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Delta-rational chord: Difference between revisions

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== DR triads in small edos ==
== DR triads in small edos ==
Shown below are approximate DR triads in edos < 24 with symmetric least-squared error < 0.05. All delta signatures are in the 3-integer limit.
Shown below are approximate DR triads in edos < 24 with symmetric least-squared error < 0.05. All delta signatures are in the 3-integer limit.
{| class="wikitable"
|edo
|steps
|delta sig
|naive LS error
|symmetric LS error
|-
|6
|(0, 2, 5)
|[1, 2]
|0.0025
|0.0026
|-
|6
|(0, 4, 5)
|[3, 1]
|0.0043
|0.0044
|-
|7
|(0, 1, 2)
|[1, 1]
|0.0447
|0.0449
|-
|7
|(0, 2, 5)
|[1, 2]
|0.0242
|0.0247
|-
|7
|(0, 4, 5)
|[3, 1]
|0.0273
|0.0277
|-
|7
|(0, 4, 6)
|[3, 2]
|0.0046
|0.0047
|-
|8
|(0, 1, 2)
|[1, 1]
|0.0391
|0.0392
|-
|8
|(0, 4, 7)
|[1, 1]
|0.0060
|0.0065
|-
|8
|(0, 2, 5)
|[1, 2]
|0.0442
|0.0450
|-
|8
|(0, 5, 7)
|[2, 1]
|0.0416
|0.0432
|-
|8
|(0, 4, 5)
|[3, 1]
|0.0443
|0.0447
|-
|8
|(0, 4, 6)
|[3, 2]
|0.0322
|0.0325
|-
|9
|(0, 1, 2)
|[1, 1]
|0.0347
|0.0348
|-
|9
|(0, 4, 7)
|[1, 1]
|0.0089
|0.0094
|-
|9
|(0, 5, 7)
|[2, 1]
|0.0231
|0.0238
|-
|10
|(0, 1, 2)
|[1, 1]
|0.0312
|0.0313
|-
|10
|(0, 4, 7)
|[1, 1]
|0.0207
|0.0217
|-
|10
|(0, 5, 9)
|[1, 1]
|0.0392
|0.0427
|-
|10
|(0, 2, 7)
|[1, 3]
|0.0463
|0.0468
|-
|10
|(0, 5, 7)
|[2, 1]
|0.0085
|0.0087
|-
|10
|(0, 6, 9)
|[3, 2]
|0.0195
|0.0197
|-
|11
|(0, 1, 2)
|[1, 1]
|0.0283
|0.0284
|-
|11
|(0, 4, 7)
|[1, 1]
|0.0303
|0.0315
|-
|11
|(0, 5, 9)
|[1, 1]
|0.0265
|0.0283
|-
|11
|(0, 6, 10)
|[1, 1]
|0.0415
|0.0454
|-
|11
|(0, 3, 8)
|[1, 2]
|0.0454
|0.0465
|-
|11
|(0, 4, 10)
|[1, 2]
|0.0193
|0.0202
|-
|11
|(0, 2, 7)
|[1, 3]
|0.0301
|0.0304
|-
|11
|(0, 5, 7)
|[2, 1]
|0.0034
|0.0034
|-
|11
|(0, 8, 10)
|[3, 1]
|0.0106
|0.0108
|-
|11
|(0, 6, 9)
|[3, 2]
|0.0088
|0.0089
|-
|12
|(0, 1, 2)
|[1, 1]
|0.0260
|0.0260
|-
|12
|(0, 4, 7)
|[1, 1]
|0.0383
|0.0395
|-
|12
|(0, 5, 9)
|[1, 1]
|0.0159
|0.0168
|-
|12
|(0, 3, 8)
|[1, 2]
|0.0321
|0.0327
|-
|12
|(0, 4, 10)
|[1, 2]
|0.0025
|0.0026
|-
|12
|(0, 2, 7)
|[1, 3]
|0.0165
|0.0166
|-
|12
|(0, 3, 10)
|[1, 3]
|0.0310
|0.0316
|-
|12
|(0, 2, 3)
|[2, 1]
|0.0489
|0.0490
|-
|12
|(0, 5, 7)
|[2, 1]
|0.0132
|0.0133
|-
|12
|(0, 8, 11)
|[2, 1]
|0.0125
|0.0130
|-
|12
|(0, 8, 10)
|[3, 1]
|0.0043
|0.0044
|-
|12
|(0, 6, 9)
|[3, 2]
|0.0322
|0.0325
|-
|13
|(0, 1, 2)
|[1, 1]
|0.0240
|0.0240
|-
|13
|(0, 2, 4)
|[1, 1]
|0.0481
|0.0485
|-
|13
|(0, 4, 7)
|[1, 1]
|0.0451
|0.0462
|-
|13
|(0, 5, 9)
|[1, 1]
|0.0070
|0.0074
|-
|13
|(0, 7, 12)
|[1, 1]
|0.0087
|0.0095
|-
|13
|(0, 3, 8)
|[1, 2]
|0.0207
|0.0210
|-
|13
|(0, 4, 10)
|[1, 2]
|0.0119
|0.0122
|-
|13
|(0, 5, 12)
|[1, 2]
|0.0215
|0.0225
