68ed7/3: Difference between revisions

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Line 1: Line 1:
{{Stub}}
{{Infobox ET}}
{{ED intro}}
== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
Line 5: Line 9:
! colspan="2" |''Pentadecatonic''
! colspan="2" |''Pentadecatonic''
!''Enneadecatonic''
!''Enneadecatonic''
!ed43\36
! colspan="2" |ed11\9~ed7/3
!Pyrite<sub>v</sub>
!ed35\29
!''ed29\24=r¢<sub>v</sub>''
!ed17\14
!18ed5/4~Golden<sub>v</sub>
!ed11\9~ed7/3
!Golden<sub>^</sub>
!ed16\13
!ed21\17
!''ed5\4=r¢<sub>^</sub>''
|-
|-
| rowspan="2" |1
| rowspan="2" |1
Line 23: Line 17:
|''Qq''
|''Qq''
| colspan="2" |Q+
| colspan="2" |Q+
| rowspan="2" |21.0784
| rowspan="2" |21.144
| rowspan="2" |21.2982
| rowspan="2" |''21.3235''
| rowspan="2" |21.4286
| rowspan="2" |21.4617
21.4684
| rowspan="2" |21.5686
| rowspan="2" |21.5686
21.5716
| rowspan="2" |21.5716
| rowspan="2" |21.6743
| rowspan="2" |21.7195
| rowspan="2" |21.7993
| rowspan="2" |''22.0588''
|-
|-
|Jv,
|Jv,
Line 50: Line 33:
| rowspan="2" |''Qp/W\\\''
| rowspan="2" |''Qp/W\\\''
| colspan="2" rowspan="2" |''Q#/Wb''
| colspan="2" rowspan="2" |''Q#/Wb''
| rowspan="2" |42.1569
| rowspan="2" |42.2881
| rowspan="2" |42.59635
| rowspan="2" |''42.6471''
| rowspan="2" |42.8571
| rowspan="2" |42.92375
42.9368
| rowspan="2" |43.13725
| rowspan="2" |43.13725
43.1433
| rowspan="2" |43.1433
| rowspan="2" |43.3485
| rowspan="2" |43.4389
| rowspan="2" |43.5986
| rowspan="2" |''44.11765''
|-
|-
|Jv
|Jv
Line 76: Line 47:
|''Qpq''
|''Qpq''
| colspan="2" |''Q#''+
| colspan="2" |''Q#''+
| rowspan="2" |63.2353
| rowspan="2" |63.4321
| rowspan="2" |63.8945
| rowspan="2" |''63.9706''
| rowspan="2" |64.2857
| rowspan="2" |64.3856
64.4052
| rowspan="2" |64.7059
| rowspan="2" |64.7059
64.7149
| rowspan="2" |64.7149
| rowspan="2" |65.1228
| rowspan="2" |65.1584
| rowspan="2" |65.3979
| rowspan="2" |''66.1765''
|-
|-
|J,
|J,
Line 105: Line 65:
| rowspan="2" |''Ab''
| rowspan="2" |''Ab''
| colspan="3" rowspan="2" |''W''
| colspan="3" rowspan="2" |''W''
| rowspan="2" |84.3137
| rowspan="2" |84.5761
| rowspan="2" |85.1927
| rowspan="2" |''85.2941''
| rowspan="2" |85.7143
| rowspan="2" |85.8475
85.8736
| rowspan="2" |86.2745
| rowspan="2" |86.2745
86.2865
| rowspan="2" |86.2865
| rowspan="2" |86.697
| rowspan="2" |86.8778
| rowspan="2" |87.1972
| rowspan="2" |''88.2353''
|-
|-
|Jbb
|Jbb
Line 134: Line 82:
| rowspan="2" |W+
| rowspan="2" |W+
| rowspan="2" |''W+/Ebd''
| rowspan="2" |''W+/Ebd''
| rowspan="2" |105.3922
| rowspan="2" |105.7202
| rowspan="2" |106.4909
| rowspan="2" |''106.61765''
| rowspan="2" |107.1429
| rowspan="2" |107.3094
107.342
| rowspan="2" |107.8431
| rowspan="2" |107.8431
107.8582
| rowspan="2" |107.8582
| rowspan="2" |108.3713
| rowspan="2" |108.5973
| rowspan="2" |108.9965
| rowspan="2" |''110.2941''
|-
|-
| colspan="2" |G#v,
| colspan="2" |G#v,
Line 161: Line 98:
| rowspan="2" |''W#''
| rowspan="2" |''W#''
| rowspan="2" |''W#/Eb''
| rowspan="2" |''W#/Eb''
| rowspan="2" |126.4706
| rowspan="2" |126.8642
| rowspan="2" |127.78905
| rowspan="2" |''127.9412''
| rowspan="2" |128.5714
| rowspan="2" |128.7712
128.8104
| rowspan="2" |129.4118
| rowspan="2" |129.4118
129.4298
| rowspan="2" |129.4298
| rowspan="2" |130.0456
| rowspan="2" |130.3167
| rowspan="2" |130.79585
| rowspan="2" |''132.3529''
|-
|-
| colspan="2" |G#v
| colspan="2" |G#v
Line 188: Line 113:
| rowspan="2" |''Wpq/E\\\''
| rowspan="2" |''Wpq/E\\\''
| colspan="2" rowspan="2" |''W#+/E(b)d''
| colspan="2" rowspan="2" |''W#+/E(b)d''
| rowspan="2" |147.549
| rowspan="2" |148.0082
