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53ed7/3: Difference between revisions

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m Intro harmonics
 
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Line 1: Line 1:
This edX is practically identical to an to an extended Pythagorean tuning distorted to repeat at 7/3. It also makes the unit step fall .093 cent sharp of 14ed5/4.
{{Stub}}
{{Infobox ET}}
{{ED intro}}


== Intervals ==
== Intervals ==
Line 8: Line 10:
! colspan="2" |''Pentadecatonic''
! colspan="2" |''Pentadecatonic''
!''Enneadecatonic''
!''Enneadecatonic''
!ed43\36
! colspan="2" |ed11\9~ed7/3
!30ed8/5~Pyrite<sub>v</sub>
!ed35\29
!''ed29\24=r¢<sub>v</sub>''
!ed17\14
!Golden<sub>v</sub>
!14ed5/4
!ed11\9~ed7/3
!Golden<sub>^</sub>
!ed16\13
!ed21\17
!''ed5\4=r¢<sub>^</sub>''
|-
|-
|1
|1
Line 27: Line 18:
|''Wb''
|''Wb''
|''Q#''
|''Q#''
|27.044
|27.1229
27.1282
|27.326
|''27.3585''
|27.4633
|27.5444
|27.5938
|27.673
|27.673
27.6768
|27.6768
|27.8085
|27.8665
|27.9689
|''28.3019''
|-
|-
|2
|2
Line 49: Line 28:
|''Q#''
|''Q#''
|''Wb''
|''Wb''
|54.08805
|54.24575
54.2564
|54.6519
|''54.717''
|54.9865
|55.0887
|55.1877
|55.3459
|55.3459
55.3536
|55.3536
|55.617
|55.73295
|55.93785
|''56.6038''
|-
|-
|3
|3
Line 68: Line 35:
| colspan="2" |F#
| colspan="2" |F#
| colspan="3" |''W''
| colspan="3" |''W''
|81.1321
|81.3686
81.3846
|81.9779
|''82.0755''
|82.4798
|82.6331
|82.7815
|83.0189
|83.0189
83.0304
|83.0304
|83.42545
|83.5994
|83.9068
|''84.9057''
|-
|-
|4
|4
Line 90: Line 45:
|''Ebb''
|''Ebb''
|''W#''
|''W#''
|108.1761
|108.4915
108.5128
|109.3838
|''109.434''
|109.97305
|110.1774
|110.37525
|110.6918
|110.6918
110.7073
|110.7073
|111.2339
|111.4659
|111.8757
|''113.20755''
|-
|-
|5
|5
Line 111: Line 54:
|''W#''
|''W#''
|''Eb''
|''Eb''
|135.2001
|135.6144
135.641
|136.6298
|''136.79245''
|137.1661
|137.7218
|137.9692
|138.3648
|138.3648
138.38405
|138.38405
|139.0424
|139.3324
|139.8776
|''141.5094''
|-
|-
| rowspan="2" |6
| rowspan="2" |6
Line 132: Line 63:
| rowspan="2" |''Eb''
| rowspan="2" |''Eb''
| rowspan="2" |''E''
| rowspan="2" |''E''
| rowspan="2" |162.26415
| rowspan="2" |162.7373
162.7692
| rowspan="2" |163.9558
| rowspan="2" |''164.1509''
| rowspan="2" |164.9696
| rowspan="2" |165.2661
| rowspan="2" |165.563
| rowspan="2" |166.0377
| rowspan="2" |166.0377
166.0609
| rowspan="2" |166.0609
| rowspan="2" |166.8509
| rowspan="2" |167.1988
| rowspan="2" |167.8135
| rowspan="2" |''169.8113''
|-
|-
|Bbbb
|Bbbb
Line 157: Line 76:
|''Wx''
|''Wx''
|''E#/Rb''
|''E#/Rb''
|189.3082
|189.8601
189.8971
|191.3817
|''191.5094''
|192.4528
|192.8105
|193.1569
|193.7107
|193.7107
193.7377
|193.7377
|194.6594
|195.0653
|195.7825
|''198.1132''
|-
|-
|8
|8
Line 177: Line 84:
| colspan="2" |''E''
| colspan="2" |''E''
|''R''
|''R''
|216.3522
|216.983
217.0256
|218.6077
|''215.8679''
|219.946
|220.3548
|220.7507
|221.38365
|221.38365
221.4145
|221.4145
|222.4679
|222.9319
|223.7514
|''226.4151''
|-
|-
|9
|9
Line 199: Line 94:
|''Rb''
|''Rb''
|''R#''
|''R#''
