Table of 159edo Intervals: Difference between revisions

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Line 336: Line 336:
| 41
| 41
| 309.4339622
| 309.4339622
| colspan="3"| ?
| ?
| ?
| ?
| 512/429
| 512/429
| 153/128
| 153/128
Line 342: Line 344:
| 42
| 42
| 316.9811321
| 316.9811321
| colspan="2"| [[6/5]]
| [[6/5]]
| colspan="3"| [[77/64]]
| ?
| [[77/64]]
| ?
| ?
|-
|-
| 43
| 43
| 324.5283019
| 324.5283019
| colspan="4"| ?  
| ?
| ?
| ?
| ?  
| 512/425
| 512/425
|-
|-
| 44
| 44
| 332.0754717
| 332.0754717
| colspan="4"| ?  
| ?
| ?
| ?
| ?  
| 144/119, 165/136
| 144/119, 165/136
|-
|-
| 45
| 45
| 339.6226415
| 339.6226415
| colspan="3"| ?  
| ?
| colspan="2"| [[39/32]]
| ?
| ?
| [[39/32]]
| ?
|-
|-
| 46
| 46
Line 367: Line 381:
| 47
| 47
| 354.7169811
| 354.7169811
| colspan="2"| ?  
| ?
| colspan="3"| [[27/22]]
| ?
| [[27/22]]
| ?
| ?
|-
|-
| 48
| 48
| 362.2641509
| 362.2641509
| colspan="3"| ?  
| ?
| colspan="2"| '''[[16/13]]'''
| ?
| ?
| '''[[16/13]]'''
| ?
|-
|-
| 49
| 49
| 369.8113208
| 369.8113208
| colspan="4"| ?  
| ?
| ?
| ?
| ?
| 68/55
| 68/55
|-
|-
| 50
| 50
| 377.3584906
| 377.3584906
| colspan="2"| ?  
| ?
| colspan="3"| 1024/825
| ?
| 1024/825
| ?
| ?
|-
|-
| 51
| 51
| 384.9056604
| 384.9056604
| colspan="2"| '''[[5/4]]'''  
| '''[[5/4]]'''  
| colspan="3"| [[96/77]]
| ?
| [[96/77]]
| ?
| ?
|-
|-
| 52
| 52
| 392.4528302
| 392.4528302
| colspan="4"| ?  
| ?
| ?
| ?
| ?
| [[64/51]]
| [[64/51]]
|-
|-
Line 398: Line 430:
| 400
| 400
| ?  
| ?  
| colspan="4"| [[63/50]]
| [[63/50]]
| ?
| ?
| ?
|-
|-
| 54
| 54
| 407.5471698
| 407.5471698
| colspan="5"| [[81/64]]
| [[81/64]]
| ?
| ?
| ?
| ?
|-
|-
| 55
| 55
| 415.0943396
| 415.0943396
| colspan="2"| ?
| ?
| ?
| [[14/11]]
| [[14/11]]
| [[33/26]]
| [[33/26]]
Line 413: Line 453:
| 56
| 56
| 422.6415094
| 422.6415094
| colspan="4"| ?
| ?
| ?
| ?
| ?
| 51/40
| 51/40
|-
|-
| 57
| 57
| 430.1886792
| 430.1886792
| colspan="5"| [[32/25]]
| [[32/25]]
| ?
| ?
| ?
| ?
|-
|-
| 58
| 58
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| ?
| ?
| [[9/7]]
| [[9/7]]
| colspan="4"| [[165/128]]
| [[165/128]]
| ?
| ?
| ?
|-
|-
| 59
| 59
| 445.2830189
| 445.2830189
| colspan="2"| ?
| ?
| colspan="3"| [[128/99]]
| ?
| [[128/99]]
| ?
| ?
|-
|-
| 60
| 60
| 452.8301887
| 452.8301887
| colspan="3"| ?
| ?
| colspan="2"| [[13/10]]
| ?
| ?
| [[13/10]]
| ?
|-
|-
| 61
| 61
| 460.3773585
| 460.3773585
| colspan="2"| ?
| ?
| colspan="3"| 176/135
| ?
| 176/135
| ?
| ?
|-
|-
| 62
| 62
| 467.9245283
| 467.9245283
| ?
| ?
| colspan="4"| [[21/16]]
