User:Overthink/Table of 311edo intervals: Difference between revisions

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Overthink (talk | contribs)
autopatrolled
2,790 edits
expand earlier section; delete some names
Overthink (talk | contribs)
autopatrolled
2,790 edits
finish replacing names with diatonic interval categories; + some more ratios
Line 1: Line 1:
{{Editable user page}}
{{Editable user page}}
Note: Second, sixth, and seventh names can be derived from the third names.
This table assumes 41-limit patent val of 311edo.
{| class="wikitable mw-collapsible right-1 right-2"
{| class="wikitable mw-collapsible right-1 right-2"
|+ Intervals of 311edo
|+ Intervals of 311edo
Line 23: Line 23:
| 3.859
| 3.859
|  
|  
|  
| [[385/384]]
|  
|  
|  
|  
Line 30: Line 30:
| 7.717
| 7.717
|  
|  
|  
| [[225/224]]
|  
|  
|  
|  
Line 150: Line 150:
|
|
|
|
|
|[[24/23]]
|
|
|-
|-
Line 157: Line 157:
|
|
|
|
|
|[[23/22]]
|
|
|-
|-
Line 177: Line 177:
| 88.746
| 88.746
| m2
| m2
|
|[[256/243]]
|
|[[20/19]]
|
|
|-
|-
Line 185: Line 185:
|
|
|
|
|
|[[19/18]]
|
|
|-
|-
Line 199: Line 199:
|
|
|
|
|
|[[18/17]]
|
|
|-
|-
Line 206: Line 206:
|
|
|
|
|
|[[17/16]]
|
|
|-
|-
Line 225: Line 225:
| 30
| 30
| 115.756
| 115.756
|
|A1
| ''[[2187/2048]]''
| ''[[2187/2048]]''
|
|
Line 337: Line 337:
| 46
| 46
| 177.492
| 177.492
|
|d3
|
|
|
|
Line 344: Line 344:
| 47
| 47
| 181.350
| 181.350
|Classical major 2nd
|
|[[10/9]]
|[[10/9]]
|
|
Line 365: Line 365:
| 50
| 50
| 192.926
| 192.926
|Mean major 2nd
|
|
|
|[[19/17]]
|[[19/17]]
Line 386: Line 386:
| 53
| 53
| 204.502
| 204.502
|Pythagorean major 2nd
|M2
|[[9/8]]
|[[9/8]]
|
|
Line 435: Line 435:
| 60
| 60
| 231.511
| 231.511
|Supermajor 2nd
|
|[[8/7]]
|[[8/7]]
|
|
Line 442: Line 442:
| 61
| 61
| 235.370
| 235.370
|
|sd3
|
|
|
|
Line 473: Line 473:
|
|
|
|
|
|[[37/32]]
|-
|-
| 66
| 66
Line 491: Line 491:
| 68
| 68
| 262.379
| 262.379
|
|sA2
|
|
|
|
Line 498: Line 498:
| 69
| 69
| 266.238
| 266.238
|Subminor 3rd
|
|[[7/6]]
|[[7/6]]
|
|
Line 521: Line 521:
|
|
|
|
|
|[[27/23]]
|
|
|-
|-
| 73
| 73
| 281.672
| 281.672
|Diatismic minor 3rd
|
|
|
|
|[[20/17]]
|
|
|-
|-
| 74
| 74
| 285.531
| 285.531
|Pentacircle minor 3rd
|
|[[33/28]]
|[[33/28]]
|
|
Line 540: Line 540:
| 75
| 75
| 289.389
| 289.389
|Major minthmic minor 3rd
|
|[[13/11]]
|[[13/11]]
|
|
Line 547: Line 547:
| 76
| 76
| 293.248
| 293.248
|Pythagorean minor 3rd
|m3
|[[32/27]]
|[[32/27]]
|
|
Line 554: Line 554:
| 77
| 77
| 297.106
| 297.106
|Boethius minor 3rd
|
|
|
|
|
Line 561: Line 561:
| 78
| 78
| 300.965
| 300.965
|Quasi-tempered minor 3rd?
