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Table of 103edo intervals: Difference between revisions

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This '''table of [[103edo]] intervals''' assumes [[13-limit]] [[patent val]] {{val|103 163 239 289 356 381}}.  
This '''table of 103edo intervals''' assumes [[17-limit]] [[patent val]] {{val| 103 163 239 289 356 381 421 }} of [[103edo]].  


Intervals highlighted in '''bold''' are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in ''italic''. Intervals that differ by more than 100% are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.
Intervals highlighted in '''bold''' are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in ''italic''. Intervals that differ by more than 100% are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.
Line 5: Line 5:
{| class="wikitable center-1 right-2 center-3"
{| class="wikitable center-1 right-2 center-3"
|-
|-
! #
! Degree
! Cents
! Cents
! Marks
! Marks
Line 12: Line 12:
! 11-limit
! 11-limit
! 13-limit
! 13-limit
! 17-limit
|-
|-
|0
| 0
|0.00
| 0.000
|P1
| P1
|colspan="4" | '''[[1/1]]'''
| colspan="5" | '''1/1'''
|-
|-
|1
| 1
|11.650
| 11.650
|
|  
|''[[81/80]]''
| ''81/80''
|[[1029/1024]]
| [[126/125]]
|[[2835/2816]]
| "
|[[512/507]], [[144/143]]
| "
| "
|-
|-
|2
| 2
|23.301
| 23.301
|
|  
|81/80
|  
|[[64/63]]
|  
|[[8192/8085]]
|  
|[[65/64]], [[78/77]]
| 65/64, 66/65, 78/77
| "
|-
|-
|3
| 3
|34.951
| 34.951
|
|  
|''[[128/125]]''
|  
|''64/63'', [[49/48]], [[50/49]]
| 49/48, 50/49, ''64/63''
|
| "
|
| "
| "
|-
|-
|4
| 4
|46.602
| 46.602
|
|  
|128/125
|  
|[[36/35]]
| 36/35
|''[[33/32]]''
| ''33/32''
|[[40/39]], [[1053/1024]], [[416/405]]
| "
| 35/34
|-
|-
|5
| 5
|58.252
| 58.252
|
|  
|
|  
|[[28/27]]
|  
|33/32, [[512/495]]
|  
|[[121/117]]
| ''27/26''
| ''34/33''
|-
|-
|6
| 6
|69.903
| 69.903
|
|  
|[[25/24]]
| 25/24
|
| ''28/27''
|[[126/121]]
| "
|[[176/169]]
| 26/25
| "
|-
|-
|7
| 7
|81.553
| 81.553
|
|  
|''25/24'', [[16384/15625]]
|  
|[[21/20]]
| 21/20
|[[22/21]]
| 22/21
|
| "
| "
|-
|-
|8
| 8
|93.204
| 93.204
|m2
|  
|[[135/128]]
|  
|''21/20''
|  
|[[128/121]], [[5120/4851]]
|  
|[[96/91]], [[325/308]]
|  
| 18/17
|-
|-
|9
| 9
|104.854
| 104.854
|
| m2
|''[[16/15]]''
|  
|[[1225/1152]], [[3584/3375]]
|  
|[[1089/1024]]
|  
|''[[273/256]]'', [[52/49]]
|  
| '''17/16'''
|-
|-
|10
| 10
|116.505
| 116.505
|
|  
|16/15
| 16/15
|[[15/14]]
| 15/14
|[[77/72]]
| "
|
| "
| "
|-
|-
|11
| 11
|128.155
| 128.155
|
|  
|
|  
|
|  
|
|  
|''[[13/12]]'', [[14/13]]
| 14/13
| "
|-
|-
|12
| 12
|139.806
| 139.806
|
|  
|
|  
|[[1024/945]]
|  
|''[[12/11]]''
|  
|[[13/12]]
| 13/12
| "
|-
|-
|13
| 13
|151.456
