Table of 159edo Intervals

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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.

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 ? ? 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 ? 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 ? ? ? ? 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 ? ? ? ?
94 709.4339622 ? ? ? ? 128/85
95 716.9811321 ? ? 50/33 ? 68/45
96 724.5283019 243/160, 1024/675 ? ? ? ?
97 732.0754717 ? 32/21 ? ? ?
98 739.6226415 ? ? 135/88 ? ?
99 747.1698113 ? ? ? 20/13 ?
100 754.7169811 ? ? 99/64 ? ?
101 762.2641509 ? 14/9 256/165 ? ?
102 769.8113208 25/16 ? ? ? ?
103 777.3584906 ? ? ? ? 80/51
104 784.9056604 ? ? 11/7 52/33 85/54
105 792.4528302 128/81 ? ? ? ?
106 800 ? 100/63 ? ? ?
107 807.5471698 ? ? ? ? 51/32
108 815.0943396 8/5 ? 77/48 ? ?
109 822.6415094 ? ? 825/512 ? ?
110 830.1886792 ? ? ? ? 55/34
111 837.7358491 ? ? ? 13/8 ?
112 845.2830189 ? ? 44/27 ? ?
113 852.8301887 ? ? 18/11 ? ?
114 860.3773585 ? ? ? 64/39 ?
115 867.9245283 ? ? ? ? 119/72, 272/165
116 875.4716981 ? ? ? ? 425/256
117 883.0188679 5/3 ? 128/77 ? ?
118 890.5660377 ? ? ? 429/256 256/153
119 898.1132075 ? 42/25 ? ? ?
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 ? ? ? ?
130 981.1320755 ? ? ? ? 30/17
131 988.6792458 ? ? ? ? 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 ? 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 ? 448/225 484/243 700/351 255/128
159 1200 2/1