Xenharmonic Wiki

34edo: Difference between revisions

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Line 117: Line 117:
! rowspan="2" |Degree
! rowspan="2" |Degree
! rowspan="2" |Solfege
! rowspan="2" |Solfege
! colspan="2"| Cents
! colspan="3" | Cents
! colspan="2" |pions
! colspan="3" |pions
! colspan="2" |7mus
! colspan="3" |7mus
! rowspan="2"| approx. ratios of
! rowspan="2" | approx. ratios of


2.3.5.13.17 [[subgroup|subgroup]]
2.3.5.13.17 [[subgroup|subgroup]]
! rowspan="2"| additional ratios
! rowspan="2" | additional ratios


of 7 and 11
of 7 and 11
Line 129: Line 129:
|-
|-
!Pure octave
!Pure octave
!45ed(7φ+6)\(5φ^2)
!2ed25/24
!2ed25/24
!Pure octave
!Pure octave
!45ed(7φ+6)\(5φ^2)
!2ed25/24
!2ed25/24
!Pure octave
!Pure octave
!45ed(7φ+6)\(5φ^2)
!2ed25/24
!2ed25/24
|-
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:center;" | do
| style="text-align:center;" | do
| colspan="6" style="text-align:right;" | 0<span style="color: #fff;">.000</span>
| colspan="9" style="text-align:right;" | 0<span style="color: #fff;">.000</span>
| style="text-align:center;" | 1/1
| style="text-align:center;" | 1/1
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 147: Line 150:
| style="text-align:center;" | di
| style="text-align:center;" | di
| style="text-align:right;" | 35.294
| style="text-align:right;" | 35.294
|35.296
|35.336
|35.336
|37.412
|37.412
|37.414
|37.456
|37.456
|45.1765 (2D.2D2<sub>16</sub>)
|45.1765 (2D.2D2<sub>16</sub>)
|45.179 (2D.2DE<sub>16</sub>)
|45.23 (2D.3AF8<sub>16</sub>)
|45.23 (2D.3AF8<sub>16</sub>)
| style="text-align:center;" | 128/125 ([[128/125|diesis]]), 51/50
| style="text-align:center;" | 128/125 ([[128/125|diesis]]), 51/50
Line 161: Line 167:
| style="text-align:center;" | rih
| style="text-align:center;" | rih
| style="text-align:right;" | 70.588
| style="text-align:right;" | 70.588
|70.592
|70.672
|70.672
|74.8235
|74.8235
|74.828
|74.913
|74.913
|90.353 (5A.5A5<sub>16</sub>)
|90.353 (5A.5A5<sub>16</sub>)
|90.358 (5A.5BB<sub>16</sub>)
|90.461 (5A.75F<sub>16</sub>)
|90.461 (5A.75F<sub>16</sub>)
| style="text-align:center;" | 25/24, 648/625 ([[648/625|large diesis]])
| style="text-align:center;" | 25/24, 648/625 ([[648/625|large diesis]])
Line 175: Line 184:
| style="text-align:center;" | ra
| style="text-align:center;" | ra
| style="text-align:right;" | 105.882
| style="text-align:right;" | 105.882
|105.8885
|106.008
|106.008
|111.235
|111.235
|112.242
|112.369
|112.369
|135.529 (87.8788<sub>16</sub>)
|135.529 (87.8788<sub>16</sub>)
|135.537 (87.899<sub>16</sub>)
|135.691 (87.B0F<sub>16</sub>)
|135.691 (87.B0F<sub>16</sub>)
| style="text-align:center;" | 17/16, 18/17, 16/15
| style="text-align:center;" | 17/16, 18/17, 16/15
Line 189: Line 201:
| style="text-align:center;" | ru
| style="text-align:center;" | ru
| style="text-align:right;" | 141.1765
| style="text-align:right;" | 141.1765
|141.185
|141.345
|141.345
|149.647
|149.647
|149.656
|149.8255
|149.8255
|180.706 (B4.B4B<sub>16</sub>)