|
|[[25/21]]
|[[25/21]]
|
|
Line 589: Line 589:
| 82
| 82
| 316.399
| 316.399
|Classical minor 3rd
|
|[[6/5]]
|[[6/5]]
|
|
Line 596: Line 596:
| 83
| 83
| 320.257
| 320.257
|Keenanismic minor 3rd
|A2
|[[77/64]]
|[[77/64]]
|
|
Line 603: Line 603:
| 84
| 84
| 324.116
| 324.116
|Marvelous minor 3rd
|
|[[135/112]]
|[[135/112]]
|
|
Line 610: Line 610:
| 85
| 85
| 327.974
| 327.974
|Undetricesimal supraminor 3rd
|
|
|
|
|29/24
|
|[[29/24]]
|-
|-
| 86
| 86
Line 631: Line 631:
| 88
| 88
| 339.550
| 339.550
|Amity supraminor 3rd
|
|
|
|
|
Line 638: Line 638:
| 89
| 89
| 343.408
| 343.408
|Tridecimal subneutral 3rd
|
|[[39/32]]
|[[39/32]]
|
|
Line 645: Line 645:
| 90
| 90
| 347.267
| 347.267
|Undecimal artoneutral 3rd
|
|[[11/9]]
|[[11/9]]
|
|
Line 652: Line 652:
| 91
| 91
| 351.125
| 351.125
|Neutral 3rd
|n3
|
|[[49/40]], [[60/49]]
|
|
|
|
Line 659: Line 659:
| 92
| 92
| 354.984
| 354.984
|Undecimal tendoneutral 3rd
|
|[[27/22]]
|[[27/22]]
|
|
Line 666: Line 666:
| 93
| 93
| 358.842
| 358.842
|Tridecimal supraneutral 3rd
|
|[[16/13]]
|[[16/13]]
|
|
Line 673: Line 673:
| 94
| 94
| 362.701
| 362.701
|Amity submajor 3rd
|
|
|
|
|
Line 682: Line 682:
|
|
|
|
|
|[[21/17]]
|
|
|-
|-
Line 688: Line 688:
| 370.418
| 370.418
|
|
|
|[[26/21]]
|
|
|
|
Line 694: Line 694:
| 97
| 97
| 374.277
| 374.277
|Undetricesimal submajor 3rd
|
|
|
|
|36/29
|
|[[36/29]]
|-
|-
| 98
| 98
| 378.135
| 378.135
|Marvelous major 3rd
|
|
|
|
|
Line 708: Line 708:
| 99
| 99
| 381.994
| 381.994
|Keenanismic major 3rd
|d4
|
|
|
|
Line 715: Line 715:
| 100
| 100
| 385.852
| 385.852
|Classical major 3rd
|
|[[5/4]]
|[[5/4]]
|
|
Line 750: Line 750:
| 105
| 105
| 405.145
| 405.145
|Boethius major 3rd
|
|
|
|
|
Line 757: Line 757:
| 106
| 106
| 409.003
| 409.003
|Pythagorean major 3rd
|M3
|
|[[81/64]]
|
|
|
|
Line 764: Line 764:
| 107
| 107
| 412.862
| 412.862
|Major minthmic major 3rd
|
|
|[[33/26]]
|
|
|
|
Line 771: Line 771:
| 108
| 108
| 416.720
| 416.720
|Pentacircle major 3rd
|
|[[14/11]]
|[[14/11]]
|
|
Line 778: Line 778:
| 109
| 109
| 420.579
| 420.579
|Diatismic major 3rd
|
|
|
|
|[[51/40]]
|
|
|-
|-
| 110
| 110
| 424.437
| 424.437
|Shrubmajor 3rd?