| rowspan="2" |149.0872
| rowspan="2" |''149.2647''
| rowspan="2" |150
| rowspan="2" |150.2331
150.2788
| rowspan="2" |150.9804
| rowspan="2" |150.9804
151.0014
| rowspan="2" |151.0014
| rowspan="2" |151.7198
| rowspan="2" |152.0362
| rowspan="2" |152.5952
| rowspan="2" |''154.4118''
|-
|-
| colspan="2" |G#,
| colspan="2" |G#,
Line 214: Line 128:
|''Eb''
|''Eb''
|''E''
|''E''
|168.62745
|169.1523
|170.3854
|''170.5882''
|171.4286
|171.695
171.7472
|172.549
|172.549
172.57305
|172.57305
|173.3941
|173.7557
|174.3945
|''176.4706''
|-
|-
| rowspan="2" |9
| rowspan="2" |9
Line 239: Line 141:
| rowspan="2" |Ed
| rowspan="2" |Ed
| rowspan="2" |E+/Rd
| rowspan="2" |E+/Rd
| rowspan="2" |189.7059
| rowspan="2" |190.2963
| rowspan="2" |191.6836
| rowspan="2" |''191.9118''
| rowspan="2" |192.8571
| rowspan="2" |193.1569
193.21555
| rowspan="2" |194.11765
| rowspan="2" |194.11765
194.1447
| rowspan="2" |194.1447
| rowspan="2" |195.0683
| rowspan="2" |195.4751
| rowspan="2" |196.1938
| rowspan="2" |''198.5294''
|-
|-
|Jv,
|Jv,
Line 265: Line 156:
| colspan="2" rowspan="2" |''E''
| colspan="2" rowspan="2" |''E''
| rowspan="2" |''R''
| rowspan="2" |''R''
| rowspan="2" |210.7843
| rowspan="2" |211.44035
| rowspan="2" |212.9817
| rowspan="2" |''213.2353''
| rowspan="2" |214.2857
| rowspan="2" |214.6187
214.68395
| rowspan="2" |215.6863
| rowspan="2" |215.6863
215.7163
| rowspan="2" |215.7163
| rowspan="2" |216.7426
| rowspan="2" |217.1946
| rowspan="2" |217.9931
| rowspan="2" |''220.5882''
|-
|-
|Jv
|Jv
Line 293: Line 172:
| rowspan="2" |''E+/Rbd''
| rowspan="2" |''E+/Rbd''
| rowspan="2" |''R+/Tbd''
| rowspan="2" |''R+/Tbd''
| rowspan="2" |231.86275
| rowspan="2" |232.5844
| rowspan="2" |234.2799
| rowspan="2" |''234.5888''
| rowspan="2" |235.7143
| rowspan="2" |236.0806
236.1523
| rowspan="2" |237.2549
| rowspan="2" |237.2549
237.2879
| rowspan="2" |237.2879
| rowspan="2" |238.4169
| rowspan="2" |238.914
| rowspan="2" |239.7924
| rowspan="2" |''242.6471''
|-
|-
|J,
|J,
Line 321: Line 189:
|''E#/Rb''
|''E#/Rb''
|''R#/Tb''
|''R#/Tb''
|252.9412
|253.7284
|255.5781
|''255.88235''
|257.1429
|257.5425
257.6207
|258.8235
|258.8235
258.8596
|258.8596
|160.0911
|260.6335
|261.5917
|''264.7059''
|-
|-
|13
|13
Line 347: Line 203:
|''E#+/Rd''
|''E#+/Rd''
|''R#+/Td''
|''R#+/Td''
|274.0196
|274.87245
|276.8763
|''277.2059''
|278.5714
|279.00435
279.0891
|280.3922
|280.3922
280.4312
|280.4312
|281.7654
|282.3529
|283.391
|''286.7647''
|-
|-
|14
|14
Line 371: Line 216:
| colspan="2" |''R''
| colspan="2" |''R''
|''T''
|''T''
|295.098
|296.0165
|298.1744
|''298.5294''
|300
|300.4662
300.5575
|301.9608
|301.9608
302.0028
|302.0028
|303.4396
|304.0721
|305.1903
|''308.8235''
|-
|-
|15
|15
Line 396: Line 230:
|''R+/Tbd''
|''R+/Tbd''
|''T+/Yb''d
|''T+/Yb''d
|316.1765
|317.1605
|319.4726
|''319.8529''
|321.4286
|321.9281
322.0259
|323.5294
|323.5294
323.5745
|323.5745
|325.1139
|325.7919
|326.9896
|''330.88235''
|-
|-
|16
|16
Line 421: Line 244:
|''R#/Tb''
|''R#/Tb''
|''T#/Yb''
|''T#/Yb''
|337.2549
|338.30455
|340.7708
|''341.1765''
|342.8571
|343.39
343.4943
|345.098
|345.098
345.1461
|345.1461
|346.7882
|347.5113
|348.7889
|''352.9412''
|-
|-
|17
|17
Line 447: Line 258:
|''R+/Tb''d
|''R+/Tb''d
|''T#+/Yd''
|''T#+/Yd''
|358.3333
|366.{{Overline|6}}
|359.4486
|366.7177
|362.069
|''362.5''
|364.2857
|364.8518
364.9627
|366.6667
366.7177
|368.4624
|369.2308
|370.5882
|''375''
|-
|-
|18
|18
Line 471: Line 271:
| colspan="2" |''T''
| colspan="2" |''T''
|''Y''
|''Y''
|379.4118
|380.5926
|383.3671
|''383.8235''
|385.7143