|243.3962
|244.1059
244.1538
|245.9336
|''248.2264''
|247.43935
|247.8992
|248.3445
|249.0566
|249.0566
249.0913
|249.0913
|250.2764
|250.7983
|254.7203
|''254.717''
|-
|-
|10
|10
Line 220: Line 103:
|''E#''
|''E#''
|''Tb''
|''Tb''
|270.44025
|271.2286
271.28195
|273.2596
|''273.5849''
|274.9326
|275.44355
|275.9384
|276.7296
|276.7296
276.7681
|276.7681
|278.08185
|278.9957
|279.6892
|''283.0289''
|-
|-
|11
|11
Line 241: Line 112:
| colspan="2" |''R''
| colspan="2" |''R''
|''T''
|''T''
|297.4842
|298.3516
298.41015
|300.5856
|''300.9434''
|302.4259
|302.9879
|303.5322
|304.4025
|304.4025
304.4449
|304.4449
|305.8933
|306.5312
|307.6582
|''311.32075''
|-
|-
|12
|12
Line 263: Line 122:
|''Tb''
|''Tb''
|''T#''
|''T#''
|324.5283
|325.4745
325.5384
|327.9115
|''328.3019''
|329.9191
|330.5323
|331.126
|332.0755
|332.0755
332.1217
|332.1217
|333.7208
|334.3977
|335.6271
|''339.6226''
|-
|-
| rowspan="2" |13
| rowspan="2" |13
Line 284: Line 131:
| rowspan="2" |''R#''
| rowspan="2" |''R#''
| rowspan="2" |''Yb''
| rowspan="2" |''Yb''
| rowspan="2" |351.5723
| rowspan="2" |652.5974
352.6665
| rowspan="2" |355.2375
| rowspan="2" |''355.6605''
| rowspan="2" |357.4124
| rowspan="2" |358.0766
| rowspan="2" |358.7199
| rowspan="2" |359.7484
| rowspan="2" |359.7484
359.7985
| rowspan="2" |359.7985
| rowspan="2" |361.8103
| rowspan="2" |362.26415
| rowspan="2" |363.596
| rowspan="2" |''367.9243''
|-
|-
|Cbb
|Cbb
Line 308: Line 143:
| colspan="2" |''T''
| colspan="2" |''T''
|''Y''
|''Y''
|378.61635
|379.7203
379.7947
|382.5634
|''383.0189''
|384.9057
|385.621
|386.3137
|387.4214
|387.4214
387.4753
|387.4753
|389.3188
|390.1306
|391.5649
|''396.2264''
|-
|-
| rowspan="2" |15
| rowspan="2" |15
Line 329: Line 152:
| rowspan="2" |''Ab''
| rowspan="2" |''Ab''
| rowspan="2" |''Y#''
| rowspan="2" |''Y#''
| rowspan="2" |405.6604
| rowspan="2" |406.8431
416.9229
| rowspan="2" |409.8894
| rowspan="2" |''410.3774''
| rowspan="2" |412.3989
| rowspan="2" |413.1653
| rowspan="2" |413.9076
| rowspan="2" |415.0943
| rowspan="2" |415.0943
415.1521
| rowspan="2" |415.1521
| rowspan="2" |417.1273
| rowspan="2" |417.9971
| rowspan="2" |419.53385
| rowspan="2" |''424.5283''
|-
|-
|Qbbb
|Qbbb
Line 354: Line 165:
|''T#''
|''T#''
|''Ab''
|''Ab''
|432.7044
|433.966
434.0511
|437.21535
|''437.73585''
|439.8922
|440.7097
|441.5014
|442.7673
|442.7673
442.82895
|442.82895
|444.93575
|445.8636
|447.5028
|''452.8302''
|-
|-
|17
|17
Line 375: Line 174:
| colspan="2" |''A''
| colspan="2" |''A''
|''U''
|''U''
|459.7484
|461.0889
461.1793
|464.5413
|''465.0943''
|467.3854
|468.254
|469.0952
|470.44025
|470.44025
470.8058
|470.8058
|472.7442
|473.73
|475.4717
|''481.1321''
|-
|-
|18
|18
Line 397: Line 184:
|''Sbb''
|''Sbb''
|''U#''
|''U#''
|486.79245
|488.2118
488.3078
|491.8673
|''492.4528''
|494.8788
|495.7984
|496.5791
|498.1132
|498.1132
498.1826
|498.1826
|500.5527
|501.5965
|502.4403
|''509.434''
|-
|-
|19
|19
Line 419: Line 194:
|''A#''
|''A#''
|''Ab''
|''Ab''
|513.8365
|515.33465
515.4357
|519.1932
|''519.8113''