|
|
|
|[[23/18]]
|[[23/18]]
Line 793: Line 793:
| 428.296
| 428.296
|
|
|[[32/25]], [[50/39]]
|
|
|
|[[41/32]]
|
|-
|-
| 112
| 112
| 432.154
| 432.154
|Swetismic supermajor 3rd
|
|
|
|
|
|
|-
|
| 113
|-
| 436.013
| 113
|Septimal major 3rd
| 436.013
|
|[[9/7]]
|[[9/7]]
|
|
Line 813: Line 813:
| 114
| 114
| 439.871
| 439.871
|
|sD4
|
|
|
|
Line 821: Line 821:
| 443.730
| 443.730
|
|
|
|[[128/99]]
|
|
|
|
Line 842: Line 842:
| 455.305
| 455.305
|
|
|
|[[13/10]]
|
|
|
|
Line 862: Line 862:
| 121
| 121
| 466.881
| 466.881
|
|sA3
|
|
|
|
Line 870: Line 870:
| 470.740
| 470.740
|
|
|
|[[21/16]]
|
|
|
|
Line 918: Line 918:
| 129
| 129
| 497.749
| 497.749
|Perfect fourth
|P4
|[[4/3]]
|[[4/3]]
|
|
Line 961: Line 961:
| 520.900
| 520.900
|
|
|
|[[27/20]]
|
|
|
|
Line 967: Line 967:
| 136
| 136
| 524.759
| 524.759
|
|A3
|
|
|
|
Line 1,017: Line 1,017:
| 551.768
| 551.768
|
|
|
|[[11/8]]
|
|
|
|
Line 1,023: Line 1,023:
| 144
| 144
| 555.627
| 555.627
|
|sA4
|
|
|
|
Line 1,073: Line 1,073:
| 582.637
| 582.637
|
|
|
|[[7/5]]
|
|
|
|
Line 1,079: Line 1,079:
| 152
| 152
| 586.495
| 586.495
|
|d5
|
|[[1024/729]]
|
|
|
|
Line 1,087: Line 1,087:
| 590.354
| 590.354
|
|
|
|[[45/32]]
|
|
|
|
Line 1,122: Line 1,122:
| 609.646
| 609.646
|
|
|
|[[64/45]]
|
|
|
|
Line 1,128: Line 1,128:
| 159
| 159
| 613.505
| 613.505
|
|A4
|
|[[729/512]]
|
|
|
|
Line 1,136: Line 1,136:
| 617.363
| 617.363
|
|
|
|[[10/7]]
|
|
|
|
Line 1,184: Line 1,184:
| 167
| 167
| 644.373
| 644.373
|
|sd5
|
|
|
|
Line 1,192: Line 1,192:
| 648.232
| 648.232
|
|
|
|[[16/11]]
|
|
|
|
Line 1,240: Line 1,240:
| 175
| 175
| 675.241
| 675.241
|
|d6
|
|
|
|
Line 1,247: Line 1,247:
| 176
| 176
| 679.100
| 679.100
|Grave fifth
|
|
|[[40/27]]
|
|
|
|
Line 1,289: Line 1,289:
| 182
| 182
| 702.251
| 702.251
|Perfect fifth
|P5
|[[3/2]]
|[[3/2]]
|
|
Line 1,339: Line 1,339:
| 729.260
| 729.260
|
|
|
|[[32/21]]
|
|
|
|
Line 1,345: Line 1,345:
| 190
| 190
| 733.119
| 733.119
|
|sd6
|
|
|
|
Line 1,367: Line 1,367:
| 744.695
| 744.695
|
|
|
|[[20/13]]
|
|
|
|
Line 1,388: Line 1,388:
| 756.270
| 756.270
|
|
|
|[[99/64]]
|
|
|
|
Line 1,394: Line 1,394:
| 197
| 197
| 760.129
| 760.129
|
|sA5
|
|
|
|
Line 1,402: Line 1,402:
| 763.987
| 763.987
|
|
|
|[[14/9]]
|
|
|
|
Line 1,416: Line 1,416:
| 771.704
| 771.704
|
|
|
|[[25/16]], [[39/25]]
|
|
|
|
Line 1,450: Line 1,450:
| 205
| 205
| 790.997
| 790.997
|
|m6
|
|[[128/81]]
|
|
|
|
Line 1,493: Line 1,493:
| 814.148
| 814.148
|
|
|
|[[8/5]]
|
|
|
|
Line 1,499: Line 1,499:
| 212
| 212
| 818.006
| 818.006
|
|A5
|
|
|
|
Line 1,542: Line 1,542:
| 841.158
| 841.158
|
|
|
|[[13/8]]
|
|
|
|
Line 1,555: Line 1,555:
| 220
| 220
| 848.875
| 848.875
|
|n6
|
|
|
|
Line 1,611: Line 1,611:
| 228
| 228
| 879.743
| 879.743
|
|d7
|
|
|
|
Line 1,619: Line 1,619:
| 883.601
| 883.601
|
|
|
|[[5/3]]
|
|
|
|
Line 1,660: Line 1,660:
| 235
| 235
| 906.752
| 906.752
|
|M6
|
|[[27/16]]
|
|
|
|
Line 1,710: Line 1,710:
| 933.762
| 933.762
|
|
|
|[[12/7]]
|
|
|
|
Line 1,716: Line 1,716:
| 243
| 243
| 937.621
| 937.621
|
|sd7
|
|
|
|
Line 1,740: Line 1,740:
|
|
|
|
|