|386.3137
386.4311
|388.2353
|388.2353
388.2894
|388.2894
|390.1367
|390.9502
|392.3875
|''397.0588''
|-
|-
|19
|19
Line 497: Line 285:
|''T#+/Ad''
|''T#+/Ad''
|''Y+/Ub''d
|''Y+/Ub''d
|400.4902
|401.7367
|404.6653
|''405.1471''
|407.1429
|407.7756
407.8995
|409.8039
|409.8039
409.861
|409.861
|411.8109
|412.6697
|414.18685
|419.11765
|-
|-
|20
|20
Line 522: Line 299:
|''T#/Ab''
|''T#/Ab''
|''Y#/Ub''
|''Y#/Ub''
|421.5686
|422.8807
|425.9635
|''426.4706''
|428.5714
|429.2375
429.3679
|431.37255
|431.37255
431.4326
|431.4326
|433.4852
|434.3891
|435.9862
|''441.1765''
|-
|-
|21
|21
Line 548: Line 313:
|''T#+/Ad''
|''T#+/Ad''
|''Y#+/Ud''
|''Y#+/Ud''
|442.6471
|444.0247
|447.2617
|''447.7941''
|450
|450.6993
450.8363
|452.9412
|452.9412
453.00425
|453.00425
|455.1595
|456.1086
|457.7855
|''463.2353''
|-
|-
|22
|22
Line 572: Line 326:
| colspan="2" |''A''
| colspan="2" |''A''
|''U''
|''U''
|463.7255
|465.1688
|468.5598
|''469.11765''
|471.4286
|472.1612
472.3047
|474.5098
|474.5098
474.5759
|474.5759
|476.8337
|477.82805
|479.5848
|''485.2941''
|-
|-
|23
|23
Line 598: Line 340:
|''A+''
|''A+''
|''U+/Abd''
|''U+/Abd''
|484.8039
|486.3263
|489.858
|''490.4412''
|492.8571
|493.6231
493.7731
|496.0784
|496.0784
496.1475
|496.1475
|498.508
|499.5475
|501.3841
|''507.3529''
|-
|-
|24
|24
Line 623: Line 354:
|''A#''
|''A#''
|''U#/Ab''
|''U#/Ab''
|505.88235
|507.4568
|511.1562
|''511.7647''
|51<span style="line-height: 1.5;">4.2857</span>
|515.08465
515.2415
|517.6471
|517.6471
517.7191
|517.7191
|520.1822
|521.267
|523.1834
|''529.4118''
|-
|-
|25
|25
Line 649: Line 368:
|''A#+/Sbd''
|''A#+/Sbd''
|''U#+/Ad''
|''U#+/Ad''
|526.9608
|528.6009
|532.4544
|533.0882
|535.7143
|536.5468
536.7099
|539.2157
|539.2157
539.2908
|539.2908
|541.3565
|542.9864
|544.9827
|''551.4706''
|-
|-
|26
|26
Line 674: Line 382:
|''Sb''
|''Sb''
|''A''
|''A''
|548.0392
|549.7449
|553.7525
|''554.0588''
|557.1429
|515.08465
515.2415
|560.7843
|560.7843
560.8624
|560.8624
|563.5308
|564.7059
|566.782
|''573.5294''
|-
|-
|27
|27
Line 700: Line 396:
|''Sd''
|''Sd''
|''A+/Sd''
|''A+/Sd''
|569.11765
|570.8889
|575.0507
|''576.7353''
|578.5714
|579.4703
579.6467
|582.3529
|582.3529
582.434
|582.434
|585.205
|586.4253
|588.5813
|''595.5882''
|-
|-
|28
|28
Line 723: Line 408:
|''C''
|''C''
| colspan="3" |''S''
| colspan="3" |''S''
|590.1961
|592.033
|596.3489
|''597.0588''
|600
|600.9324
601.16505
|603.9216
|603.9216
604.0057
|604.0057
|606.8793
|608.1448
|610.3806
|''617.6471''
|-
|-
|29
|29
Line 748: Line 421:
|''Sq/D\\\''
|''Sq/D\\\''
| colspan="2" |''S+/Db''d
| colspan="2" |''S+/Db''d
|611.2745
|613.177
|617.6471
|''618.38235''
|621.4286
|622.3943
622.58345
|625.4902
|625.4902
625.5773
|625.5773
|628.5535
|629.86425
|632.1799
|''639.7059''
|-
|-
|30
|30
Line 772: Line 434:
|''Sp/D\\''
|''Sp/D\\''
| colspan="2" |''S#/Db''
| colspan="2" |''S#/Db''
|632.3529
|634.321
|638.9452
|''639.7059''
|642.8571
|643.8562
644.0518
|647.0588
|647.0588
647.1489
|647.1489
|650.2278
|651.5837
|653.9792
|''661.7647''
|-
|-
|31
|31
Line 797: Line 447:
|''Spq/D\''
|''Spq/D\''
| colspan="2" |''S#+/Db''d
| colspan="2" |''S#+/Db''d
|653.4314
|655.4651
|660.2434
|''661.0294''
|664.2857
|665.3181
665.5203
|668.62745
|668.62745
668.7206
|668.7206
|671.9021
|673.3032
|675.77855
|''683.8235''
|-
|-
|32
|32
Line 820: Line 459:
|''Q''
|''Q''
| colspan="3" |''D''
| colspan="3" |''D''
|674.5098
|690.1961
|676.6091
|690.2922
|681.5416
|''682.3529''
|685.7143
|686.7799
 
686.9886
|590.1961
690.2922
|693.5763
|695.0226
|697.57786
|''705.88235''
|-
|-
|33
|33
