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

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expand a bit
Overthink (talk | contribs)
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expand earlier section; delete some names
Line 6: Line 6:
! rowspan="2" | Steps
! rowspan="2" | Steps
! rowspan="2" | Cents
! rowspan="2" | Cents
! rowspan="2" | Name
! rowspan="2" | Marks
! colspan="3" | Approximate Ratios
! colspan="3" | Approximate Ratios
|-
|-
Line 15: Line 15:
| 0
| 0
| 0.000
| 0.000
|Unison
| P1
|[[1/1]]
| [[1/1]]
|
|  
|
|  
|-
|-
| 1
| 1
| 3.859
| 3.859
|Keenanisma?
|  
|
|  
|
|  
|
|  
|-
|-
| 2
| 2
| 7.717
| 7.717
|Kleisma
|  
|
|  
|
|  
|
|  
|-
|-
| 3
| 3
| 11.576
| 11.576
|Semicomma
|  
|
|
|
|
Line 43: Line 43:
| 4
| 4
| 15.434
| 15.434
|Subcomma (idk)
|  
|
|
|
|
Line 50: Line 50:
| 5
| 5
| 19.293
| 19.293
|Diaschisma
|  
|
|
|
|
Line 57: Line 57:
| 6
| 6
| 23.151
| 23.151
|Comma
|  
|[[81/80]]
| [[81/80]]
|
|
|
|
Line 64: Line 64:
| 7
| 7
| 27.010
| 27.010
|Superprime?
|[[64/63]]
|
|
|
| [[64/63]], [[65/64]], [[66/65]]
| [[69/68]]
| [[63/62]]
|-
|-
| 8
| 8
| 30.868
| 30.868
|
| sd2
|
| [[55/54]], [[56/55]]
|
| [[57/56]]
|
| [[58/57]]
|-
|-
| 9
| 9
| 34.727
| 34.727
|
|
|
| [[49/48]], [[50/49]]
|
| [[51/50]], [[52/51]]
|
|
|-
|-
Line 86: Line 86:
| 38.585
| 38.585
|
|
|
| [[45/44]]
|
| [[46/45]]
|
|
|-
|-
Line 93: Line 93:
| 42.444
| 42.444
|
|
|
| [[40/39]]
|
|  
|
| [[41/40]], [[42/41]]
|-
|-
| 12
| 12
| 46.302
| 46.302
|
|
|
| [[39/38]]
|
|  
|
| [[37/36]], [[38/37]]
|-
|-
| 13
| 13
| 50.161
| 50.161
|
|
|[[36/35]]
| [[36/35]]
|
| [[34/33]], [[35/34]]
|
|  
|-
|-
| 14
| 14
| 54.019
| 54.019
|
|
|[[33/32]]
| [[33/32]]
|
|
|
| [[32/31]]
|-
|-
| 15
| 15
| 57.878
| 57.878
| sA1
|
|
|
|
|
| [[30/29]], [[31/30]]
|
|-
|-
| 16
| 16
| 61.736
| 61.736
|Subminor 2nd
|  
|[[28/27]]
| [[28/27]]
|
|
|
| [[29/28]]
|-
|-
| 17
| 17
| 65.595
| 65.595
|
|
|[[27/26]]
| [[27/26]]
|
|
|
|
Line 142: Line 142:
| 69.453
| 69.453
|
|
|[[25/24]], [[26/25]]
| [[25/24]], [[26/25]]
|
|
|
|
Line 176: Line 176:
| 23
| 23
| 88.746
| 88.746
|Pythagorean minor 2nd
| m2
|
|
|
|
Line 218: Line 218:
| 29
| 29
| 111.897
| 111.897
|Classical minor 2nd
|
|[[16/15]]
| [[16/15]]
|
|
|
|
Line 226: Line 226:
| 115.756
| 115.756
|
|
|''[[2187/2048]]''
| ''[[2187/2048]]''
|
|
|[[31/29]]
| [[31/29]]
|-
|-
| 31
| 31
| 119.614
| 119.614
|
|
|[[15/14]]
| [[15/14]]
|
|
|
|
Line 247: Line 247:
| 127.331
| 127.331
|
|
|[[14/13]]
| [[14/13]]
|
|
|
|
Line 256: Line 256:
|
|
|
|
|[[41/38]]
| [[41/38]]
|-
|-
| 35
| 35
Line 268: Line 268:
| 138.907
| 138.907
|
|
|[[13/12]]
| [[13/12]]
|
|
|
|
Line 281: Line 281:
| 38
| 38
| 146.624
| 146.624
|Neutral 2nd
| n2
|
|
|
|
Line 288: Line 288:
| 39
| 39
| 150.482
| 150.482
|Undecimal tendoneutral 2nd
|
|[[12/11]]
| [[12/11]]
|
|
|
|
Line 317: Line 317:
| 165.916
| 165.916
|
|
|[[11/10]]
| [[11/10]]
|
|
|
|

Revision as of 17:10, 6 February 2026

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Note: Second, sixth, and seventh names can be derived from the third names.

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