Table of 167edo intervals: Difference between revisions

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Let's start with the basics -- get the diatonic marks and prime harmonics right
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Intervals highlighted in '''bold''' are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in ''italic''. Intervals that differ by more than 100% or with odd limit over 800 are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.
Intervals highlighted in '''bold''' are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in ''italic''. Intervals that differ by more than 100% or with odd limit over 800 are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.
{{Todo|complete table|inline=1|text=Add missing ratios}}


{| class="wikitable center-1 right-2 center-3"
{| class="wikitable center-1 right-2 center-3"
Line 24: Line 26:
|  
|  
|  
|  
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| [[169/168]], [[196/195]]
|-
|-
| 2
| 2
Line 30: Line 32:
|  
|  
|  
|  
|  
| [[225/224]]
|  
| [[100/99]]
|  
| [[144/143]]
|-
|-
| 3
| 3
Line 38: Line 40:
|  
|  
|  
|  
| [[64/63]]
|  
|  
|  
| [[105/104]]
|
|-
|-
| 4
| 4
| 28.743
| 28.743
|  
|  
|  
| [[81/80]]
|  
|  
|  
|  
Line 56: Line 58:
|  
|  
|  
|  
|
|875/858
|-
|-
| 6
| 6
Line 63: Line 65:
|  
|  
|  
|  
|  
| [[45/44]]
|  
| 729/715
|-
|-
| 7
| 7
Line 70: Line 72:
|  
|  
|  
|  
|  
| [[36/35]]
|  
|  
|
|
Line 77: Line 79:
| 57.485
| 57.485
|  
|  
|  
| [[6561/6400]]
|  
| [[28/27]]
|  
|  
|  
|  
Line 87: Line 89:
|  
|  
|  
|  
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| 80/77
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| 660/637
|-
|-
| 10
| 10
Line 95: Line 97:
|  
|  
|  
|  
|  
| [[729/704]]
|  
| 176/169
|-
|-
| 11
| 11
| 79.042
| 79.042
| m2
| m2
|  
| [[256/243]]
|  
| 729/700
|  
|  
|  
|  
Line 110: Line 112:
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|  
|  
|  
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| [[21/20]]
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|  
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|  
Line 119: Line 121:
|  
|  
|  
|  
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| 81/77
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|  
|-
|-
Line 127: Line 129:
|  
|  
|  
|  
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| 35/33
|  
|  
|-
|-
| 15
| 15
| 107.784
| 107.784
|  
|
|  
| [[16/15]]
|  
|  
|  
|  
Line 143: Line 145:
|  
|  
|  
|  
|  
| 576/539
|  
|  
|-
|-
Line 149: Line 151:
| 122.156
| 122.156
|  
|  
|  
|
|  
| [[15/14]]
|  
|  
|  
|  
Line 160: Line 162:
|  
|  
|  
|  
|  
| [[14/13]]
|-
|-
| 19
| 19
Line 168: Line 170:
|  
|  
|  
|  
|  
| [[13/12]]
|-
|-
| 20
| 20
Line 174: Line 176:
|  
|  
|  
|  
|  
| [[49/45]]
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|  
|  
|  
Line 183: Line 185:
|  
|  
|  
|  
|  
| [[12/11]]
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|  
|-
|-
Line 190: Line 192:
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|  
|  
|  
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| [[35/32]]
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|  
|  
|  
Line 199: Line 201:
|  
|  
|  
|  
|  
| [[11/10]]
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|  
|-
|-
Line 207: Line 209:
|  
|  
|  
|  
|  
| 875/792
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|  
|-
|-
Line 213: Line 215:
| 179.641
| 179.641
|  
|  
| [[10/9]]
|  
|  
|
|
|  
|  
|  
|-
|-
Line 223: Line 225:
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| 352/315
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|-
|-
Line 230: Line 232:
|  
|  
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| 125/112
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|  
|  
Line 238: Line 240:
|
|
|  
|  
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| 640/567
|  
|  
|  
|  
Line 245: Line 247:
| 208.383
| 208.383
| M2
| M2
|  
| ''[[9/8]]''
|  
|  
|  
|  
Line 254: Line 256:
|  
|  
|  
|  
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| 245/216, 500/441
|  
|  
|  
|  
Line 263: Line 265:
|  
|  
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| 154/135
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|-
|-
Line 278: Line 280:
|  
|  
|  
|  
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| 729/640
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|  
|  
|  
Line 288: Line 290:
|  
|  
|  
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| 52/45
|-
|-
| 35
| 35
Line 294: Line 296:
|  
|  
|  
|  
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| 512/441
|  
|  
|  
|  
Line 301: Line 303:
| 258.683
| 258.683
|  
|  
|  
| 2560/2187
|  
|  
|  
|  
Line 310: Line 312:
|  
|  
|  
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| [[7/6]]
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|  
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|  
Line 319: Line 321:
|  
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| 90/77
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|  
|-
|-
Line 328: Line 330:
|  
|  
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|
|168/143
|-
|-
| 40
| 40
| 287.425
| 287.425
| m3
| m3
| [[32/27]]
|  
|  
|  
|  
|  
| [[13/11]]
|
|-
|-
| 41
| 41
Line 342: Line 344:
|
|
|  
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| 189/160
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|  
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| 245/208
|
|-
|-
| 42
| 42
Line 365: Line 367:
| 316.168
| 316.168
|  
|  
|  
| [[6/5]]
|  
|  
|  
|  
Line 477: Line 479:
| 416.766
| 416.766
| M3
| M3
| [[81/64]]
|  
|  
|  
| [[14/11]]
|
|
|
|-
|-
Line 653: Line 655:
| 574.850
| 574.850
| d5
| d5
|  
| [[1024/729]]
|  
|  
|  
|  
Line 709: Line 711:
| 625.150
| 625.150
| A4
| A4
|  
| [[729/512]]
|  
|  
|  
|  
Line 885: Line 887:
| 783.234
| 783.234
| m6
| m6
|  
| [[128/81]]
|  
|  
|  
|  
Line 997: Line 999:
| 883.832
| 883.832
|  
|  
|  
| [[5/3]]
|  
|  
|  
|  
Line 1,029: Line 1,031:
| 912.575
| 912.575
| M6
| M6
|  
| [[27/16]]
|  
|  
|  
|  
Line 1,117: Line 1,119:
| 991.617
| 991.617
| m7
| m7
|  
| [[16/9]]
|  
|  
|  
|  
Line 1,261: Line 1,263:
| 1120.958
| 1120.958
| M7
| M7
|  
| [[243/128]]
|  
|  
|  
|  