|522.372
|523.34275
|524.2829
|525.7862
|525.7862
525.8594
|525.8594
|528.3612
|529.463
|531.40955
|''537.73585''
|-
|-
|20
|20
Line 441: Line 204:
|''Sb''
|''Sb''
|''A''
|''A''
|540.8805
|542.4575
542.5639
|546.5192
|''547.1698''
|549.8652
|550.8871
|551.8767
|553.4591
|553.4591
553.5362
|553.5362
|556.1697
|557.3295
|559.3785
|''566.0377''
|-
|-
|21
|21
Line 463: Line 214:
|''Ax''
|''Ax''
|''A#/Sb''
|''A#/Sb''
|567.9245
|569.5804
569.6921
|573.84515
|''574.5283''
|577.3585
|578.4315
|579.4706
|581.1321
|581.1321
581.213
|581.213
|583.9782
|585.1959
|584.3474
|''594.3396''
|-
|-
|22
|22
Line 483: Line 222:
|''A*/Sbb''
|''A*/Sbb''
| colspan="3" |''S''
| colspan="3" |''S''
|594.96855
|569.7033
596.8203
|601.1711
|''601.8868''
|604.85175
|605.9758
|607.0644
|608.805
|608.805
608.889
|608.889
|611.7867
|613.0624
|615.3163
|''922.6415''
|-
|-
|23
|23
Line 505: Line 232:
|''Db''
|''Db''
|''S#''
|''S#''
|622.0126
|623.82615
623.9484
|628.4971
|''629.2453''
|632.345
|633.52022
|634.6582
|636.478
|636.478
636.5666
|636.5666
|639.59515
|640.9289
|643.285
|''650.9434''
|-
|-
|24
|24
Line 527: Line 242:
|''S#''
|''S#''
|''Db''
|''Db''
|649.0566
|650.949
651.0767
|655.823
|''656.6038''
|659.8383
|661.0645
|662.2521
|664.1509
|664.1509
664.2434
|664.2434
|667.4306
|668.7954
|671.2541
|''679.2453''
|-
|-
|25
|25
Line 547: Line 250:
|''Db''
|''Db''
| colspan="3" |''D''
| colspan="3" |''D''
|676.1006
|678.0719
678.2049
|683.149
|''683.9623''
|687.3315
|688.6089
|689.8459
|691.8239
|691.8239
691.9202
|691.9202
|695.2121
|696.6618
|699.2231
|''707.5472''
|-
|-
|26
|26
Line 569: Line 260:
|''Fb''
|''Fb''
|''D#''
|''D#''
|703.14465
|705.1948
705.3331
|710.47495
|''711.32075''
|714.8248
|716.1532
|717.43975
|719.4969
|719.4969
719.59705
|719.59705
|723.0206
|724.5283
|727.192
|''735.8491''
|-
|-
|27
|27
Line 591: Line 270:
|''D#''
|''D#''
|''Fb''
|''Fb''
|730.1887
|732.3177
732.4613
|737.8003
|''738.67925''
|742.3181
|743.6976
|717.43975
|747.1698
|747.1698
747.2739
|747.2739
|750.8291
|752.3948
|755.1609
|''764.1509''
|-
|-
|28
|28
Line 611: Line 278:
|''Q#''
|''Q#''
| colspan="3" |''F''
| colspan="3" |''F''
|757.2327
|759.4405
759.5895
|765.1269
|''766.0377''
|769.8113
|771.24195
|772.6274
|774.8428
|774.8428
774.9507
|774.9507
|778.6376
|780.26125
|783.1299
|''792.4528''
|-
|-
| rowspan="2" |29
| rowspan="2" |29
Line 633: Line 288:
| rowspan="2" |''Gb''
| rowspan="2" |''Gb''
| rowspan="2" |''F#''
| rowspan="2" |''F#''
| rowspan="2" |784.2767
| rowspan="2" |802.6275
| rowspan="2" |786.5634
| rowspan="2" |802.6275
786.4177
| rowspan="2" |792.7\4528
| rowspan="2" |''793.3962''
| rowspan="2" |797.3046
| rowspan="2" |798.7863
| rowspan="2" |800.2213
| rowspan="2" |802.5157
802.6275
| rowspan="2" |803.44605
| rowspan="2" |808.1277
| rowspan="2" |811.0988
| rowspan="2" |''820.7547''
|-
|-
| colspan="2" |Ebbb
| colspan="2" |Ebbb
Line 657: Line 300:
|''F#''
|''F#''
|''Gb''
|''Gb''
|811.32075
|813.6863
813.8459
|819.7788
|''820.7547''
|821.7978
|826.3307
|827.8151
|830.1887
|830.1887
 