|-
|13
|(0, 2, 7)
|[1, 3]
|0.0049
|0.0050
|-
|13
|(0, 3, 10)
|[1, 3]
|0.0145
|0.0147
|-
|13
|(0, 2, 3)
|[2, 1]
|0.0451
|0.0452
|-
|13
|(0, 5, 7)
|[2, 1]
|0.0214
|0.0217
|-
|13
|(0, 8, 11)
|[2, 1]
|0.0005
|0.0005
|-
|13
|(0, 8, 10)
|[3, 1]
|0.0167
|0.0170
|-
|13
|(0, 8, 12)
|[3, 2]
|0.0275
|0.0279
|-
|14
|(0, 1, 2)
|[1, 1]
|0.0222
|0.0223
|-
|14
|(0, 2, 4)
|[1, 1]
|0.0447
|0.0449
|-
|14
|(0, 5, 9)
|[1, 1]
|0.0006
|0.0006
|-
|14
|(0, 6, 11)
|[1, 1]
|0.0401
|0.0426
|-
|14
|(0, 7, 12)
|[1, 1]
|0.0186
|0.0201
|-
|14
|(0, 1, 3)
|[1, 2]
|0.0468
|0.0469
|-
|14
|(0, 3, 8)
|[1, 2]
|0.0110
|0.0111
|-
|14
|(0, 4, 10)
|[1, 2]
|0.0242
|0.0247
|-
|14
|(0, 5, 12)
|[1, 2]
|0.0363
|0.0377
|-
|14
|(0, 2, 7)
|[1, 3]
|0.0050
|0.0050
|-
|14
|(0, 3, 10)
|[1, 3]
|0.0002
|0.0002
|-
|14
|(0, 4, 13)
|[1, 3]
|0.0294
|0.0301
|-
|14
|(0, 2, 3)
|[2, 1]
|0.0418
|0.0419
|-
|14
|(0, 5, 7)
|[2, 1]
|0.0284
|0.0287
|-
|14
|(0, 8, 11)
|[2, 1]
|0.0116
|0.0119
|-
|14
|(0, 4, 9)
|[2, 3]
|0.0461
|0.0464
|-
|14
|(0, 7, 9)
|[3, 1]
|0.0393
|0.0397
|-
|14
|(0, 8, 10)
|[3, 1]
|0.0273
|0.0277
|-
|14
|(0, 8, 12)
|[3, 2]
|0.0046
|0.0047
|-
|15
|(0, 1, 2)
|[1, 1]
|0.0208
|0.0208
|-
|15
|(0, 2, 4)
|[1, 1]
|0.0417
|0.0419
|-
|15
|(0, 5, 9)
|[1, 1]
|0.0071
|0.0074
|-
|15
|(0, 6, 11)
|[1, 1]
|0.0319
|0.0336
|-
|15
|(0, 7, 12)
|[1, 1]
|0.0273
|0.0291
|-
|15
|(0, 8, 14)
|[1, 1]
|0.0149
|0.0164
|-
|15
|(0, 1, 3)
|[1, 2]
|0.0437
|0.0437
|-
|15
|(0, 3, 8)
|[1, 2]
|0.0025
|0.0025
|-
|15
|(0, 4, 10)
|[1, 2]
|0.0349
|0.0355
|-
|15
|(0, 2, 7)
|[1, 3]
|0.0137
|0.0137
|-
|15
|(0, 3, 10)
|[1, 3]
|0.0122
|0.0123
|-
|15
|(0, 4, 13)
|[1, 3]
|0.0134
|0.0137
|-
|15
|(0, 2, 3)
|[2, 1]
|0.0390
|0.0391
|-
|15
|(0, 5, 7)
|[2, 1]
|0.0345
|0.0348
|-
|15
|(0, 7, 10)
|[2, 1]
|0.0415
|0.0423
|-
|15
|(0, 8, 11)
|[2, 1]
|0.0211
|0.0216
|-
|15
|(0, 3, 7)
|[2, 3]
|0.0496
|0.0498
|-
|15
|(0, 4, 9)
|[2, 3]
|0.0294
|0.0296
|-
|15
|(0, 5, 11)
|[2, 3]
|0.0356
|0.0359
|-
|15
|(0, 7, 9)
|[3, 1]
|0.0304
|0.0306
|-
|15
|(0, 8, 10)
|[3, 1]
|0.0364
|0.0368
|-
|15
|(0, 8, 12)
|[3, 2]
|0.0151
|0.0152
|-
|16
|(0, 1, 2)
|[1, 1]
|0.0195
|0.0195
|-
|16
|(0, 2, 4)
|[1, 1]
|0.0391
|0.0392
|-
|16
|(0, 5, 9)
|[1, 1]
|0.0129
|0.0132
|-
|16
|(0, 6, 11)
|[1, 1]
|0.0248
|0.0259
|-
|16
|(0, 7, 12)
|[1, 1]
|0.0348
|0.0368
|-
|16
|(0, 8, 14)
|[1, 1]
|0.0060
|0.0065
|-
|16
|(0, 9, 15)
|[1, 1]
|0.0373
|0.0410
|-
|16
|(0, 1, 3)
|[1, 2]
|0.0410
|0.0410
|-
|16
|(0, 3, 8)
|[1, 2]
|0.0049
|0.0050
|-
|16
|(0, 4, 10)
|[1, 2]
|0.0442
|0.0450
|-
|16
|(0, 5, 13)
|[1, 2]
|0.0386
|0.0398
|-
|16
|(0, 6, 15)
|[1, 2]
|0.0257
|0.0268
|-
|16
|(0, 2, 7)
|[1, 3]
|0.0213
|0.0213
|-
|16
|(0, 3, 10)
|[1, 3]
|0.0231
|0.0233
|-
|16
|(0, 4, 13)
|[1, 3]
|0.0007
|0.0008
|-
|16
|(0, 2, 3)
|[2, 1]
|0.0365