|180.706 (B4.B4B<sub>16</sub>)
|180.716 (B4.B77<sub>16</sub>)
|180.921 (B4.EBE<sub>16</sub>)
|180.921 (B4.EBE<sub>16</sub>)
| style="text-align:center;" | 13/12
| style="text-align:center;" | 13/12
Line 203: Line 218:
| style="text-align:center;" | reh
| style="text-align:center;" | reh
| style="text-align:right;" | 176.471
| style="text-align:right;" | 176.471
|176.481
|176.681
|176.681
|187.059
|187.059
|187.07
|187.282
|187.282
|225.882 (E1.E1E<sub>16</sub>)
|225.882 (E1.E1E<sub>16</sub>)
|225.896 (E1.E54<sub>16</sub>)
|226.152 (E2.26E<sub>16</sub>)
|226.152 (E2.26E<sub>16</sub>)
| style="text-align:center;" | 10/9
| style="text-align:center;" | 10/9
Line 217: Line 235:
| style="text-align:center;" | re
| style="text-align:center;" | re
| style="text-align:right;" | 211.765
| style="text-align:right;" | 211.765
|211.777
|212.017
|212.017
|224.471
|224.471
|224.484
|224.738
|224.738
|271.059 (10F.0F1<sub>16</sub>)
|271.059 (10F.0F1<sub>16</sub>)
|271.075 (10F.132<sub>16</sub>)
|271.382 (10F.61D<sub>16</sub>)
|271.382 (10F.61D<sub>16</sub>)
| style="text-align:center;" | 9/8, 17/15
| style="text-align:center;" | 9/8, 17/15
Line 231: Line 252:
| style="text-align:center;" | raw
| style="text-align:center;" | raw
| style="text-align:right;" | 247.059
| style="text-align:right;" | 247.059
|247.073
|247.3535
|247.3535
|261.882
|261.882
|261.898
|262.195
|262.195
|326.235 (13C.3C3<sub>16</sub>)
|326.235 (13C.3C3<sub>16</sub>)
|316.254 (13C.40F8<sub>16</sub>)
|316.6125 (13C.7EA<sub>16</sub>)
|316.6125 (13C.7EA<sub>16</sub>)
| style="text-align:center;" | 15/13
| style="text-align:center;" | 15/13
Line 245: Line 269:
| style="text-align:center;" | meh
| style="text-align:center;" | meh
| style="text-align:right;" | 282.353
| style="text-align:right;" | 282.353
|282.3695
|282.69
|282.69
|299.294
|299.294
|299.312
|299.651
|299.651
|361.412 (169.696<sub>16</sub>)
|361.412 (169.696<sub>16</sub>)
|361.433 (169.6ED<sub>16</sub>)
|361.843 (169.D7C<sub>16</sub>)
|361.843 (169.D7C<sub>16</sub>)
| style="text-align:center;" | 20/17, 75/64
| style="text-align:center;" | 20/17, 75/64
Line 259: Line 286:
| style="text-align:center;" | me
| style="text-align:center;" | me
| style="text-align:right;" | 317.647
| style="text-align:right;" | 317.647
|317.666
|318.026
|318.026
|336.706
|336.706
|336.726
|337.1075
|337.1075
|406.588 (196.969<sub>16</sub>)
|406.588 (196.969<sub>16</sub>)
|406.612 (196.9CB<sub>16</sub>)
|407.073 (197.12C<sub>16</sub>)
|407.073 (197.12C<sub>16</sub>)
| style="text-align:center;" | 6/5
| style="text-align:center;" | 6/5
Line 273: Line 303:
| style="text-align:center;" | mu
| style="text-align:center;" | mu
| style="text-align:right;" | 352.941
| style="text-align:right;" | 352.941
|352.962
|353.362
|353.362
|374.118
|374.118
|374.1395
|374.564
|374.564
|451.765 (1C3.C3C<sub>16</sub>)
|451.765 (1C3.C3C<sub>16</sub>)
|451.791 (1C3.CA8<sub>16</sub>)
|452.3035 (1C4.4DB<sub>16</sub>)
|452.3035 (1C4.4DB<sub>16</sub>)
