 369.8113208
| ?
| ?
| ?
| ?
| 68/55
|-
| 50
| 377.3584906
| ?
| ?
| 1024/825
| ?
| ?
|-
| 51
| 384.9056604
| '''[[5/4]]'''
| ?
| [[96/77]]
| ?
| ?
|-
| 52
| 392.4528302
| ?
| ?
| ?
| ?
| [[64/51]]
|-
| 53
| 400
| ?
| [[63/50]]
| ?
| ?
| ?
|-
| 54
| 407.5471698
| [[81/64]]
| ?
| ?
| ?
| ?
|-
| 55
| 415.0943396
| ?
| ?
| [[14/11]]
| [[33/26]]
| 108/85
|-
| 56
| 422.6415094
| ?
| ?
| ?
| ?
| 51/40
|-
| 57
| 430.1886792
| [[32/25]]
| ?
| ?
| ?
| ?
|-
| 58
| 437.7358491
| ?
| [[9/7]]
| [[165/128]]
| ?
| ?
|-
| 59
| 445.2830189
| ?
| ?
| [[128/99]]
| ?
| ?
|-
| 60
| 452.8301887
| ?
| ?
| ?
| [[13/10]]
| ?
|-
| 61
| 460.3773585
| ?
| ?
| 176/135
| ?
| ?
|-
| 62
| 467.9245283
| ?
| [[21/16]]
| ?
| ?
| ?
|-
| 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]]
| ?
| ?
| ?
|-
| 68
| 513.2075472
| ?
| ?
| [[121/90]]
| ?
| ?
|-
| 69
| 520.7547170
| [[27/20]]
| ?
| ?
| ?
| ?
|-
| 70
| 528.3018868
| ?
| ?
| [[110/81]]
| ?
| ?
|-
| 71
| 535.8490566
| ?
| ?
| [[15/11]]
| ?
| ?
|-
| 72
| 543.3962264
| ?
| ?
| ?
| ?
| 256/187
|-
| 73
| 550.9433962
| ?
| ?
| '''[[11/8]]'''
| ?
| ?
|-
| 74
| 558.4905660
| ?
| [[112/81]]
| ?
| ?
| ?
|-
| 75
| 566.0377358
| [[25/18]]
| ?
| ?
| ?
| ?
|-
| 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]]
| ?
| ?
| ?
| ?
|-
| 85
| 641.5094340
| ?
| [[81/56]]
| ?
| ?
| ?
|-
| 86
| 649.0566038
| ?
| ?
| '''[[16/11]]'''
| ?
| ?
|-
| 87
| 656.6037736
| ?
| ?
| ?
| ?
| 187/128
|-
| 88
| 664.1509434
| ?
| ?
| [[22/15]]
| ?
| ?
|-
| 89
| 671.6981132
| ?
| ?
| [[81/55]]
| ?
| ?
|-
| 90
| 679.2452830
| [[40/27]]
| ?
| ?
| ?
| ?
|-
| 91
| 686.7924528
| ?
| ?
| [[180/121]]
| ?
| ?
|-
| 92
| 694.3396226
| ?
| [[112/75]]
| ?
| ?
| ?
|-
| 93
| 701.8867925
| '''[[3/2]]'''
| ?
| ?
| ?
| ?
|-
|}

Latest revision as of 21:58, 7 November 2021

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