Line 845: Line 472:
|''Dq/F\\\''
|''Dq/F\\\''
| colspan="2" |''D+/Fb''d
| colspan="2" |''D+/Fb''d
|695.5882
|697.7531
|702.8398
|''703.6765''
|707.1429
|708.2418
708.457
|711.7647
|711.7647
711.8638
|711.8638
|715.2506
|716.7421
|719.3772
|727.9412
|-
|-
|34
|34
Line 869: Line 485:
|''Dp/F\\''
|''Dp/F\\''
| colspan="2" |''D#/Fb''
| colspan="2" |''D#/Fb''
|716.6667
|733.{{Overline|3}}
|718.8972
|733.43545
|724.1379
|''725''
|728.5714
|729.7037
 
729.9254
|733.3333
733.43545
|736.9248
|738.4615
|741.1765
|''750''
|-
|-
|35
|35
Line 894: Line 498:
|''Dp/F\\''
|''Dp/F\\''
| colspan="2" |''D#/Fb''
| colspan="2" |''D#/Fb''
|737.745
|740.0412
|754.4361
|''746.3235''
|750
|751.16555
751.3938
|754.902
|754.902
755.0071
|755.0071
|758.5991
|760.181
|762.9758
|''772.0588''
|-
|-
|36
|36
Line 917: Line 510:
|''Db''
|''Db''
| colspan="3" |''F''
| colspan="3" |''F''
|758.8235
|761.1852
|766.7343
|''767.6471''
|771.4286
|772.6274
772.8622
|776.4706
|776.4706
776.5787
|776.5787
|780.2734
|781.9005
|784.7751
|''794.11765''
|-
|-
|37
|37
Line 942: Line 523:
|''Fq/G\\\''
|''Fq/G\\\''
| colspan="2" |''F+/Gb''d
| colspan="2" |''F+/Gb''d
|779.902
|782.3293
|788.03245
|''788.9706''
|792.8571
|794.0893
794.3306
|798.0392
|798.0392
798.15035
|798.15035
|801.9476
|803.6199
|806.5744
|''816.1765''
|-
|-
|38
|38
Line 966: Line 536:
|''Fp/G\\''
|''Fp/G\\''
| colspan="2" |''F#/Gb''
| colspan="2" |''F#/Gb''
|800.9804
|803.4733
|809.3306
|''810.2941''
|814.2857
|815.5512
815.799
|819.6078
|819.6078
819.722
|819.722
|823.6219
|825.3394
|828.3737
|''838.2353''
|-
|-
|39
|39
Line 991: Line 549:
|''Fpq/G\''
|''Fpq/G\''
| colspan="2" |''F+/Gd''
| colspan="2" |''F+/Gd''
|822.0588
|824.61735
|830.6288
|''831.61765''
|835.7143
|837.01305
837.2674
|841.1765
|841.1765
841.2936
|841.2936
|845.2961
|847.0588
|850.173
|''860.2941''
|-
|-
|40
|40
Line 1,014: Line 561:
|''Q#''
|''Q#''
| colspan="3" |''G''
| colspan="3" |''G''
|843.13725
|845.7614
|851.927
|''852.9412''
|857.1429
|858.4749
858.7358
|862.7451
|862.7451
862.8982
|862.8982
|866.9704
|868.7783
|871.9723
|''882.3529''
|-
|-
|41
|41
Line 1,040: Line 575:
|''G+''
|''G+''
|G+\Hd
|G+\Hd
|864.2157
|866.9054
|873.22515
|''874.2647''
|878.5714
|879.9368
880.2042
|884.3137
|884.3137
884.4369
|884.4369
|888.6447
|890.4977
|893.7716
|''914.4118''
|-
|-
|42
|42
Line 1,065: Line 589:
|''G#''
|''G#''
|''H''
|''H''
|885.2941
|888.04945
|894.5233
|''895.5882''
|900
|901.3987
901.6726
|905.88235
|905.88235
906.0085
|906.0085
|910.3189
|912.2172
|915.5709
|''926.4706''
|-
|-
|43
|43
Line 1,091: Line 603:
|''G#+/Zbd''
|''G#+/Zbd''
|''Hd''
|''Hd''
|906.37255
|909.1935
|915.8215
|''916.9118''
|921.4286
|922.8605
923.141
|927.451
|927.451
927.5801
|927.5801
|931.9932
|933.93665
|937.3702.
|''948.5294''
|-
|-
|44
|44
Line 1,116: Line 617:
|''Zb''
|''Zb''
|''H#''
|''H#''
|927.451
|930.3375
|937.1197
|''938.2353''
|942.8571
|944.3224
944.6094
|949.0196
|949.0196
949.1518
|949.1518
|953.6674
|955.6561
|959.16955
|''970.5882''
|-
|-
|45
|45
Line 1,142: Line 631:
|''Zd''
|''Zd''
|''H#+/Jbd''
|''H#+/Jbd''
|948.5294
|951.4816
|958.41785
|''959.5588.''
|964.2857
|965.7843
966.0778
|970.5882
|970.5882
970.7234
|970.7234
|975.3417
|977.3756
|980.9689
|''992.6471''
|-
|-
|46
|46
Line 1,166: Line 644:
| colspan="2" |''Z''
| colspan="2" |''Z''
|''Jb''
|''Jb''
|969.6078
|972.6526
|979.716
|''980.88235''
|985.7143
|987.2462
987.54615
|992.1569
|992.1569
922.295
|992.295
|997.016
|999.095
|1002.7682
|''1014.7059''
|-
|-
|47
|47
Line 1,192: Line 658:
|''Z+/Xb''d
|''Z+/Xb''d
|''Jd''
|''Jd''
|990.6863.