|0.0366
|-
|16
|(0, 5, 7)
|[2, 1]
|0.0398
|0.0401
|-
|16
|(0, 7, 10)
|[2, 1]
|0.0334
|0.0340
|-
|16
|(0, 8, 11)
|[2, 1]
|0.0294
|0.0300
|-
|16
|(0, 10, 14)
|[2, 1]
|0.0416
|0.0432
|-
|16
|(0, 11, 15)
|[2, 1]
|0.0010
|0.0010
|-
|16
|(0, 3, 7)
|[2, 3]
|0.0383
|0.0384
|-
|16
|(0, 4, 9)
|[2, 3]
|0.0148
|0.0149
|-
|16
|(0, 5, 11)
|[2, 3]
|0.0178
|0.0179
|-
|16
|(0, 6, 13)
|[2, 3]
|0.0348
|0.0352
|-
|16
|(0, 7, 9)
|[3, 1]
|0.0227
|0.0228
|-
|16
|(0, 8, 10)
|[3, 1]
|0.0443
|0.0447
|-
|16
|(0, 12, 15)
|[3, 1]
|0.0162
|0.0166
|-
|16
|(0, 8, 12)
|[3, 2]
|0.0322
|0.0325
|-
|16
|(0, 10, 15)
|[3, 2]
|0.0325
|0.0330
|-
|17
|(0, 1, 2)
|[1, 1]
|0.0183
|0.0183
|-
|17
|(0, 2, 4)
|[1, 1]
|0.0367
|0.0369
|-
|17
|(0, 5, 9)
|[1, 1]
|0.0179
|0.0184
|-
|17
|(0, 6, 11)
|[1, 1]
|0.0185
|0.0192
|-
|17
|(0, 7, 12)
|[1, 1]
|0.0414
|0.0434
|-
|17
|(0, 8, 14)
|[1, 1]
|0.0019
|0.0020
|-
|17
|(0, 9, 15)
|[1, 1]
|0.0454
|0.0494
|-
|17
|(0, 9, 16)
|[1, 1]
|0.0327
|0.0360
|-
|17
|(0, 1, 3)
|[1, 2]
|0.0386
|0.0386
|-
|17
|(0, 3, 8)
|[1, 2]
|0.0115
|0.0116
|-
|17
|(0, 5, 13)
|[1, 2]
|0.0281
|0.0288
|-
|17
|(0, 6, 15)
|[1, 2]
|0.0134
|0.0139
|-
|17
|(0, 2, 7)
|[1, 3]
|0.0280
|0.0281
|-
|17
|(0, 3, 10)
|[1, 3]
|0.0328
|0.0331
|-
|17
|(0, 4, 13)
|[1, 3]
|0.0133
|0.0135
|-
|17
|(0, 5, 16)
|[1, 3]
|0.0164
|0.0168
|-
|17
|(0, 2, 3)
|[2, 1]
|0.0344
|0.0344
|-
|17
|(0, 5, 7)
|[2, 1]
|0.0444
|0.0447
|-
|17
|(0, 7, 10)
|[2, 1]
|0.0264
|0.0267
|-
|17
|(0, 8, 11)
|[2, 1]
|0.0366
|0.0373
|-
|17
|(0, 10, 14)
|[2, 1]
|0.0318
|0.0328
|-
|17
|(0, 11, 15)
|[2, 1]
|0.0110
|0.0114
|-
|17
|(0, 12, 16)
|[2, 1]
|0.0477
|0.0499
|-
|17
|(0, 3, 7)
|[2, 3]
|0.0283
|0.0284
|-
|17
|(0, 4, 9)
|[2, 3]
|0.0020
|0.0020
|-
|17
|(0, 5, 11)
|[2, 3]
|0.0021
|0.0021
|-
|17
|(0, 6, 13)
|[2, 3]
|0.0163
|0.0164
|-
|17
|(0, 7, 15)
|[2, 3]
|0.0389
|0.0394
|-
|17
|(0, 3, 4)
|[3, 1]
|0.0499
|0.0500
|-
|17
|(0, 7, 9)
|[3, 1]
|0.0159
|0.0160
|-
|17
|(0, 11, 14)
|[3, 1]
|0.0474
|0.0483
|-
|17
|(0, 12, 15)
|[3, 1]
|0.0053
|0.0054
|-
|17
|(0, 13, 16)
|[3, 1]
|0.0310
|0.0318
|-
|17
|(0, 8, 12)
|[3, 2]
|0.0472
|0.0476
|-
|17
|(0, 10, 15)
|[3, 2]
|0.0133
|0.0135
|-
|18
|(0, 1, 2)
|[1, 1]
|0.0173
|0.0173
|-
|18
|(0, 2, 4)
|[1, 1]
|0.0347
|0.0348
|-
|18
|(0, 5, 9)
|[1, 1]
|0.0224
|0.0229
|-
|18
|(0, 6, 11)
|[1, 1]
|0.0129
|0.0134
|-
|18
|(0, 7, 12)
|[1, 1]
|0.0472
|0.0493
|-
|18
|(0, 7, 13)
|[1, 1]
|0.0430
|0.0452
|-
|18
|(0, 8, 14)
|[1, 1]
|0.0089
|0.0094
|-
|18
|(0, 9, 16)
|[1, 1]
|0.0246
|0.0267
|-
|18
|(0, 10, 17)
|[1, 1]
|0.0145
|0.0160
|-
|18
|(0, 1, 3)
|[1, 2]
|0.0364
|0.0365
|-
|18
|(0, 3, 8)
|[1, 2]
|0.0173
|0.0174
|-
|18
|(0, 5, 13)
|[1, 2]
|0.0186
|0.0191
|-
|18
|(0, 6, 15)
|[1, 2]
|0.0025
|0.0026
|-
|18
|(0, 7, 17)
|[1, 2]
|0.0038
|0.0040
|-
|18