|[[64/37]]
|-
|-
| 247
| 247
| 953.055
| 953.055
|
|
|
|[[26/15]]
|
|
|
|
Line 1,765: Line 1,765:
| 250
| 250
| 964.630
| 964.630
|
|sA6
|
|
|
|
Line 1,773: Line 1,773:
| 968.489
| 968.489
|
|
|
|[[7/4]]
|
|
|
|
Line 1,821: Line 1,821:
| 258
| 258
| 995.498
| 995.498
|
|m7
|
|[[16/9]]
|
|
|
|
Line 1,864: Line 1,864:
| 1018.650
| 1018.650
|
|
|
|[[9/5]]
|
|
|
|
Line 1,870: Line 1,870:
| 265
| 265
| 1022.508
| 1022.508
|
|A6
|
|
|
|
Line 1,920: Line 1,920:
| 1049.518
| 1049.518
|
|
|
|[[11/6]]
|
|
|
|
Line 1,926: Line 1,926:
| 273
| 273
| 1053.376
| 1053.376
|
|n7
|
|[[90/49]]
|
|
|
|
Line 1,976: Line 1,976:
| 1080.386
| 1080.386
|
|
|
|[[28/15]]
|
|
|
|
Line 1,982: Line 1,982:
| 281
| 281
| 1084.244
| 1084.244
|
|d8
|
|
|
|
Line 1,990: Line 1,990:
| 1088.103
| 1088.103
|
|
|
|[[15/8]]
|
|
|
|
Line 2,031: Line 2,031:
| 288
| 288
| 1111.254
| 1111.254
|
|M7
|
|[[243/128]]
|
|[[19/10]]
|
|
|-
|-
Line 2,087: Line 2,087:
| 296
| 296
| 1142.122
| 1142.122
|
|sd8
|
|
|
|
Line 2,136: Line 2,136:
| 303
| 303
| 1169.132
| 1169.132
|
|sA7
|
|
|
|
Line 2,144: Line 2,144:
| 1172.990
| 1172.990
|
|
|
|[[63/32]]
|
|
|
|

Revision as of 23:35, 6 February 2026

This user page is editable by any wiki editor.

As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages.

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This table assumes 41-limit patent val of 311edo.

Intervals of 311edo
Steps Cents Marks Approximate Ratios
13-limit 23-limit 41-limit
0 0.000 P1 1/1
1 3.859 385/384
2 7.717 225/224
3 11.576
4 15.434
5 19.293
6 23.151 81/80
7 27.010 64/63, 65/64, 66/65 69/68 63/62
8 30.868 sd2 55/54, 56/55 57/56 58/57
9 34.727 49/48, 50/49 51/50, 52/51
10 38.585 45/44 46/45
11 42.444 40/39 41/40, 42/41
12 46.302 39/38 37/36, 38/37
13 50.161 36/35 34/33, 35/34
14 54.019 33/32 32/31
15 57.878 sA1 30/29, 31/30
16 61.736 28/27 29/28
17 65.595 27/26
18 69.453 25/24, 26/25
19 73.312 24/23
20 77.170 23/22
21 81.029 22/21
22 84.887 21/20
23 88.746 m2 256/243 20/19
24 92.605 19/18
25 96.463
26 100.322 18/17
27 104.180 17/16
28 108.039
29 111.897 16/15
30 115.756 A1 2187/2048 31/29
31 119.614 15/14
32 123.473
33 127.331 14/13
34 131.190 41/38
35 135.048
36 138.907 13/12
37 142.765
38 146.624 n2
39 150.482 12/11
40 154.341
41 158.199
42 162.058
43 165.916 11/10
44 169.775
45 173.633
46 177.492 d3
47 181.350 10/9
48 185.209
49 189.068 29/26
50 192.926 19/17
51 196.785 28/25
52 200.643
53 204.502 M2 9/8
54 208.360
55 212.219
56 216.077
57 219.936
58 223.794
59 227.653
60 231.511 8/7
61 235.370 sd3
62 239.228
63 243.087
64 246.945 15/13
65 250.804 37/32
66 254.662
67 258.521
68 262.379 sA2
69 266.238 7/6
70 270.096
71 273.955
72 277.814 27/23
73 281.672 20/17
74 285.531 33/28
75 289.389 13/11
76 293.248 m3 32/27
77 297.106
78 300.965 25/21
79 304.823
80 308.682
81 312.540
82 316.399 6/5
83 320.257 A2 77/64
84 324.116 135/112
85 327.974 29/24
86 331.833 40/33
87 335.691 17/14
88 339.550
89 343.408 39/32
90 347.267 11/9
91 351.125 n3 49/40, 60/49
92 354.984 27/22
93 358.842 16/13
94 362.701
95 366.559 21/17
96 370.418 26/21
97 374.277 36/29