| 151.456
|
|  
|
|  
|
|  
|12/11, [[275/252]]
| 12/11
|[[16384/15015]]
| "
| "
|-
|-
|14
| 14
|163.107
| 163.107
|
|  
|[[1125/1024]]
|  
|''[[35/32]]''
|  
|[[11/10]]
| 11/10
|[[100/91]]
| "
| "
|-
|-
|15
| 15
|174.757
| 174.757
|
|  
|''[[10/9]]''
|  
|[[567/512]], [[448/405]]
|  
|[[256/231]]
|  
|
| 72/65
| "
|-
|-
|16
| 16
|186.408
| 186.408
|
|  
|10/9
| 10/9
|
| "
|[[49/44]]
| "
|
| "
| "
|-
|-
|17
| 17
|198.058
| 198.058
|
| M2
|''[[9/8]]''
| ''9/8''
|[[28/25]], [[18375/16384]]
| "
|[[121/108]]
| "
|[[175/156]]
| "
| "
|-
|-
|18
| 18
|209.709
| 209.708
|M2
|  
|9/8
|  
|[[640/567]]
|  
|[[2048/1815]]
|  
|[[44/39]]
| 44/39
| "
|-
|-
|19
| 19
|221.359
| 221.359
|
|  
|[[256/225]]
|  
|'''''[[8/7]]'''''
|  
|[[25/22]]
| 25/22
|
| "
| 17/15
|-
|-
|20
| 20
|233.010
| 233.010
|
|  
|[[9375/8192]]
|  
|'''8/7'''
| '''8/7'''
|
| "
|[[143/125]]
| "
| "
|-
|-
|21
| 21
|244.660
| 244.660
|
|  
|[[144/125]]
|  
|[[147/128]]
|  
|
|  
|[[15/13]]
| 15/13
| "
|-
|-
|22
| 22
|256.311
| 256.311
|
|  
|
|  
|''[[7/6]]''
|  
|''[[64/55]]'', [[297/256]]
|
|[[196/169]]
| ''52/45''
| "
|-
|-
|23
| 23
|267.961
| 267.961
|
|  
|
|  
|7/6
| 7/6
|
| "
|[[2048/1755]]
| "
| "
|-
|-
|24
| 24
|279.612
| 279.712
|
|
|[[75/64]]
|  
|[[288/245]]
|  
|[[33/28]], [[88/75]], [[1280/1089]]
|  
|[[169/144]], [[1053/896]]
|  
| 20/17
|-
|-
|25
| 25
|291.262
| 291.262
|m3
|  
|[[32/27]]
|  
|
|  
|[[4096/3465]]
|  
|[[13/11]], [[200/169]]
| 13/11
| "
|-
|-
|26
| 26
|302.913
| 303.013
|
| m3
|''32/27''
| ''32/27''
|[[25/21]], [[343/288]]
| 25/21
|
| "
|[[512/429]], [[143/120]]
| "
| "
|-
|-
|27
| 27
|314.563
| 314.563
|
|  
|[[6/5]]
| 6/5
|
| "
|
| "
|[[2457/2048]]
| "
| "
|-
|-
|28
| 28
|326.214
| 326.214
|
|  
|''6/5''
|  
|
|  
|''[[77/64]]'', [[1024/847]], [[2475/2048]]
|  
|''[[63/52]]'', [[169/140]]
| ''63/52'', 65/54
| "
|-
|-
|29
| 29
|337.864
| 337.864
|
|  
|
|  
|[[175/144]]
|  
|
|  
|[[39/32]], [[1280/1053]]
| 39/32
| 17/14
|-
|-
|30
| 30
|349.515
| 349.615
|
|  
|
|  
|[[49/40]], [[60/49]]
| 49/40, 60/49
|[[11/9]]
| 11/9, 27/22
|'''''[[16/13]]''''', ''39/32'', [[175/143]]
| "
| "
|-
|-
|31
| 31
|361.165
| 361.165
|
|  
|
|  
|
|  
|[[8192/6655]], [[154/125]]
|  
|'''16/13''', [[832/675]]
| '''16/13'''
| 21/17
|-
|-
|32
| 32
|372.816
| 372.816
|
|  
|
|  
|
|  
|''[[96/77]]'', [[1024/825]], [[2541/2048]], [[32768/26411]]
|  
|[[26/21]]
| 26/21, ''81/65''
| "
|-
|-
|33
| 33
|384.466
| 384.466
|
|  
|'''[[5/4]]''', [[8192/6561]]
| '''5/4'''
|
| "
|
| "
|[[156/125]]
| "
| "
|-
|-
|34
| 34
|396.117
| 396.117
|
| M3
|'''''5/4'''''
|  
|
| 63/50
|[[121/96]], [[44/35]]
| 44/35
|
| "
| "
|-
|-
|35
| 35
|407.767
| 407.767
|M3
|  
|[[81/64]]