|993.7696
|1001.0142
|''1002.2059''
|1007.1429
|1008.708
1009.01455
|1013.7255
|1013.7255
1013.8667
|1013.8667
|1018.9602
|1020.8145
|1024.5675
|''1036.7647''
|-
|-
|48
|48
Line 1,217: Line 672:
|''Z#/Xb''
|''Z#/Xb''
|''J''
|''J''
|1011.7647
|1014.9137
|1022.3124
|''1023.5294''
|1028.5714
|1030.1699
1030.4829
|1035.2941
|1035.2941
1035.4383
|1035.4383
|1040.3645
|1042.5339
|1046.3668
|''1058.8235''
|-
|-
| rowspan="2" |49
| rowspan="2" |49
Line 1,243: Line 686:
| rowspan="2" |''Z#+/Xd''
| rowspan="2" |''Z#+/Xd''
| rowspan="2" |''J+/Zb''d
| rowspan="2" |''J+/Zb''d
| rowspan="2" |1032.8431
| rowspan="2" |1036.0577
| rowspan="2" |1043.61055
| rowspan="2" |''1044.8529''
| rowspan="2" |1050
| rowspan="2" |1051.6318
1051.9514
| rowspan="2" |1056.86275
| rowspan="2" |1056.86275
1057.0099
| rowspan="2" |1057.0099
| rowspan="2" |1062.0387
| rowspan="2" |1064.2534
| rowspan="2" |1068.1661
| rowspan="2" |''1070.82235''
|-
|-
| colspan="2" |Ebv,
| colspan="2" |Ebv,
Line 1,269: Line 701:
| colspan="2" rowspan="2" |''X''
| colspan="2" rowspan="2" |''X''
| rowspan="2" |''J#/Zb''
| rowspan="2" |''J#/Zb''
| rowspan="2" |1053.9216
| rowspan="2" |1057.2017
| rowspan="2" |1064.9087
| rowspan="2" |''1066.1765''
| rowspan="2" |1071.4286
| rowspan="2" |1073.09365
1073.4197
| rowspan="2" |1078.4314
| rowspan="2" |1078.4314
1078.58155
| rowspan="2" |1078.58155
| rowspan="2" |1083.713
| rowspan="2" |1085.97285
| rowspan="2" |1089.9654
| rowspan="2" |''1102.9412''
|-
|-
| colspan="2" |Ebv
| colspan="2" |Ebv
Line 1,296: Line 716:
| rowspan="2" |''X+/Cb''d
| rowspan="2" |''X+/Cb''d
| rowspan="2" |''J#+/Zd''
| rowspan="2" |''J#+/Zd''
| rowspan="2" |1075
| rowspan="2" |1078.3458
| rowspan="2" |1086.2069
| rowspan="2" |''1087.5''
| rowspan="2" |1092.8571
| rowspan="2" |1094.5555
1094.8881
| rowspan="2" |1100
| rowspan="2" |1100
1100.1532
| rowspan="2" |1100.1532
| rowspan="2" |1105.3873
| rowspan="2" |1107.6923
| rowspan="2" |1111.7947
| rowspan="2" |''1125''
|-
|-
| colspan="2" |Eb,
| colspan="2" |Eb,
Line 1,321: Line 730:
|''X#/Cb''
|''X#/Cb''
|''Z''
|''Z''
|1096.0784
|1099.4898
|1107.5051
|''1108.8235''
|1114.2857
|1116.0174
1116.3565
|1121.5686
|1121.5686
1121.7248
|1121.7248
|1127.0615
|1129.4118
|1133.564
|''1147.0588''
|-
|-
| rowspan="2" |53
| rowspan="2" |53
Line 1,345: Line 742:
| rowspan="2" |''X#+/Cb''d
| rowspan="2" |''X#+/Cb''d
| rowspan="2" |''Z+/Xd''
| rowspan="2" |''Z+/Xd''
| rowspan="2" |1117.1569
| rowspan="2" |1120.6338
| rowspan="2" |1128.80325
| rowspan="2" |''1130.1471''
| rowspan="2" |1135.7143
| rowspan="2" |1137.4793
1137.8249
| rowspan="2" |1143.13725
| rowspan="2" |1143.13725
1143.2964
| rowspan="2" |1143.2964
| rowspan="2" |1148.7358
| rowspan="2" |1151.1312
| rowspan="2" |1155.3633
| rowspan="2" |''1169.11765''
|-
|-
| colspan="2" |Fv,
| colspan="2" |Fv,
Line 1,371: Line 757:
| colspan="2" rowspan="2" |''C''
| colspan="2" rowspan="2" |''C''
| rowspan="2" |''X''
| rowspan="2" |''X''
| rowspan="2" |1138.2353
| rowspan="2" |1141.7779
| rowspan="2" |1150.1014
| rowspan="2" |''1151.4706''
| rowspan="2" |1157.1429
| rowspan="2" |1158.9411
1159.2933
| rowspan="2" |1164.7059
| rowspan="2" |1164.7059
1164.8681
| rowspan="2" |1164.8681
| rowspan="2" |1170.41
| rowspan="2" |1172.8507
| rowspan="2" |1177.1626
| rowspan="2" |''1191.1765''
|-
|-
| colspan="2" |Fv
| colspan="2" |Fv
Line 1,399: Line 773:
| rowspan="2" |''C+/Vb''d
| rowspan="2" |''C+/Vb''d
| rowspan="2" |''X+/Cb''d
| rowspan="2" |''X+/Cb''d
| rowspan="2" |1159.3137
| rowspan="2" |1162.9219
| rowspan="2" |1171.3996
| rowspan="2" |''1172.6941''
| rowspan="2" |1178.5714
| rowspan="2" |1180.403
1180.7617
| rowspan="2" |1186.2745
| rowspan="2" |1186.2745
1186.4397
| rowspan="2" |1186.4397
| rowspan="2" |1192.0843
| rowspan="2" |1194.5701
| rowspan="2" |1198.9619
| rowspan="2" |''1213.2353''
|-
|-
| colspan="2" |F,
| colspan="2" |F,
Line 1,426: Line 789:
|''C#/Vb''
|''C#/Vb''
|''X#/Cb''
|''X#/Cb''
|1180.3922
|1184.0659
|1192.6978
|''1194.11765''
|1200
|1201.8649
1202.3301
|1207.8731
|1207.8731
1208.0113
|1208.0113
|1213.7586
|1216.2896
|1220.76125
|''1235.2941''
|-
|-
| rowspan="2" |57
| rowspan="2" |57
Line 1,450: Line 801:
| rowspan="2" |''C#+/Vd''
| rowspan="2" |''C#+/Vd''
| rowspan="2" |''X#+/Cd''
| rowspan="2" |''X#+/Cd''
| rowspan="2" |1201.4706
| rowspan="2" |1205.21
| rowspan="2" |1213.9959
| rowspan="2" |''1215.4412''
| rowspan="2" |1221.4286
| rowspan="2" |1223.3268
1223.6985
| rowspan="2" |1229.4118
| rowspan="2" |1229.4118
1229.583
| rowspan="2" |1229.583
| rowspan="2" |1235.4328
| rowspan="2" |1238.009
| rowspan="2" |1242.56055
| rowspan="2" |''1257.3529''
|-
|-
| colspan="2" |Ev,
| colspan="2" |Ev,
Line 1,474: Line 814:
| colspan="2" rowspan="2" |''V''
| colspan="2" rowspan="2" |''V''
| rowspan="2" |''C''
| rowspan="2" |''C''