|(0, 2, 7)
|[1, 3]
|0.0340
|0.0341
|-
|18
|(0, 3, 10)
|[1, 3]
|0.0414
|0.0417
|-
|18
|(0, 4, 13)
|[1, 3]
|0.0244
|0.0248
|-
|18
|(0, 5, 16)
|[1, 3]
|0.0028
|0.0028
|-
|18
|(0, 2, 3)
|[2, 1]
|0.0324
|0.0325
|-
|18
|(0, 5, 7)
|[2, 1]
|0.0485
|0.0488
|-
|18
|(0, 7, 10)
|[2, 1]
|0.0201
|0.0204
|-
|18
|(0, 8, 11)
|[2, 1]
|0.0430
|0.0437
|-
|18
|(0, 10, 14)
|[2, 1]
|0.0231
|0.0238
|-
|18
|(0, 11, 15)
|[2, 1]
|0.0198
|0.0205
|-
|18
|(0, 3, 7)
|[2, 3]
|0.0194
|0.0194
|-
|18
|(0, 4, 9)
|[2, 3]
|0.0094
|0.0095
|-
|18
|(0, 5, 11)
|[2, 3]
|0.0119
|0.0120
|-
|18
|(0, 6, 13)
|[2, 3]
|0.0002
|0.0002
|-
|18
|(0, 7, 15)
|[2, 3]
|0.0198
|0.0201
|-
|18
|(0, 8, 17)
|[2, 3]
|0.0453
|0.0461
|-
|18
|(0, 3, 4)
|[3, 1]
|0.0471
|0.0472
|-
|18
|(0, 7, 9)
|[3, 1]
|0.0099
|0.0099
|-
|18
|(0, 11, 14)
|[3, 1]
|0.0380
|0.0386
|-
|18
|(0, 12, 15)
|[3, 1]
|0.0043
|0.0044
|-
|18
|(0, 13, 16)
|[3, 1]
|0.0407
|0.0417
|-
|18
|(0, 5, 8)
|[3, 2]
|0.0495
|0.0497
|-
|18
|(0, 10, 15)
|[3, 2]
|0.0036
|0.0036
|-
|19
|(0, 1, 2)
|[1, 1]
|0.0164
|0.0164
|-
|19
|(0, 2, 4)
|[1, 1]
|0.0329
|0.0330
|-
|19
|(0, 3, 6)
|[1, 1]
|0.0494
|0.0498
|-
|19
|(0, 5, 9)
|[1, 1]
|0.0264
|0.0269
|-
|19
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|-
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|-
|19
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|-
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|-
|19
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|-
|19
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|-
|19
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|-
|19
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|-
|19
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|-
|19
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|-
|19
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|-
|19
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|-
|19
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|-
|19
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|-
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|-
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|-
|19
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|-
|19
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|-
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|-
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|-
|19
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|-
|19
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|0.0115
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|-
|19
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|-
|19
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|-
|19
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|-
|19