98 378.135
99 381.994 d4
100 385.852 5/4
101 389.711
102 393.569
103 397.428
104 401.286
105 405.145
106 409.003 M3 81/64
107 412.862 33/26
108 416.720 14/11
109 420.579 51/40
110 424.437 23/18
111 428.296 32/25, 50/39 41/32
112 432.154
113 436.013 9/7
114 439.871 sD4
115 443.730 128/99
116 447.588
117 451.447
118 455.305 13/10
119 459.164
120 463.023
121 466.881 sA3
122 470.740 21/16
123 474.598
124 478.457
125 482.315
126 486.174
127 490.032
128 493.891
129 497.749 P4 4/3
130 501.608
131 505.466
132 509.325
133 513.183
134 517.042
135 520.900 27/20
136 524.759 A3
137 528.617
138 532.476
139 536.334
140 540.193
141 544.051
142 547.910
143 551.768 11/8
144 555.627 sA4
145 559.486
146 563.344
147 567.203
148 571.061
149 574.920
150 578.778
151 582.637 7/5
152 586.495 d5 1024/729
153 590.354 45/32
154 594.212
155 598.071
156 601.929
157 605.788
158 609.646 64/45
159 613.505 A4 729/512
160 617.363 10/7
161 621.222
162 625.080
163 628.939
164 632.797
165 636.656
166 640.514
167 644.373 sd5
168 648.232 16/11
169 652.090
170 655.949
171 659.807
172 663.666
173 667.524
174 671.383
175 675.241 d6
176 679.100 40/27
177 682.958
178 686.817
179 690.675
180 694.534
181 698.392
182 702.251 P5 3/2
183 706.109
184 709.968
185 713.826
186 717.685
187 721.543
188 725.402
189 729.260 32/21
190 733.119 sd6
191 736.977
192 740.836
193 744.695 20/13
194 748.553
195 752.412
196 756.270 99/64
197 760.129 sA5
198 763.987 14/9
199 767.846
200 771.704 25/16, 39/25
201 775.563
202 779.421
203 783.280
204 787.138
205 790.997 m6 128/81
206 794.855
207 798.714
208 802.572
209 806.431
210 810.289
211 814.148 8/5
212 818.006 A5
213 821.865
214 825.723
215 829.582
216 833.441
217 837.299
218 841.158 13/8
219 845.016
220 848.875 n6
221 852.733
222 856.592
223 860.450
224 864.309
225 868.167
226 872.026
227 875.884
228 879.743 d7
229 883.601 5/3
230 887.460
231 891.318
232 895.177
233 899.035
234 902.894
235 906.752 M6 27/16
236 910.611
237 914.469
238 918.328
239 922.186
240 926.045
241 929.904
242 933.762 12/7
243 937.621 sd7
244 941.479
245 945.338
246 949.196 64/37
247 953.055 26/15
248 956.913
249 960.772
250 964.630 sA6
251 968.489 7/4
252 972.347
253 976.206
254 980.064
255 983.923
256 987.781
257 991.640
258 995.498 m7 16/9
259 999.357
260 1003.215
261 1007.074
262 1010.932
263 1014.791
264 1018.650 9/5
265 1022.508 A6
266 1026.367
267 1030.225
268 1034.084
269 1037.942
270 1041.801
271 1045.659
272 1049.518 11/6
273 1053.376 n7 90/49
274 1057.235
275 1061.093
276 1064.952
277 1068.810
278 1072.669
279 1076.527
280 1080.386 28/15
281 1084.244 d8
282 1088.103 15/8
283 1091.961
284 1095.820
285 1099.678
286 1103.537
287 1107.395
288 1111.254 M7 243/128 19/10
289 1115.113
290 1118.971
291 1122.830
292 1126.688
293 1130.547
294 1134.405
295 1138.264
296 1142.122 sd8
297 1145.981
298 1149.839
299 1153.698
300 1157.556
301 1161.415
302 1165.273
303 1169.132 sA7
304 1172.990 63/32
305 1176.849
306 1180.707
307 1184.566
308 1188.424
309 1192.283
310 1196.141
311 1200.000 Octave 2/1
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