|830.3043
830.3043
|834.2545
|835.9942
|839.0678
|''849.0567''
|-
|-
|31
|31
Line 678: Line 308:
|''Cx''
|''Cx''
| colspan="3" |''G''
| colspan="3" |''G''
|838.3648
|840.8092
840.97405
|847.10475
|''848.1132''
|852.2911
|853.875
|855.4089
|857.8616
|857.8616
857.9811
|857.9811
|862.063
|863.8607
|867.0366
|''877.3585''
|-
|-
|32
|32
Line 700: Line 318:
|''Zbb''
|''Zbb''
|''G#''
|''G#''
|865.4088
|867.932
868.10225
|874.4307
|''875.4717''
|879.7844
|881.4194
|883.0028
|885.5346
|885.5346
885.6579
|885.6579
|889.8715
|891.7271
|895.00555
|''905.6604''
|-
|-
|33
|33
Line 722: Line 328:
|''G#''
|''G#''
|''Hb''
|''Hb''
|892.4528
|895.0549
895.23045
|901.7567
|''902.8302''
|907.3776
|908.9637
|910.5966
|913.20755
|913.20755
913.3347.
|913.3347
|917.68
|919.5936
|922.9745
|''933.9633''
|-
|-
|34
|34
Line 743: Line 337:
|''Zb''
|''Zb''
|''H''
|''H''
|919.4969
|922.1778
922.3586
|929.0826
|''930.1887''
|934.7709
|936.5081
|938.19045
|940.8805
|940.8805
941.0115
|941.0115
|945.4885
|947.4601
|980.9434
|''962.26415''
|-
|-
|35
|35
Line 765: Line 347:
|''Gx''
|''Gx''
|''H#''
|''H#''
|946.5409
|949.3007
949.4868
|956.4086
|''957.5472''
|962.26415
|964.0524
|965.7843
|968.5535
|968.5535
968.6883
|968.6883
|973.297
|975.3266
|978.9123
|''990.566''
|-
|-
| rowspan="2" |36
| rowspan="2" |36
Line 786: Line 356:
| colspan="2" rowspan="2" |''Z''
| colspan="2" rowspan="2" |''Z''
| rowspan="2" |''Jb''
| rowspan="2" |''Jb''
| rowspan="2" |973.5489
| rowspan="2" |976.4235
976.615
| rowspan="2" |983.73455
| rowspan="2" |''984.9057''
| rowspan="2" |989.7574
| rowspan="2" |991.5968
| rowspan="2" |993.3781
| rowspan="2" |996.2264
| rowspan="2" |996.2264
 