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|0.0028
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|-
|19
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|0.0260
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|-
|19
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|0.0446
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|-
|19
|(0, 7, 9)
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|0.0045
|0.0045
|-
|19
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|0.0296
|0.0300
|-
|19
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|0.0128
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|-
|19
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|0.0412
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|-
|19
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|0.0464
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|-
|19
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|0.0187
|0.0189
|-
|19
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|0.0359
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|-
|20
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|-
|20
|(0, 2, 4)
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|-
|20
|(0, 3, 6)
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|0.0469
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|-
|20
|(0, 5, 9)
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|0.0300
|0.0305
|-
|20
|(0, 6, 11)
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|0.0035
|0.0036
|-
|20
|(0, 7, 13)
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|0.0317
|0.0330
|-
|20
|(0, 8, 14)
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|0.0207
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|-
|20
|(0, 9, 16)
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|0.0109
|0.0116
|-
|20
|(0, 10, 17)
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|0.0287
|0.0310
|-
|20
|(0, 10, 18)
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|0.0392
|0.0427
|-
|20
|(0, 11, 19)
|[1, 1]
|0.0036
|0.0039
|-
|20
|(0, 1, 3)
|[1, 2]
|0.0328
|0.0328
|-
|20
|(0, 3, 8)
|[1, 2]
|0.0272
|0.0274
|-
|20
|(0, 4, 11)
|[1, 2]
|0.0369
|0.0374
|-
|20
|(0, 5, 13)
|[1, 2]
|0.0026
|0.0026
|-
|20
|(0, 6, 15)
|[1, 2]
|0.0162
|0.0166
|-
|20
|(0, 7, 17)
|[1, 2]
|0.0250
|0.0259
|-
|20
|(0, 7, 18)
|[1, 2]
|0.0467
|0.0485
|-
|20
|(0, 8, 19)
|[1, 2]
|0.0271
|0.0283
|-
|20
|(0, 2, 7)
|[1, 3]
|0.0442
|0.0443
|-
|20
|(0, 4, 13)
|[1, 3]
|0.0436
|0.0440
|-
|20
|(0, 4, 14)
|[1, 3]
|0.0463
|0.0468
|-
|20
|(0, 5, 16)
|[1, 3]
|0.0206
|0.0209
|-
|20
|(0, 6, 19)
|[1, 3]
|0.0076
|0.0078
|-
|20
|(0, 2, 3)
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|0.0292
|0.0292
|-
|20
|(0, 7, 10)
|[2, 1]
|0.0095
|0.0096
|-
|20
|(0, 10, 14)