|  
|
|  
|''[[14/11]]''
|  
|
| 33/26
| "
|-
|-
|36
| 36
|419.417
| 419.417
|
|  
|''[[32/25]]''
|  
|[[125/98]], [[32768/25725]]
|  
|14/11, [[275/216]]
| 14/11
|[[8192/6435]], [[312/245]]
| "
| "
|-
|-
|37
| 37
|431.068
| 431.068
|
|  
|32/25
|  
|
| 9/7
|[[77/60]], [[440/343]]
| "
|[[50/39]]
| "
| "
|-
|-
|38
| 38
|442.718
| 442.708
|
|
|
|  
|''[[9/7]]'', [[1323/1024]]
|  
|[[128/99]]
|  
|
|  
| 22/17
|-
|-
|39
| 39
|454.369
| 454.369
|
|  
|
|  
|''[[64/49]]''
|  
|
|  
|[[13/10]]
| 13/10
| "
|-
|-
|40
| 40
|466.019
| 466.019
|
|  
|
|  
|[[21/16]], [[64/49]]
| 21/16
|[[72/55]]
| "
|[[1089/832]]
| "
| 17/13
|-
|-
|41
| 41
|477.670
| 477.670
|
|  
|[[675/512]]
|  
|''21/16''
|  
|
|  
|[[169/128]]
|  
|
|-
|-
|42
| 42
|489.320
| 489.320
|
|  
|'''''[[4/3]]'''''
|  
|[[4096/3087]]
|  
|[[512/385]], [[297/224]]
|  
|''169/128'', [[224/169]], [[65/49]]
| 65/49
| "
|-
|-
|43
| 43
|500.971
| 500.971
|P4
| P4
|'''4/3''', [[10935/8192]]
| '''4/3'''
|[[21875/16384]]
| "
|[[385/288]], [[147/110]], [[720/539]]
| "
|[[243/182]]
| "
| "
|-
|-
|44
| 44
|512.621
| 512.621
|
|  
|''[[27/20]]''
| ''27/20''
|''[[343/256]]'', [[168/125]]
| "
|[[121/90]]
| "
|[[192/143]], [[35/26]], [[3328/2475]]
| "
| "
|-
|-
|45
| 45
|524.272
| 524.272
|
|  
|27/20
|  
|[[256/189]]
|  
|[[693/512]]
|  
|[[65/48]], [[88/65]]
| 65/48
| "
|-
|-
|46
| 46
|535.922
| 535.922
|
|  
|
|  
|''[[48/35]]''
|  
|[[15/11]]
| 15/11
|[[567/416]]
| "
| "
|-
|-
|47
| 47
|547.573
| 547.573
|
|  
|
|  
|48/35
|  
|'''[[11/8]]'''
| '''11/8'''
|
| "
| "
|-
|-
|48
| 48
|559.223
| 559.223
|
|  
|
|  
|[[112/81]]
|  
|'''''11/8''''', [[243/176]], [[8192/5929]], [[2475/1792]]
|  
|[[18/13]]
| 18/13
| "
|-
|-
|49
| 49
|570.874
| 570.874
|
|  
|[[25/18]]
| 25/18
|''[[7/5]]''
| "
|[[245/176]], [[2816/2025]]
| "
|''18/13''
| "
| "
|-
|-
|50
| 50
|582.524
| 582.524
|d5
|  
|
| ''45/32''
|[[7/5]]
| 7/5
|
| "
|
| "
| "
|-
|-
|51
| 51
|594.175
| 594.175
|
| A4
|[[45/32]]
|  
|
|  
|[[512/363]], [[5775/4096]]
|  
|[[128/91]], [[55/39]]
|  
| 24/17
|-
|-
|52
| 52
|605.825
| 605.825
|A4
| d5
|[[64/45]]
|
|
|  
|[[363/256]], [[78/55]], [[8192/5775]]
|  
|[[91/64]]
|  
| 17/12
|-
|-
|53
| 53
|617.476
| 617.476
|
|  
|
| 64/45
|[[10/7]]
| 10/7
|
| "
|
| "
| "
|-
|-
|54
| 54
|629.126
| 629.126
|
|  
|[[36/25]]
| 36/25
|''10/7''
| "
|[[352/245]], [[2025/1408]]
| "
|''[[13/9]]''
| "
| "
|-
|-
|55
| 55
|640.777
| 640.777
|
|  
|
|  
|[[81/56]]
|  
|'''''[[16/11]]''''', [[352/243]], [[5929/4096]], [[3584/2475]]
|  
|13/9
| 13/9
| "
|-
|-
|56
| 56
|652.427
| 652.427
|
|  
|
|  
|[[35/24]]
|  
|'''16/11'''
| '''16/11'''
|
| "
| "
|-
|-
|57
| 57
|664.078
| 664.078
|
|  
|
|  
|''35/24''