| rowspan="2" |996.3651
996.3651
| rowspan="2" |1001.10545
| rowspan="2" |1003.193
| rowspan="2" |1006.7712
| rowspan="2" |''1018.8679''
|-
|-
| colspan="2" |Fbbb
| colspan="2" |Fbbb
Line 811: Line 368:
|''Z#''
|''Z#''
|''J''
|''J''
|1000.6289
|1003.5464
1003.7432
|1011.0605
|''1012.26415''
|1017.2057
|1019.14115
|1020.972
|1023.8994
|1023.8994
1024.04195
|1024.04195
|1028.9139
|1031.0595
|1034.8502
|''1047.1698''
|-
|-
| rowspan="2" |38
| rowspan="2" |38
Line 833: Line 378:
| rowspan="2" |''Xb''
| rowspan="2" |''Xb''
| rowspan="2" |''J#''
| rowspan="2" |''J#''
| rowspan="2" |1027.673
| rowspan="2" |1030.6693
1030.8714
| rowspan="2" |1038.3865
| rowspan="2" |''1039.6226''
| rowspan="2" |1044.7439
| rowspan="2" |1046.6855
| rowspan="2" |1048.5658
| rowspan="2" |1051.5723
| rowspan="2" |1051.5723
1051.7188
| rowspan="2" |1051.7188
| rowspan="2" |1056.7224
| rowspan="2" |1058.926
| rowspan="2" |1062.8191
| rowspan="2" |''1075.4717''
|-
|-
| colspan="2" |Gbbb
| colspan="2" |Gbbb
Line 855: Line 388:
| colspan="2" |''X''
| colspan="2" |''X''
|''Zb''
|''Zb''
|1054.717
|1057.7922
1057.9996
|1065.7124
|''1066.9811''
|1072.2372
|1074.2299
|1076.1596
|1079.2453
|1079.2453
1079.3956
|1079.3956
|1084.5309
|1086.79245
|1090.788
|''1103.7736''
|-
|-
|40
|40
Line 877: Line 398:
|''X#''
|''X#''
|''Z''
|''Z''
|1081.761
|1084.91505
1085.1278
|1093.3038
|''1094.3396''
|1099.7305
|1101.7742
|1103.7535
|1106.9182
|1106.9182
1107.0724
|1107.0724
|1112.3394
|1114.6589
|1118.7569
|''1132.0755''
|-
|-
|41
|41
Line 898: Line 407:
|''Cb''
|''Cb''
|''Z#/Xb''
|''Z#/Xb''
|1108.805
|1112.0379
1112.256
|1120.36435
|''1121.6981''
|1127.2237
|1129.3186
|1131.3473
|1134.5912
|1134.5912
1134.7492
|1134.7492
|1140.1479
|1142.5254
|1146.7259
|''1160.3774''
|-
|-
|42
|42
Line 919: Line 416:
| colspan="2" |''C''
| colspan="2" |''C''
|''X''
|''X''
|1135.8491
|1139.1608
1139.3842
|1147.6903
|''1149.0566''
|1154.717
|1156.8629
|1158.9411
|1162.26415
|1162.26415
 