|[2, 1]
|0.0085
|0.0087
|-
|20
|(0, 11, 15)
|[2, 1]
|0.0348
|0.0357
|-
|20
|(0, 13, 18)
|[2, 1]
|0.0238
|0.0247
|-
|20
|(0, 14, 19)
|[2, 1]
|0.0087
|0.0091
|-
|20
|(0, 3, 7)
|[2, 3]
|0.0043
|0.0043
|-
|20
|(0, 4, 9)
|[2, 3]
|0.0289
|0.0290
|-
|20
|(0, 5, 11)
|[2, 3]
|0.0356
|0.0358
|-
|20
|(0, 6, 13)
|[2, 3]
|0.0283
|0.0285
|-
|20
|(0, 7, 15)
|[2, 3]
|0.0125
|0.0127
|-
|20
|(0, 8, 17)
|[2, 3]
|0.0086
|0.0087
|-
|20
|(0, 9, 19)
|[2, 3]
|0.0335
|0.0341
|-
|20
|(0, 3, 4)
|[3, 1]
|0.0423
|0.0424
|-
|20
|(0, 7, 9)
|[3, 1]
|0.0003
|0.0003
|-
|20
|(0, 11, 14)
|[3, 1]
|0.0221
|0.0223
|-
|20
|(0, 12, 15)
|[3, 1]
|0.0205
|0.0208
|-
|20
|(0, 5, 8)
|[3, 2]
|0.0336
|0.0337
|-
|20
|(0, 7, 11)
|[3, 2]
|0.0361
|0.0362
|-
|20
|(0, 10, 15)
|[3, 2]
|0.0322
|0.0325
|-
|20
|(0, 12, 18)
|[3, 2]
|0.0195
|0.0197
|-
|20
|(0, 13, 19)
|[3, 2]
|0.0460
|0.0468
|-
|21
|(0, 1, 2)
|[1, 1]
|0.0148
|0.0148
|-
|21
|(0, 2, 4)
|[1, 1]
|0.0297
|0.0298
|-
|21
|(0, 3, 6)
|[1, 1]
|0.0447
|0.0449
|-
|21
|(0, 5, 9)
|[1, 1]
|0.0333
|0.0338
|-
|21
|(0, 6, 11)
|[1, 1]
|0.0006
|0.0006
|-
|21
|(0, 7, 13)
|[1, 1]
|0.0269
|0.0278
|-
|21
|(0, 8, 14)
|[1, 1]
|0.0257
|0.0268
|-
|21
|(0, 9, 16)
|[1, 1]
|0.0051
|0.0054
|-
|21
|(0, 10, 17)
|[1, 1]
|0.0348
|0.0372
|-
|21
|(0, 10, 18)
|[1, 1]
|0.0325
|0.0351
|-
|21
|(0, 11, 19)
|[1, 1]
|0.0033
|0.0036
|-
|21
|(0, 12, 20)
|[1, 1]
|0.0350
|0.0387
|-
|21
|(0, 1, 3)
|[1, 2]
|0.0312
|0.0313
|-
|21
|(0, 3, 8)
|[1, 2]
|0.0315
|0.0317
|-
|21
|(0, 4, 11)
|[1, 2]
|0.0311
|0.0315
|-
|21
|(0, 5, 13)
|[1, 2]
|0.0043
|0.0044
|-
|21
|(0, 6, 15)
|[1, 2]
|0.0242
|0.0247
|-
|21
|(0, 7, 17)
|[1, 2]
|0.0341
|0.0351
|-
|21
|(0, 7, 18)
|[1, 2]
|0.0372
|0.0385
|-
|21
|(0, 8, 19)
|[1, 2]
|0.0372
|0.0388
|-
|21
|(0, 8, 20)
|[1, 2]
|0.0290
|0.0303
|-
|21
|(0, 1, 4)
|[1, 3]
|0.0476
|0.0477
|-
|21
|(0, 2, 7)
|[1, 3]
|0.0485
|0.0486
|-
|21
|(0, 3, 11)
|[1, 3]
|0.0475
|0.0478
|-
|21
|(0, 4, 14)
|[1, 3]
|0.0378
|0.0382
|-
|21
|(0, 5, 16)
|[1, 3]
|0.0306
|0.0311
|-
|21
|(0, 5, 17)
|[1, 3]
|0.0451
|0.0459
|-
|21
|(0, 6, 19)
|[1, 3]
|0.0042
|0.0043
|-
|21
|(0, 2, 3)
|[2, 1]
|0.0278
|0.0278
|-
|21
|(0, 7, 10)
|[2, 1]
|0.0050
|0.0051
|-
|21
|(0, 10, 14)
|[2, 1]
|0.0023
|0.0023
|-
|21
|(0, 11, 15)
|[2, 1]
|0.0411
|0.0421
|-
|21
|(0, 13, 18)
|[2, 1]
|0.0157
|0.0163
|-
|21
|(0, 14, 19)
|[2, 1]
|0.0169
|0.0176
|-
|21
|(0, 15, 20)
|[2, 1]
|0.0458
|0.0480
|-
|21
|(0, 3, 7)
|[2, 3]
|0.0022
|0.0022
|-
|21
|(0, 4, 9)
|[2, 3]
|0.0372
|0.0373
|-
|21
|(0, 5, 11)
|[2, 3]
|0.0458
|0.0460
|-
|21
|(0, 6, 13)
|[2, 3]
|0.0403
|0.0406
|-
|21
|(0, 7, 15)
|[2, 3]
|0.0264
|0.0266
|-
|21
|(0, 8, 17)
|[2, 3]
|0.0071
|0.0072
|-
|21
|(0, 9, 19)
|[2, 3]
|0.0160
|0.0162
|-
|21
|(0, 3, 4)
|[3, 1]
|0.0403
|0.0403
|-
|21
|(0, 7, 9)