Latest revision as of 16:17, 27 May 2026

This table of 167edo intervals assumes 13-limit patent val ⟨167 265 388 469 578 618] of 167edo.

Intervals highlighted in bold are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in italic. Intervals that differ by more than 100% or with odd limit over 800 are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.

Todo: complete table

Add missing ratios

# Cents Marks 5-limit 7-limit 11-limit 13-limit
0 0.00 P1 1/1
1 7.186 169/168, 196/195
2 14.371 225/224 100/99 144/143
3 21.557 64/63 105/104
4 28.743 81/80
5 35.928 875/858
6 43.114 45/44 729/715
7 50.299 36/35
8 57.485 6561/6400 28/27
9 64.671 80/77 660/637
10 71.856 729/704 176/169
11 79.042 m2 256/243 729/700
12 86.228 21/20
13 93.413 81/77
14 100.599 35/33
15 107.784 16/15
16 114.970 576/539
17 122.156 15/14
18 129.341 14/13
19 136.527 13/12
20 143.713 49/45
21 150.898 12/11
22 158.084 35/32
23 165.269 11/10
24 172.455 875/792
25 179.641 10/9
26 186.826 352/315
27 194.012 125/112
28 201.198 640/567
29 208.383 M2 9/8
30 215.569 245/216, 500/441
31 222.754 154/135
32 229.940 8/7
33 237.126 729/640
34 244.311 52/45
35 251.497 512/441
36 258.683 2560/2187
37 265.868 7/6
38 273.054 90/77
39 280.240 168/143
40 287.425 m3 32/27 13/11
41 294.611 189/160 245/208
42 301.796
43 308.982
44 316.168 6/5
45 323.353
46 330.539
47 337.725
48 344.910
49 352.096
50 359.281 16/13
51 366.467
52 373.653
53 380.838
54 388.024 5/4
55 395.210
56 402.395
57 409.581
58 416.766 M3 81/64 14/11
59 423.952
60 431.138
61 438.323
62 445.509
63 452.695
64 459.880
65 467.066
66 474.251
67 481.437
68 488.623
69 495.808 P4 4/3
70 502.994
71 510.180
72 517.365
73 524.551
74 531.737
75 538.922
76 546.108
77 553.293 11/8
78 560.479
79 567.665
80 574.850 d5 1024/729
81 582.036
82 589.222
83 596.407
84 603.593
85 610.778
86 617.964
87 625.150 A4 729/512
88 632.335
89 639.521
90 646.707 16/11
91 653.892
92 661.078
93 668.263
94 675.449
95 682.635
96 689.820
97 697.006
98 704.192 P5 3/2
99 711.377
100 718.563
101 725.749
102 732.934
103 740.120
104 747.305
105 754.491
106 761.677
107 768.862
108 776.048
109 783.234 m6 128/81
110 790.419
111 797.605
112 804.790
113 811.976 8/5
114 819.162
115 826.347
116 833.533
117 840.719 13/8
118 847.904
119 855.090
120 862.275
121 869.461
122 876.647
123 883.832 5/3
124 891.018
125 898.204
126 905.389
127 912.575 M6 27/16
128 919.760
129 926.946
130 934.132
131 941.317
132 948.503
133 955.689
134 962.874
135 970.060 7/4
136 977.246
137 984.431
138 991.617 m7 16/9
139 998.802
140 1005.988
141 1013.174
142 1020.359
143 1027.545
144 1034.731
145 1041.916
146 1049.102
147 1056.287
148 1063.473
149 1070.659
150 1077.844
151 1085.030
152 1092.216
153 1099.401
154 1106.587
155 1113.772
156 1120.958 M7 243/128
157 1128.144
158 1135.329
159 1142.515
160 1149.701
161 1156.886
162 1164.072
163 1171.257
164 1178.443
165 1185.629
166 1192.814
167 1200.000 P8 2/1
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