|1162.426
1162.426
|1167.95365
|1170.3919
|1174.6948
|''1188.67925''
|-
|-
|43
|43
Line 941: Line 425:
|''C#''
|''C#''
|''X#''
|''X#''
|1162.8931
|1166.2838
1166.5124
|1175.0163
|''1176.4151''
|1182.2102
|1184.4073
|1186.535
|1189.9371
|1189.9371
 
|1190.1028
1190.1028
|1195.7648
|1198.25835
|1202.6638
|''1216.9811''
|-
|-
|44
|44
Line 963: Line 434:
|''Vb''
|''Vb''
|''Cb''
|''Cb''
|1189.9371
|1193.40655
1193.6406
|1202.3422
|''1203.7736''
|1209.7035
|1211.9516
|1214.1288
|1217.6101
|1217.6101
 
|1217.7796
1217.7796
|1223.5733
|1226.1248
|1230.6326
|''1245.283''
|-
|-
|45
|45
Line 985: Line 443:
| colspan="2" |''V''
| colspan="2" |''V''
|''C''
|''C''
|1216.9811
|1220.5291
1220.7688
|1229.6682
|''1231.1321''
|1237.7197
|1239.496
|1241.72265
|1245.253
|1245.253
1245.4564
|1245.4564
|1251.3818
|1253.9913
|1258.60155
|''1273.5849''
|-
|-
|46
|46
Line 1,006: Line 452:
|''Bbb''
|''Bbb''
|''C#/Vb''
|''C#/Vb''
|1244.0252
|1247.6523
1247.897
|1256.9941
|''1258.4906''
|1264.69
|1267.04035
|1269.3165
|1272.956
|1272.956
1273.1332
|1273.1332
|1279.1903
|1281.8578
|1286.5705
|''1301.8868''
|-
|-
|47
|47
Line 1,028: Line 462:
|''V#''
|''V#''
|''V''
|''V''
|1271.0692
|1274.7752
1275.0252
|1284.3201
|''1285.8461''
|1292.1833
|1294.5847
|1296.9103
|1300.6289
|1300.6289
1300.81005
|1300.81005
|1306.9988
|1309.7242
|1314.5394
|''1330.1887''
|-
|-
|48
|48
Line 1,049: Line 471:
|''Bb''
|''Bb''
|''V#''
|''V#''
|1298.1132
|1301.8981
1302.1534
|1311.646
|''1313.20755''
|1319.67655
|1322.1291
|1324.5042
|1328.3019
|1328.3019
 
|1328.4869
1328.4869
|1334.8073
|1337.5927
|1342.5083
|''1358.4906''
|-
|-
|49
|49
Line 1,071: Line 480:
|''Vx''
|''Vx''
|''Bb''
|''Bb''
|1325.1572
|1326.0209
1329.2816
|1338.972
|''1340.566''
|1347.1698
|1349.6734
|1352.098
|1355.9748
|1355.9748
1356.11637
|1356.1164
|1362.6157
|1365.4572
|1370.4773
|''1386.79245''
|-
|-
|50
|50
Line 1,091: Line 488:
|''Abb''
|''Abb''
| colspan="3" |''B''
| colspan="3" |''B''
|1352.20125
|1356.1438
1356.4098
|1366.298
|''1367.9245''
|1374.5531
|1377.2178
|1379.6918
|1383.6478
|1383.6478
 
|1383.8405
1383.8405
|1390.4242
|1393.3237
|1398.4462
|''1415.0943''
|-
|-
|51
|51
Line 1,113: Line 497:
|''Qb''
|''Qb''
|''B#''
|''B#''
|1379.2453
|1383.3667
1383.538
|1393.6239
|''1395.286''
|1402.1563
|1404.7621
|1407.2857
|1411.3208
|1411.3208
1411.5173
|1411.5173
|1418.2327
|1421.1*01
|1426.4151
|''1443.3962''
|-
|-
|52
|52
Line 1,135: Line 507:
|''B#''
|''B#''
|''Qb''
|''Qb''
|1403.2893
|1410.3896
1410.6662
|1420.9499
|''1422.6415''
|1429.6496
|1432.0648
|1434.8795
|1438.9937
|1438.9937
 
|1439.1941
1439.1941
|1443.0412
|1449.0566
|1424.354
|''1471.6981''
|-
|-
|53
|53
Line 1,155: Line 514:
| colspan="2" |G
| colspan="2" |G
| colspan="3" |''Q''
| colspan="3" |''Q''
|1433.3333
|1466.{{Overline|6}}
|1437.5124
|1466.8709
1437.79435
|1448.2759
|''1450''
|1457.1429
|1459.8508
|1462.47335
|1466.6667
1466.8709
|1473.8497
|1476.9231
|1482.3529
|''1500''
|}
|}
== Harmonics ==
{{Harmonics in equal
| steps = 53
| num = 7
| denom = 3
}}
{{Harmonics in equal
| steps = 53
| num = 7
| denom = 3
| start = 12
| collapsed = 1
}}
Retrieved from "https://en.xen.wiki/w/53ed7/3"