|[3, 1]
|0.0046
|0.0046
|-
|21
|(0, 11, 14)
|[3, 1]
|0.0153
|0.0155
|-
|21
|(0, 12, 15)
|[3, 1]
|0.0273
|0.0277
|-
|21
|(0, 16, 20)
|[3, 1]
|0.0191
|0.0196
|-
|21
|(0, 5, 8)
|[3, 2]
|0.0268
|0.0269
|-
|21
|(0, 7, 11)
|[3, 2]
|0.0268
|0.0269
|-
|21
|(0, 9, 14)
|[3, 2]
|0.0480
|0.0483
|-
|21
|(0, 10, 15)
|[3, 2]
|0.0444
|0.0448
|-
|21
|(0, 12, 18)
|[3, 2]
|0.0046
|0.0047
|-
|22
|(0, 1, 2)
|[1, 1]
|0.0141
|0.0141
|-
|22
|(0, 2, 4)
|[1, 1]
|0.0283
|0.0284
|-
|22
|(0, 3, 6)
|[1, 1]
|0.0426
|0.0429
|-
|22
|(0, 5, 9)
|[1, 1]
|0.0362
|0.0367
|-
|22
|(0, 6, 11)
|[1, 1]
|0.0042
|0.0043
|-
|22
|(0, 7, 13)
|[1, 1]
|0.0225
|0.0232
|-
|22
|(0, 8, 14)
|[1, 1]
|0.0303
|0.0315
|-
|22
|(0, 8, 15)
|[1, 1]
|0.0461
|0.0481
|-
|22
|(0, 9, 16)
|[1, 1]
|0.0003
|0.0003
|-
|22
|(0, 10, 17)
|[1, 1]
|0.0403
|0.0428
|-
|22
|(0, 10, 18)
|[1, 1]
|0.0265
|0.0283
|-
|22
|(0, 11, 19)
|[1, 1]
|0.0096
|0.0104
|-
|22
|(0, 12, 20)
|[1, 1]
|0.0415
|0.0454
|-
|22
|(0, 12, 21)
|[1, 1]
|0.0182
|0.0201
|-
|22
|(0, 1, 3)
|[1, 2]
|0.0298
|0.0298
|-
|22
|(0, 3, 8)
|[1, 2]
|0.0354
|0.0355
|-
|22
|(0, 4, 11)
|[1, 2]
|0.0259
|0.0261
|-
|22
|(0, 5, 13)
|[1, 2]
|0.0106
|0.0108
|-
|22
|(0, 6, 15)
|[1, 2]
|0.0315
|0.0321
|-
|22
|(0, 6, 16)
|[1, 2]
|0.0454
|0.0465
|-
|22
|(0, 7, 17)
|[1, 2]
|0.0424
|0.0435
|-
|22
|(0, 7, 18)
|[1, 2]
|0.0286
|0.0295
|-
|22
|(0, 8, 19)
|[1, 2]
|0.0465
|0.0482
|-
|22
|(0, 8, 20)
|[1, 2]
|0.0193
|0.0202
|-
|22
|(0, 9, 21)
|[1, 2]
|0.0459
|0.0481
|-
|22
|(0, 1, 4)
|[1, 3]
|0.0455
|0.0455
|-
|22
|(0, 3, 11)
|[1, 3]
|0.0415
|0.0418
|-
|22
|(0, 4, 14)
|[1, 3]
|0.0301
|0.0304
|-
|22
|(0, 5, 16)
|[1, 3]
|0.0398
|0.0404
|-
|22
|(0, 5, 17)
|[1, 3]
|0.0357
|0.0363
|-
|22
|(0, 6, 19)
|[1, 3]
|0.0151
|0.0154
|-
|22
|(0, 2, 3)
|[2, 1]
|0.0265
|0.0265
|-
|22
|(0, 7, 10)
|[2, 1]
|0.0010
|0.0010
|-
|22
|(0, 9, 13)
|[2, 1]
|0.0478
|0.0485
|-
|22
|(0, 10, 14)
|[2, 1]
|0.0034
|0.0034
|-
|22
|(0, 11, 15)
|[2, 1]
|0.0469
|0.0478
|-
|22
|(0, 12, 17)
|[2, 1]
|0.0457
|0.0469
|-
|22
|(0, 13, 18)
|[2, 1]
|0.0085
|0.0088
|-
|22
|(0, 14, 19)
|[2, 1]
|0.0242
|0.0251
|-
|22
|(0, 3, 7)
|[2, 3]
|0.0080
|0.0081
|-
|22
|(0, 4, 9)
|[2, 3]
|0.0448
|0.0449
|-
|22
|(0, 7, 15)
|[2, 3]
|0.0390
|0.0393
|-
|22
|(0, 8, 17)
|[2, 3]
|0.0214
|0.0216
|-
|22
|(0, 9, 19)
|[2, 3]
|0.0000
|0.0000
|-
|22
|(0, 10, 21)
|[2, 3]
|0.0240
|0.0244
|-
|22
|(0, 3, 4)
|[3, 1]
|0.0384
|0.0384
|-
|22
|(0, 7, 9)
|[3, 1]
|0.0085
|0.0085
|-
|22
|(0, 11, 14)
|[3, 1]
|0.0092
|0.0093
|-
|22
|(0, 12, 15)
|[3, 1]
|0.0335
|0.0339
|-
|22
|(0, 15, 19)
|[3, 1]
|0.0415
|0.0423
|-
|22
|(0, 16, 20)
|[3, 1]
|0.0106
|0.0108
|-
|22
|(0, 17, 21)
|[3, 1]
|0.0171
|0.0175
|-
|22
|(0, 5, 8)
|[3, 2]
|0.0207
|0.0207
|-
|22
|(0, 7, 11)
|[3, 2]
|0.0184
|0.0184
|-
|22
|(0, 9, 14)
|[3, 2]