| style="text-align:center;" | 16/13
| style="text-align:center;" | 16/13
Line 287: Line 320:
| style="text-align:center;" | mi
| style="text-align:center;" | mi
| style="text-align:right;" | 388.235
| style="text-align:right;" | 388.235
|388.258
|388.698
|388.698
|411.529
|411.529
|411.5535
|412.02
|412.02
|496.941 (1F0.F0F<sub>16</sub>)
|496.941 (1F0.F0F<sub>16</sub>)
|496.97 (1F0.F86<sub>16</sub>)
|497.534 (1F1.88B<sub>16</sub>)
|497.534 (1F1.88B<sub>16</sub>)
| style="text-align:center;" | 5/4
| style="text-align:center;" | 5/4
Line 301: Line 337:
| style="text-align:center;" | maa
| style="text-align:center;" | maa
| style="text-align:right;" | 423.529
| style="text-align:right;" | 423.529
|423.554
|424.035
|424.035
|448.941
|448.941
|448.967
|449.477
|449.477
|542.118 (21E.1E1<sub>16</sub>)
|542.118 (21E.1E1<sub>16</sub>)
|542.149 (21E.264<sub>16</sub>)
|542.764 (21E.C3A<sub>16</sub>)
|542.764 (21E.C3A<sub>16</sub>)
| style="text-align:center;" | [[51/40|51/40]], 32/25
| style="text-align:center;" | [[51/40|51/40]], 32/25
Line 315: Line 354:
| style="text-align:center;" | maw
| style="text-align:center;" | maw
| style="text-align:right;" | 458.8235
| style="text-align:right;" | 458.8235
|458.85
|459.371
|459.371
|486.353
|486.353
|486.381
|486.933
|486.933
|587.294 (24B.4B4<sub>16</sub>)
|587.294 (24B.4B4<sub>16</sub>)
|587.3285 (24B.541<sub>16</sub>)
|587.995 (24B.FEA<sub>16</sub>)
|587.995 (24B.FEA<sub>16</sub>)
| style="text-align:center;" | 13/10, 17/13
| style="text-align:center;" | 13/10, 17/13
Line 329: Line 371:
| style="text-align:center;" | fa
| style="text-align:center;" | fa
| style="text-align:right;" | 494.118
| style="text-align:right;" | 494.118
|494.1465
|494.707
|494.707
|523.765
|523.765
|523.795
|524.389
|524.389
|632.471 (278.7878<sub>16</sub>)
|632.471 (278.7878<sub>16</sub>)
|632.508 (278.81F<sub>16</sub>)
|633.225 (279.399A<sub>16</sub>)
|633.225 (279.399A<sub>16</sub>)
| style="text-align:center;" | 4/3
| style="text-align:center;" | 4/3
Line 343: Line 388:
| style="text-align:center;" | fih
| style="text-align:center;" | fih
| style="text-align:right;" | 529.412
| style="text-align:right;" | 529.412
|529.443
|530.043
|530.043
|561.1765
|561.1765
|561.209
|561.846
|561.846
|677.647 (2A5.A5A<sub>16</sub>)
|677.647 (2A5.A5A<sub>16</sub>)
|677.687 (2A5.AFD<sub>16</sub>)
|678.455 (2A6.749<sub>16</sub>)
|678.455 (2A6.749<sub>16</sub>)
| style="text-align:center;" |512/375, 34/25
| style="text-align:center;" |512/375, 34/25
Line 357: Line 405:
| style="text-align:center;" | fu
| style="text-align:center;" | fu
| style="text-align:right;" | 564.706
| style="text-align:right;" | 564.706
|564.739
|565.379
|565.379
|598.588
|598.588
|598.623
|599.302
|599.302
|722.8235 (2D2.D2D<sub>16</sub>)
|722.8235 (2D2.D2D<sub>16</sub>)
|722.866 (2D2.DDA<sub>16</sub>)
|723.686 (2D3.AF8<sub>16</sub>)
|723.686 (2D3.AF8<sub>16</sub>)
| style="text-align:center;" | 36/25, 18/13
| style="text-align:center;" | 36/25, 18/13