| rowspan="2" |1222.549
| rowspan="2" |1226.354
| rowspan="2" |1235.2941
| rowspan="2" |''1236.7647''
| rowspan="2" |1242.8571
| rowspan="2" |1244.7886
1245.1669
| rowspan="2" |1250.9804
| rowspan="2" |1250.9804
1251.1546
| rowspan="2" |1251.1546
| rowspan="2" |1257.1071
| rowspan="2" |1259.7285
| rowspan="2" |1264.3599
| rowspan="2" |''1279.4118''
|-
|-
| colspan="2" |Ev
| colspan="2" |Ev
Line 1,500: Line 828:
| rowspan="2" |''V+''
| rowspan="2" |''V+''
| rowspan="2" |C+/Vd
| rowspan="2" |C+/Vd
| rowspan="2" |1243.6274
| rowspan="2" |1247.498
| rowspan="2" |1256.5923
| rowspan="2" |''1258.0882''
| rowspan="2" |1264.2857
| rowspan="2" |1266.2505
1266.6353
| rowspan="2" |1272.2549
| rowspan="2" |1272.2549
1272.7262
| rowspan="2" |1272.7262
| rowspan="2" |1278.7813
| rowspan="2" |1281.448
| rowspan="2" |1286.1592
| rowspan="2" |''1301.4706''
|-
|-
| colspan="2" |E,
| colspan="2" |E,
Line 1,524: Line 841:
|''V#''
|''V#''
|''V''
|''V''
|1264.7059
|1268.6421
|1277.8905
|''1279.4118''
|1285.7143
|1287.7124
1288.1037
|1294.11765
|1294.11765
1294.2979
|1294.2979
|1300.4556
|1303.1674
|1307.9585
|''1323.5294''
|-
|-
|61
|61
Line 1,547: Line 852:
|''V#+/Bbd''
|''V#+/Bbd''
|''V+/Bbd''
|''V+/Bbd''
|1285.7843
|1289.7861
|1299.1886
|''1300.7353''
|1307.1429
|1309.17425
1309.5721
|1315.6863
|1315.6863
1315.8695
|1315.8695
|1322.1299
|1324.8869
|1329.7578
|''1347.5882''
|-
|-
|62
|62
Line 1,569: Line 863:
|''Bb''
|''Bb''
|''V#/Bb''
|''V#/Bb''
|1306.86275
|1310.9301
|1320.4868
|''1322.0588''
|1328.5714
|1330.6361
1331.0405
|1337.2549
|1337.2549
1337.4411
|1337.4411
|1343.8041
|1346.6603
|1351.5571
|''1367.6471''
|-
|-
|63
|63
Line 1,592: Line 874:
|''Bd''
|''Bd''
|''V#+/Bd''
|''V#+/Bd''
|1327.9412
|1332.0741
|1341.785
|1343.38235
|1350
|1352.098
1352.5089
|1358.8235
|1358.8235
1359.01275
|1359.01275
|1365.4784
|1368.3258
|1373.3564
|''1388.7059''
|-
|-
|64
|64
Line 1,612: Line 883:
| colspan="2" |F
| colspan="2" |F
| colspan="3" |''B''
| colspan="3" |''B''
|1349.0196
|1353.2182
|1363.0832
|''1364.7059''
|1371.4286
|1373.5599
1373.9773
|1380.3922
|1380.3922
1380.5844
|1380.5844
|1387.1526
|1390.04525
|1395.1557
|''1411.7647''
|-
|-
| rowspan="2" |65
| rowspan="2" |65
Line 1,634: Line 893:
| rowspan="2" |''Bpq/Q\\''
| rowspan="2" |''Bpq/Q\\''
| colspan="2" rowspan="2" |''B+/Qbd''
| colspan="2" rowspan="2" |''B+/Qbd''
| rowspan="2" |1370.098
| rowspan="2" |1374.36225
| rowspan="2" |1384.3814
| rowspan="2" |''1386.0294''
| rowspan="2" |1392.8571
| rowspan="2" |1395.02175
1395.44565
| rowspan="2" |1401.9608
| rowspan="2" |1401.9608
1402.156
| rowspan="2" |1402.156
| rowspan="2" |1408.8269
| rowspan="2" |1411.7647
| rowspan="2" |1416.955
| rowspan="2" |''1433.8235''
|-
|-
| colspan="4" |Gv
| colspan="4" |Gv
Line 1,657: Line 905:
| rowspan="2" |''Bp/Q\\''
| rowspan="2" |''Bp/Q\\''
| colspan="2" rowspan="2" |''B#/Qb''
| colspan="2" rowspan="2" |''B#/Qb''
| rowspan="2" |1391.1765
| rowspan="2" |1395.5063
| rowspan="2" |1405.6795
| rowspan="2" |''1407.3529''
| rowspan="2" |1414.2857
| rowspan="2" |1416.4836
1416.91405
| rowspan="2" |1423.5294
| rowspan="2" |1423.5294
1423.7276
| rowspan="2" |1423.7276
| rowspan="2" |1430.5012
| rowspan="2" |1433.4842
| rowspan="2" |1438.7543
| rowspan="2" |''1455.88235''
|-
|-
| colspan="4" |Gv
| colspan="4" |Gv
Line 1,681: Line 917:
| rowspan="2" |''Bpq/Q\''
| rowspan="2" |''Bpq/Q\''
| colspan="2" rowspan="2" |''B#+/Qd''
| colspan="2" rowspan="2" |''B#+/Qd''
| rowspan="2" |1412.2549
| rowspan="2" |1416.6503
| rowspan="2" |1426.9777
| rowspan="2" |''1428.6765''
| rowspan="2" |1435.7143
| rowspan="2" |1437.9455
1438.3824
| rowspan="2" |1445.098
| rowspan="2" |1445.098
1445.993
| rowspan="2" |1445.993
| rowspan="2" |1452.1754
| rowspan="2" |1455.2036
| rowspan="2" |1460.5536
| rowspan="2" |''1477.9412''
|-
|-
| colspan="4" |Gv,
| colspan="4" |Gv,
Line 1,701: Line 926:
| colspan="6" |G
| colspan="6" |G
| colspan="3" |''Q''
| colspan="3" |''Q''
|1433.3333
|1466.{{Overline|6}}
|1437.79435
|1466.8709
|1448.2759
|}
|''1450''
|1457.1429
|1459.4073


1459.8508
== Harmonics ==
|1466.6667
{{Harmonics in equal
1466.8709
| steps = 135
|1473.8497
| num = 7
|1476.9231
| denom = 3
|1482.3529
}}
|''1500''
{{Harmonics in equal
|}
| steps = 135
| num = 7
| denom = 3
| start = 12
| collapsed = 1
}}

Latest revision as of 08:07, 5 October 2024

This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 67ed7/3 68ed7/3 69ed7/3 →
Prime factorization 22 × 17
Step size 21.5716 ¢ 
Octave 56\68ed7/3 (1208.01 ¢) (→ 14\17ed7/3)
Twelfth 88\68ed7/3 (1898.3 ¢) (→ 22\17ed7/3)
Consistency limit 2
Distinct consistency limit 2

68 equal divisions of 7/3 (abbreviated 68ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 68 equal parts of about 21.6 ¢ each. Each step represents a frequency ratio of (7/3)1/68, or the 68th root of 7/3.