|0.0372
|0.0374
|-
|22
|(0, 12, 18)
|[3, 2]
|0.0088
|0.0089
|-
|22
|(0, 14, 21)
|[3, 2]
|0.0384
|0.0391
|-
|23
|(0, 1, 2)
|[1, 1]
|0.0135
|0.0135
|-
|23
|(0, 2, 4)
|[1, 1]
|0.0271
|0.0272
|-
|23
|(0, 3, 6)
|[1, 1]
|0.0408
|0.0410
|-
|23
|(0, 5, 9)
|[1, 1]
|0.0389
|0.0394
|-
|23
|(0, 6, 11)
|[1, 1]
|0.0076
|0.0077
|-
|23
|(0, 7, 13)
|[1, 1]
|0.0185
|0.0190
|-
|23
|(0, 8, 14)
|[1, 1]
|0.0345
|0.0357
|-
|23
|(0, 8, 15)
|[1, 1]
|0.0415
|0.0431
|-
|23
|(0, 9, 16)
|[1, 1]
|0.0051
|0.0053
|-
|23
|(0, 10, 17)
|[1, 1]
|0.0453
|0.0478
|-
|23
|(0, 10, 18)
|[1, 1]
|0.0210
|0.0223
|-
|23
|(0, 11, 19)
|[1, 1]
|0.0153
|0.0164
|-
|23
|(0, 11, 20)
|[1, 1]
|0.0448
|0.0484
|-
|23
|(0, 12, 21)
|[1, 1]
|0.0118
|0.0129
|-
|23
|(0, 13, 22)
|[1, 1]
|0.0176
|0.0195
|-
|23
|(0, 1, 3)
|[1, 2]
|0.0285
|0.0285
|-
|23
|(0, 3, 8)
|[1, 2]
|0.0389
|0.0391
|-
|23
|(0, 4, 11)
|[1, 2]
|0.0211
|0.0213
|-
|23
|(0, 5, 13)
|[1, 2]
|0.0163
|0.0166
|-
|23
|(0, 6, 15)
|[1, 2]
|0.0381
|0.0388
|-
|23
|(0, 6, 16)
|[1, 2]
|0.0385
|0.0393
|-
|23
|(0, 7, 18)
|[1, 2]
|0.0207
|0.0213
|-
|23
|(0, 8, 20)
|[1, 2]
|0.0105
|0.0109
|-
|23
|(0, 9, 22)
|[1, 2]
|0.0059
|0.0062
|-
|23
|(0, 1, 4)
|[1, 3]
|0.0435
|0.0435
|-
|23
|(0, 3, 11)
|[1, 3]
|0.0360
|0.0362
|-
|23
|(0, 4, 14)
|[1, 3]
|0.0230
|0.0232
|-
|23
|(0, 5, 16)
|[1, 3]
|0.0482
|0.0488
|-
|23
|(0, 5, 17)
|[1, 3]
|0.0271
|0.0275
|-
|23
|(0, 6, 19)
|[1, 3]
|0.0250
|0.0254
|-
|23
|(0, 6, 20)
|[1, 3]
|0.0403
|0.0412
|-
|23
|(0, 7, 22)
|[1, 3]
|0.0012
|0.0013
|-
|23
|(0, 2, 3)
|[2, 1]
|0.0253
|0.0253
|-
|23
|(0, 7, 10)
|[2, 1]
|0.0028
|0.0028
|-
|23
|(0, 9, 13)
|[2, 1]
|0.0428
|0.0433
|-
|23
|(0, 10, 14)
|[2, 1]
|0.0085
|0.0086
|-
|23
|(0, 12, 17)
|[2, 1]
|0.0392
|0.0401
|-
|23
|(0, 13, 18)
|[2, 1]
|0.0019
|0.0020
|-
|23
|(0, 14, 19)
|[2, 1]
|0.0309
|0.0320
|-
|23
|(0, 16, 22)
|[2, 1]
|0.0199
|0.0208
|-
|23
|(0, 3, 7)
|[2, 3]
|0.0134
|0.0134
|-
|23
|(0, 8, 17)
|[2, 3]
|0.0344
|0.0347
|-
|23
|(0, 9, 19)
|[2, 3]
|0.0146
|0.0148
|-
|23
|(0, 10, 21)
|[2, 3]
|0.0079
|0.0080
|-
|23
|(0, 3, 4)
|[3, 1]
|0.0367
|0.0367
|-
|23
|(0, 7, 9)
|[3, 1]
|0.0121
|0.0121
|-
|23
|(0, 11, 14)
|[3, 1]
|0.0036
|0.0037
|-
|23
|(0, 12, 15)
|[3, 1]
|0.0392
|0.0396
|-
|23
|(0, 15, 19)
|[3, 1]
|0.0338
|0.0344
|-
|23
|(0, 16, 20)
|[3, 1]
|0.0028
|0.0028
|-
|23
|(0, 17, 21)
|[3, 1]
|0.0249
|0.0255
|-
|23
|(0, 5, 8)
|[3, 2]
|0.0150
|0.0151
|-
|23
|(0, 7, 11)
|[3, 2]
|0.0107
|0.0107
|-
|23
|(0, 9, 14)
|[3, 2]
|0.0274
|0.0276
|-
|23
|(0, 12, 18)
|[3, 2]
|0.0210
|0.0213
|-
|23
|(0, 14, 21)
|[3, 2]
|0.0240
|0.0244
|-
|23
|(0, 15, 22)
|[3, 2]
|0.0325
|0.0331
|}


== Higher-order differences of frequency ==
== Higher-order differences of frequency ==
Retrieved from "https://en.xen.wiki/w/Delta-rational_chord"