| [[21/16]]
| ?
| ?
| ?
|-
|-
| 63
| 63
| 475.4716981
| 475.4716981
| colspan="5"| 320/243, 675/512
| 320/243, 675/512
| ?
| ?
| ?
|-
|-
| 64
| 64
| 483.0188679
| 483.0188679
| colspan="2"| ?
| ?
| colspan="2"| [[33/25]]
| ?
| [[33/25]]
| ?
| [[45/34]]
| [[45/34]]
|-
|-
| 65
| 65
| 490.5660377
| 490.5660377
| colspan="4"| ?
| ?
| ?
| ?
| ?
| [[85/64]]
| [[85/64]]
|-
|-
| 66
| 66
| 498.1132075
| 498.1132075
| colspan="5"| '''[[4/3]]'''
| '''[[4/3]]'''
| ?
| ?
| ?
| ?
|-
|-
| 67
| 67
| 505.6603774
| 505.6603774
| ?
| ?
| colspan="4"| [[75/56]]
| [[75/56]]
| ?
| ?
| ?
|-
|-
| 68
| 68
| 513.2075472
| 513.2075472
| colspan="2"| ?
| ?
| colspan="3"| [[121/90]]
| ?
| [[121/90]]
| ?
| ?
|-
|-
| 69
| 69
| 520.7547170
| 520.7547170
| colspan="5"| [[27/20]]
| [[27/20]]
| ?
| ?
| ?
| ?
|-
|-
| 70
| 70
| 528.3018868
| 528.3018868
| colspan="2"| ?
| ?
| colspan="3"| [[110/81]]
| ?
| [[110/81]]
| ?
| ?
|-
|-
| 71
| 71
| 535.8490566
| 535.8490566
| colspan="2"| ?
| ?
| colspan="3"| [[15/11]]
| ?
| [[15/11]]
| ?
| ?
|-
|-
| 72
| 72
| 543.3962264
| 543.3962264
| colspan="4"| ?
| ?
| ?
| ?
| ?
| 256/187
| 256/187
|-
|-
| 73
| 73
| 550.9433962
| 550.9433962
| colspan="2"| ?
| ?
| colspan="3"| '''[[11/8]]'''
| ?
| '''[[11/8]]'''
| ?
| ?
|-
|-
| 74
| 74
| 558.4905660
| 558.4905660
| ?
| ?
| colspan="4"| [[112/81]]
| [[112/81]]
| ?
| ?
| ?
|-
|-
| 75
| 75
| 566.0377358
| 566.0377358
| colspan="5"| [[25/18]]
| [[25/18]]
| ?
| ?
| ?
| ?
|-
|-
| 76
| 76
| 573.5849057
| 573.5849057
| colspan="4"| ?
| ?
| ?
| ?
| ?
| 357/256
| 357/256
|-
|-
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| 581.1320755
| 581.1320755
| ?
| ?
| colspan="4"| [[7/5]]
| [[7/5]]
| ?
| ?
| ?
|-
|-
| 78
| 78
| 588.6792458
| 588.6792458
| colspan="5"| [[1024/729]], [[45/32]]
| [[1024/729]], [[45/32]]
| ?
| ?
| ?
| ?
|-
|-
| 79
| 79
| 596.2264151
| 596.2264151
| colspan="4"| ?
| ?
| ?
| ?
| ?
| [[24/17]]
| [[24/17]]
|-
|-
| 80
| 80
| 603.7735849
| 603.7735849
| colspan="4"| ?
| ?
| ?
| ?
| ?
| [[17/12]]
| [[17/12]]
|-
|-
| 81
| 81
| 611.3207547
| 611.3207547
| colspan="5"| [[729/512]], [[64/45]]
| [[729/512]], [[64/45]]
| ?
| ?
| ?
| ?
|-
|-
| 82
| 82
| 618.8679245
| 618.8679245
| ?
| ?
| colspan="4"| [[10/7]]
| [[10/7]]
| ?
| ?
| ?
|-
|-
|}
|}

Revision as of 02:59, 17 September 2020

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.

Step Cents 5 limit 7 limit 11 limit 13 limit 17 limit
0 0 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 ? ? ?
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