Line 371: Line 422:
| style="text-align:center;" | fi/se
| style="text-align:center;" | fi/se
| style="text-align:right;" | 600<span style="color: #fff;">.000</span>
| style="text-align:right;" | 600<span style="color: #fff;">.000</span>
|600.035
|600.716
|600.716
|636
|636
|636.037
|636.758
|636.758
|768 (300<sub>16</sub>)
|768 (300<sub>16</sub>)
|768.045 (300.0B8<sub>16</sub>)
|768.916 (300.EA8<sub>16,)</sub>
|768.916 (300.EA8<sub>16,)</sub>
| style="text-align:center;" | 17/12, 24/17
| style="text-align:center;" | 17/12, 24/17
Line 385: Line 439:
| style="text-align:center;" | su
| style="text-align:center;" | su
| style="text-align:right;" | 635.294
| style="text-align:right;" | 635.294
|635.331
|636.052
|636.052
|673.412
|673.412
|673.451
|674.215
|674.215
|813.1765 (32D.2D2<sub>16</sub>)
|813.1765 (32D.2D2<sub>16</sub>)
|813.224 (32D.396<sub>16</sub>)
|814.146 (32E.2578<sub>16</sub>)
|814.146 (32E.2578<sub>16</sub>)
| style="text-align:center;" | 25/18, 13/9
| style="text-align:center;" | 25/18, 13/9
Line 399: Line 456:
| style="text-align:center;" | sih
| style="text-align:center;" | sih
| style="text-align:right;" | 670.588
| style="text-align:right;" | 670.588
|670.627
|671.388
|671.388
|710.8235
|710.8235
|710.865
|711.671
|711.671
|858.353 (35A.5A5<sub>16</sub>)
|858.353 (35A.5A5<sub>16</sub>)
|858.403 (35A.673<sub>16</sub>)
|859.377 (35B.607<sub>16</sub>)
|859.377 (35B.607<sub>16</sub>)
| style="text-align:center;" |375/256, 25/17
| style="text-align:center;" |375/256, 25/17
Line 413: Line 473:
| style="text-align:center;" | sol
| style="text-align:center;" | sol
| style="text-align:right;" | 705.882
| style="text-align:right;" | 705.882
|705.924
|706.724
|706.724
|748.235
|748.235
|748.279
|749.128
|749.128
|903.529 (387.8788<sub>16</sub>)
|903.529 (387.8788<sub>16</sub>)
|903.582 (387.951<sub>16</sub>)
|904.607 (388.9B7<sub>16</sub>)
|904.607 (388.9B7<sub>16</sub>)
| style="text-align:center;" | 3/2
| style="text-align:center;" | 3/2
Line 427: Line 490:
| style="text-align:center;" | saw
| style="text-align:center;" | saw
| style="text-align:right;" | 741.1765
| style="text-align:right;" | 741.1765
|741.22
|742.0605
|742.0605
|785.647
|785.647
|785.693
|786.584
|786.584
|948.706 (3B4.B4B<sub>16</sub>)
|948.706 (3B4.B4B<sub>16</sub>)
|948.761 (3B4.C2E8<sub>16</sub>)
|949.837 (3B5.D66<sub>16</sub>)
|949.837 (3B5.D66<sub>16</sub>)
| style="text-align:center;" | 20/13, 26/17
| style="text-align:center;" | 20/13, 26/17
Line 441: Line 507:
| style="text-align:center;" | leh
| style="text-align:center;" | leh
| style="text-align:right;" | 776.471
| style="text-align:right;" | 776.471
|776.516
|777.397
|777.397
|823.059
|823.059
|823.107
|824.0405
|824.0405
|993.882 (3E1.E1E<sub>16</sub>)
|993.882 (3E1.E1E<sub>16</sub>)
|993.9405 (3E1.F0C<sub>16</sub>)
|995.068 (3E3.116<sub>16</sub>)
|995.068 (3E3.116<sub>16</sub>)
| style="text-align:center;" | 25/16, 80/51
| style="text-align:center;" | 25/16, 80/51