Intervals

Degrees Enneatonic Pentadecatonic Enneadecatonic ed11\9~ed7/3
1 1+ G+ G' Qq Q+ 21.5686 21.5716
Jv, Av, Jbv, Abv, W\\v Wbv
2 1# G# G^ Qp/W\\\ Q#/Wb 43.13725 43.1433
Jv Av Jbv Abv
3 1#+ G#+ G^' Qpq Q#+ 64.7059 64.7149
J, A, Jb, Ab, W\ Wd
4 1x/2bb Gx J A Jb Ab W 86.2745 86.2865
Jbb Abb
5 2bv Jbv Abv J'/A\\v, A'/B\\v, Jb' Ab' Wq W+ W+/Ebd 107.8431 107.8582
G#v,
6 2b Jb Ab J^/A\\v A^/B\\v Jb^ Ab^ Wp W# W#/Eb 129.4118 129.4298
G#v
7 2d Jd Ad J^'/A\\, A^'/B\\, Jb^' Ab^' Wpq/E\\\ W#+/E(b)d 150.9804 151.0014
G#,
8 2 J A A\\ B\\ G# E\\ Eb E 172.549 172.57305
9 2+ J+ A+ A\\'\/Jpv, B\\'/Apv, G#' E\ Ed E+/Rd 194.11765 194.1447
Jv, Av,
10 2# J# A# A\\^/Jpv B\\^/Apv G#^ E R 215.6863 215.7163
Jv Av
11 2#+ J#+ A#+ Jp, Ap, G#^' Epq/R\\\ E+/Rbd R+/Tbd 237.2549 237.2879
J, A,
12 2x/3bb Jx/Abb Ax/Bbb Jp Ap J A Ep/R\\ E#/Rb R#/Tb 258.8235 258.8596
13 3bd Abd Bbd Jp'/Av, Ap^/Bv J'/A, A'/Bv, Epq/R\ E#+/Rd R#+/Td 280.3922 280.4312
14 3b Ab Bb Jp^/Av Ap^/Bv J^/Av A^/Bv R T 301.9608 302.0028
15 3d Ad Bd Jp^'/A, Ap^'/B, J^'/A, A^'/Bv, Rq/T\\\ R+/Tbd T+/Ybd 323.5294 323.5745
16 3 A B A B A B Rp/T\\ R#/Tb T#/Yb 345.098 345.1461
17 3+ A+ B+ A'/Bv, B'/Cv, A'/Bbv, B^'/Cbv, Rpq/T\ R+/Tbd T#+/Yd 366.6 366.7177
18 3# A# B# A^/Bv B^/Cv A^/Bbv B^/Cbv T Y 388.2353 388.2894
19 3#+ A#+ B#+ A^'/B, B^'/Cv, A^'/Bb, B^'/Cbv, Tq\A\\\ T#+/Ad Y+/Ubd 409.8039 409.861
20 3x/4b Ax/Bbb Bx/Cbb B C Bb Cb Tp\A\\ T#/Ab Y#/Ub 431.37255 431.4326
21 4bd Bbd Cbd B^'C\\v, C'/Q\\v, Bb'/A#v, Cb'/B#v, Tpq\A\ T#+/Ad Y#+/Ud 452.9412 453.00425
22 4b Bb Cb B^/C\\v C^/Q\\v Bb^/A#v Cb^/B#v A U 474.5098 474.5759
23 4d B Cd B^'/C\\v, C^'/Q\\, Bb^'/A#, Cb^'/B#, Apq A+ U+/Abd 496.0784 496.1475
24 4 B C C\\ Q\\ A# B# Ap A# U#/Ab 517.6471 517.7191
25 4+ B+ C+ C\\'/Bpv, Q\\'/Cpv, A#'/Bv, B#'/Cv, Apq/S\\\ A#+/Sbd U#+/Ad 539.2157 539.2908
26 4# B# C# C\\^/Bpv Q\\^/Cpv A#^/Bv B#^/Cv S\\ Sb A 560.7843 560.8624
27 4#+/5bd B#+/Cbd C#/Dbd C\\^'/Bp, Q\\^'/Cpv, A#^'/B, B#^'/C, S\ Sd A+/Sd 582.3529 582.434
28 5b Cb Qb Bp Cp B C S 603.9216 604.0057
29 5d Cd Qd Bp'/Cv, Cp'/Qv, B'/Cv, C'/Qv, Sq/D\\\ S+/Dbd 625.4902 625.5773
30 5 C Q Bp^/Cv Cp^/Qv B^/Cv C^/Qv Sp/D\\ S#/Db 647.0588 647.1489
31 5+ C+ Q+ Bp^'/C, Cp^/'Q, B^'/C, C^'/Q, Spq/D\ S#+/Dbd 668.62745 668.7206
32 5# C# Q# C Q C Q D 690.1961 690.2922
33 5#+ C#+ Q#+ C'/Qv, Q'/Dv, C'/Qbv, Q'/Dbv, Dq/F\\\ D+/Fbd 711.7647 711.8638
34 5x/6bb Cx/Qbb Qx/Dbb C^/Qv Q^/Dv C^/Qbv Q^/Dbv Dp/F\\ D#/Fb 733.3 733.43545
35 6bd Qbd Dbd C^/Qv Q^/Dv C^/Qbv Q^/Dbv Dp/F\\ D#/Fb 754.902 755.0071
36 6b Qb Db Q D Qb Db F 776.4706 776.5787
37 6d Qd Dd Q'/D\\v, D'/E\\v, Qb'/C#v, Db'/Q#v, Fq/G\\\ F+/Gbd 798.0392 798.15035
38 6 Q D Q^/D\\v D^/E\\v Qb^/C#v Db^/Q#v Fp/G\\ F#/Gb 819.6078 819.722
39 6+ Q+ D+ Q^'/D\\, D^'/E\\, Qb^'/C#, Db^'/Q#, Fpq/G\ F+/Gd 841.1765 841.2936
40 6# Q# D# D\\ E\\ C# Q# G 862.7451 862.8982
41 6#+ Q#+ D#+ D\\'/Qpv, E\\'/Dpv, C#'/Qv, Q#'/Dv, Gq G+ G+\Hd 884.3137 884.4369
42 6x/7bb Qx/Dbb Dx/Sbb D\\^/Qpv E\\^/Dpv C#^/Qv Q#^/Dv Gp G# H 905.88235 906.0085
43 7bd Dbd Sbd D\\^'/Qp, E\\^'/Dp, C#^'/Qv, Q#^'/Dv, Gpq/Z\\\ G#+/Zbd Hd 927.451 927.5801
44 7b Db Sb Qp Dp Q D Z\\ Zb H# 949.0196 949.1518
45 7d Dd Sd Qp'/Dv, Dp'/Ev, Q'/Dv, D'/Sv, Z\ Zd H#+/Jbd 970.5882 970.7234
46 7 D S Qp^/Dv Dp^/Ev Q^/Dv D^/Sv Z Jb 992.1569 992.295
47 7+ D+ S+ Qp^'/D, Dp^'/E, Q^'/D, D^'/S, Zq/X\\\ Z+/Xbd Jd 1013.7255 1013.8667
48 7# D# S# D E D S Zp/X\\ Z#/Xb J 1035.2941 1035.4383
49 7#+ D#+ S#+ D'/Ev, E'/Sv, D' S' Zpq/X\ Z#+/Xd J+/Zbd 1056.86275 1057.0099
Ebv,
50 7x/8bb Dx/Ebb Sx/Ebb D^/Ev E^/Sv D^ S^ X J#/Zb 1078.4314 1078.58155
Ebv
51 8bd Ebd D^'/E, E^'/Sv, D^' S^' Xq/C\\\ X+/Cbd J#+/Zd 1100 1100.1532
Eb,
52 8b Eb E S Eb Xp/C\\ X#/Cb Z 1121.5686 1121.7248
53 8d Ed E' S' Eb' Xpq/C\ X#+/Cbd Z+/Xd 1143.13725 1143.2964
Fv, D#v, S#v,
54 8 E E^ S^ Eb^ C X 1164.7059 1164.8681
Fv D#v S#v
55 8+ E+ E^' S^' Eb^' Cq/V\\\ C+/Vbd X+/Cbd 1186.2745 1186.4397
F, D#, S#,
56 8# E# F D# S# Cp/V\\ C#/Vb X#/Cb 1207.8731 1208.0113
57 8#+ E#+ F'/G\\v, D#' S#' Cpq/V\ C#+/Vd X#+/Cd 1229.4118 1229.583
Ev,
58 8x/9bb Ex/Fbb F^/G\\v D#^ S#^ V C 1250.9804 1251.1546
Ev
59 9bd Fbd F^'/G\\, D#^' S#^' Vq V+ C+/Vd 1272.2549 1272.7262
E,
60 9b Fb G\\ E Vp V# V 1294.11765 1294.2979
61 9d Fd G\\'/Fpv, E'/Fv, Vpq/B\\\ V#+/Bbd V+/Bbd 1315.6863 1315.8695
62 9 F G\\^/Fpv E^/Fv B\\ Bb V#/Bb 1337.2549 1337.4411
63 9+ F+ G\\^/'Fp, E^'/F, B\ Bd V#+/Bd 1358.8235 1359.01275
64 9# F# Fp F B 1380.3922 1380.5844
65 9#+/1bd F#+/Gbd Fp' F' Bpq/Q\\ B+/Qbd 1401.9608 1402.156
Gv
66 1b Gb Fp^ F^ Bp/Q\\ B#/Qb 1423.5294 1423.7276
Gv
67 1d Gd Fp^' F^' Bpq/Q\ B#+/Qd 1445.098 1445.993
Gv,
68 1 G Q 1466.6 1466.8709

Harmonics

Approximation of harmonics in 135ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -4.77 -0.46 +1.32 -4.69 -5.23 -0.46 -3.45 -0.91 +1.40 -0.62 +0.87
Relative (%) -43.9 -4.2 +12.2 -43.2 -48.1 -4.2 -31.7 -8.4 +12.9 -5.7 +8.0
Steps
(reduced) 		110
(110) 		175
(40) 		221
(86) 		256
(121) 		285
(15) 		310
(40) 		331
(61) 		350
(80) 		367
(97) 		382
(112) 		396
(126)
Approximation of harmonics in 135ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +3.55 -5.23 -5.15 +2.64 -4.52 +5.18 -1.49 -3.37 -0.91 -5.39 +4.58
Relative (%) +32.7 -48.1 -47.4 +24.3 -41.6 +47.7 -13.8 -31.0 -8.4 -49.6 +42.2
Steps
(reduced) 		409
(4) 		420
(15) 		431
(26) 		442
(37) 		451
(46) 		461
(56) 		469
(64) 		477
(72) 		485
(80) 		492
(87) 		500
(95)
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