Line 455: Line 524:
| style="text-align:center;" | le
| style="text-align:center;" | le
| style="text-align:right;" | 811.765
| style="text-align:right;" | 811.765
|811.812
|812.733
|812.733
|860.471
|860.471
|860.521
|861.497
|861.497
|1039.059 (40F.0F1<sub>16</sub>)
|1039.059 (40F.0F1<sub>16</sub>)
|1039.12 (40F.1EA<sub>16</sub>)
|1040.298 (410.4C5<sub>16</sub>)
|1040.298 (410.4C5<sub>16</sub>)
| style="text-align:center;" | 8/5
| style="text-align:center;" | 8/5
Line 469: Line 541:
| style="text-align:center;" | lu
| style="text-align:center;" | lu
| style="text-align:right;" | 847.059
| style="text-align:right;" | 847.059
|847.108
|848.069
|848.069
|897.882
|897.882
|897.935
|898.953
|898.953
|1084.235 (43C.3C3<sub>16</sub>)
|1084.235 (43C.3C3<sub>16</sub>)
|1084.299 (43C.4C7<sub>16</sub>)
|1085.5285 (43D.874<sub>16</sub>)
|1085.5285 (43D.874<sub>16</sub>)
| style="text-align:center;" | 13/8
| style="text-align:center;" | 13/8
Line 483: Line 558:
| style="text-align:center;" | la
| style="text-align:center;" | la
| style="text-align:right;" | 882.353
| style="text-align:right;" | 882.353
|882.4045
|883.405
|883.405
|935.294
|935.294
|935.349
|936.41
|936.41
|1129.412 (469.696<sub>16</sub>)
|1129.412 (469.696<sub>16</sub>)
|1129.478 (469.7A5<sub>16</sub>)
|1130.759 (46A.C42<sub>16</sub>)
|1130.759 (46A.C42<sub>16</sub>)
| style="text-align:center;" | 5/3
| style="text-align:center;" | 5/3
Line 497: Line 575:
| style="text-align:center;" | laa
| style="text-align:center;" | laa
| style="text-align:right;" | 917.647
| style="text-align:right;" | 917.647
|917.701
|918.7415
|918.7415
|972.706
|972.706
|972.763
|973.866
|973.866
|1174.588 (496.969<sub>16</sub>)
|1174.588 (496.969<sub>16</sub>)
|1174.657 (496.A83<sub>16</sub>)
|1175.989 (497.FD4<sub>16</sub>)
|1175.989 (497.FD4<sub>16</sub>)
| style="text-align:center;" | [[17/10|17/10]]
| style="text-align:center;" | [[17/10|17/10]]
Line 511: Line 592:
| style="text-align:center;" | law
| style="text-align:center;" | law
| style="text-align:right;" | 952.941
| style="text-align:right;" | 952.941
|952.997
|954.078
|954.078
|1010.118
|1010.118
|1010.177
|1011.322
|1011.322
|1219.765 (4C3.C3C<sub>16</sub>)
|1219.765 (4C3.C3C<sub>16</sub>)
|1219.836 (4C3.D6<sub>16</sub>)
|1221.2195 (4C5.383<sub>16</sub>)
|1221.2195 (4C5.383<sub>16</sub>)
| style="text-align:center;" | 26/15
| style="text-align:center;" | 26/15
Line 525: Line 609:
| style="text-align:center;" | teh
| style="text-align:center;" | teh
| style="text-align:right;" | 988.235
| style="text-align:right;" | 988.235
|988.293
|989.414
|989.414
|1047.529
|1047.529
|1047.591
|1048.779
|1048.779
|1264.941 (4F0.F0F<sub>16</sub>)
|1264.941 (4F0.F0F<sub>16</sub>)
|1265.015 (4F1.03E<sub>16</sub>)
|1266.45 (4F2.733<sub>16</sub>)
|1266.45 (4F2.733<sub>16</sub>)
| style="text-align:center;" | 16/9, 30/17
| style="text-align:center;" | 16/9, 30/17
Line 539: Line 626:
| style="text-align:center;" | te
| style="text-align:center;" | te
| style="text-align:right;" | 1023.529
| style="text-align:right;" | 1023.529
|1,023.589
|1024.75
|1024.75
|1084.941
|1084.941
|1085.005
|1086.235
|1086.235
|1310.118 (51E.1E1<sub>16</sub>)
|1310.118 (51E.1E1<sub>16</sub>)
|1310.194 (51E.31C<sub>16</sub>)
|1311.68 (51F.AE2<sub>16</sub>)
|1311.68 (51F.AE2<sub>16</sub>)
| style="text-align:center;" | 9/5
| style="text-align:center;" | 9/5
Line 553: Line 643:
| style="text-align:center;" | tu
| style="text-align:center;" | tu
| style="text-align:right;" | 1058.8235
| style="text-align:right;" | 1058.8235
|1,058.885
|1060.086
|1060.086
|1122.353
|1122.353
|1122.419
|1123.692
|1123.692
|1355.294 (54B.4B4<sub>16</sub>)
|1355.294 (54B.4B4<sub>16</sub>)
|1355.373 (54B.5F9<sub>16</sub>)
|1356.911 (54C.E91<sub>16</sub>)
|1356.911 (54C.E91<sub>16</sub>)
| style="text-align:center;" | 24/13
| style="text-align:center;" | 24/13
Line 567: Line 660:
| style="text-align:center;" | ti
| style="text-align:center;" | ti
| style="text-align:right;" | 1094.118
| style="text-align:right;" | 1094.118
|1,094.182
|1095.423
|1095.423
|1149.765
|1149.765
|1159.8325
|1161.148
|1161.148
|1400.471 (578.7878<sub>16</sub>)
|1400.471 (578.7878<sub>16</sub>)
|1400.5525 (578.8D7<sub>16</sub>)
|1402.141 (57A.241<sub>16</sub>)
|1402.141 (57A.241<sub>16</sub>)
| style="text-align:center;" | 32/17, 17/9, 15/8
| style="text-align:center;" | 32/17, 17/9, 15/8
Line 581: Line 677:
| style="text-align:center;" | taa
| style="text-align:center;" | taa
| style="text-align:right;" | 1129.412
| style="text-align:right;" | 1129.412
|1,129.478
|1130.759
|1130.759
|1197.1765
|1197.1765
|1197.2465
|1198.604
|1198.604
|1445.647 (5A5.A5A<sub>16</sub>)
|1445.647 (5A5.A5A<sub>16</sub>)
|1445.732 (5A5.BB5<sub>16</sub>)
|1447.371 (5A7.5F1<sub>16</sub>)
|1447.371 (5A7.5F1<sub>16</sub>)
| style="text-align:center;" | 48/25, 625/324
| style="text-align:center;" | 48/25, 625/324
Line 595: Line 694:
| style="text-align:center;" | da
| style="text-align:center;" | da
| style="text-align:right;" | 1164.706
| style="text-align:right;" | 1164.706
|1,164.774
|1166.095
|1166.095
|1234.588
|1234.588
|1234.66
|1236.061
|1236.061
|1490.8235 (5D2.D2D<sub>16</sub>)
|1490.8235 (5D2.D2D<sub>16</sub>)
|1490.911 (5D2.E92<sub>16</sub>)
|1492.602 (5D4.9A1<sub>16</sub>)
|1492.602 (5D4.9A1<sub>16</sub>)
| style="text-align:center;" | 125/64, 100/51
| style="text-align:center;" | 125/64, 100/51
Line 609: Line 711:
| style="text-align:center;" | do
| style="text-align:center;" | do
| style="text-align:right;" | 1200<span style="color: #fff;">.000</span>
| style="text-align:right;" | 1200<span style="color: #fff;">.000</span>
|1,200.07
|1201.431
|1201.431
|1272
|1272
|1272.074
|1273.52
|1273.52
|1536 (600<sub>16</sub>)
|1536 (600<sub>16</sub>)
|1536.09 (600.17<sub>16</sub>)
|1537.832 (601.D5<sub>6F</sub>)
|1537.832 (601.D5<sub>6F</sub>)
| style="text-align:center;" | 2/1
| style="text-align:center;" | 2/1
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