|  
|[[22/15]]
| 22/15
|[[832/567]]
| "
| "
|-
|-
|58
| 58
|675.728
| 675.728
|
|  
|[[40/27]]
|  
|[[189/128]]
|  
|[[1024/693]]
|  
|[[96/65]], [[65/44]]
| 96/65
| "
|-
|-
|59
| 59
|687.379
| 687.379
|
|  
|''40/27''
| 40/27
|''[[512/343]]'', [[125/84]]
| "
|[[180/121]]
| "
|[[143/96]], [[52/35]], [[2475/1664]]
| "
| "
|-
|-
|60
| 60
|699.029
| 699.029
|P5
| P5
|'''[[3/2]]''', [[16384/10935]]
| '''3/2'''
|[[32768/21875]]
| "
|[[576/385]], [[220/147]], [[539/360]]
| "
|[[364/243]]
| "
| "
|-
|-
|61
| 61
|710.680
| 710.680
|
|  
|'''''3/2'''''
|  
|[[3087/2048]]
|  
|[[385/256]], [[448/297]]
|  
|''[[256/169]]'', [[169/112]], [[98/65]]
| 98/65
| "
|-
|-
|62
| 62
|722.330
| 722.330
|
|  
|[[1024/675]]
|  
|''[[32/21]]''
|  
|
|  
|256/169
|  
|
|-
|-
|63
| 63
|733.981
| 733.981
|
|  
|
|  
|32/21, [[49/32]]
| 32/21
|[[55/36]]
| "
|[[1664/1089]]
| "
| "
|-
|-
|64
| 64
|745.631
| 745.631
|
|  
|
|  
|''49/32''
|  
|
|  
|[[20/13]]
| 20/13
| "
|-
|-
|65
| 65
|757.282
| 757.282
|
|  
|
|  
|''[[14/9]]'', [[2048/1323]]
|  
|[[99/64]]
|  
|
|  
| 17/11
|-
|-
|66
| 66
|768.932
| 768.932
|
|  
|[[25/16]]
|  
|
| 14/9
|[[120/77]], [[343/220]]
| "
|[[39/25]]
| "
| "
|-
|-
|67
| 67
|780.583
| 780.583
|
|  
|''25/16''
|  
|[[196/125]], [[25725/16384]]
|  
|[[11/7]], [[432/275]]
| 11/7
|[[6435/4096]], [[245/156]]
| "
| "
|-
|-
|68
| 68
|792.233
| 792.233
|m6
|  
|[[128/81]]
|  
|
|  
|''11/7''
|  
|
| 52/33
| "
|-
|-
|69
| 69
|803.883
| 803.883
|
| m6
|'''''[[8/5]]'''''
|  
|
| 100/63
|[[192/121]], [[35/22]]
| 35/22
|
| "
| "
|-
|-
|70
| 70
|815.534
| 815.534
|
|
|'''8/5''', [[6561/4096]]
|  
|
| '''8/5'''
|
| "
|[[125/78]]
| "
| "
|-
|-
|71
| 71
|827.184
| 827.184
|
|  
|
|  
|
|  
|''[[77/48]]'', [[825/512]], [[4096/2541]], [[26411/16384]]
|  
|[[21/13]]
| 21/13, 130/81
| "
|-
|-
|72
| 72
|838.835
| 838.835
|
|  
|
|  
|
|  
|[[6655/4096]], [[125/77]]
|  
|'''[[13/8]]''', [[675/416]]
| '''13/8'''
| 34/21
|-
|-
|73
| 73
|850.485
| 850.485
|
|  
|
|  
|[[80/49]], [[49/30]]
| 49/30, 80/49
|[[18/11]]
| 18/11, 44/27
|'''''13/8''''', ''[[64/39]]''
| "
| "
|-
|-
|74
| 74
|862.136
| 862.136
|
|  
|
|  
|[[288/175]]
|  
|
|  
|64/39, [[1053/640]]
| 64/39
| 28/17
|-
|-
|75
| 75
|873.786
| 873.786
|
|  
|''[[5/3]]''
|  
|
|  
|''[[128/77]]'', [[847/512]], [[4096/2475]]
|  
|''[[104/63]]'', [[280/169]]
| ''104/63'', 108/65
| "
|-
|-
|76
| 76
|885.437
| 885.437
|
|
|5/3
|  
|
| 5/3
|
| "
|[[4096/2457]]
| "
| "
|-
|-
|77
| 77
|897.087
| 897.087
|
| M6
|''[[27/16]]''
| ''27/16''
|[[42/25]], [[576/343]]
| 42/25
|
| "
|[[429/256]], [[240/143]]
| "
| "
|-
|-
|78
| 78
|908.738
| 908.738
|M6
|  
|27/16
|  
|
|  
|[[3465/2048]]
|  
|[[22/13]], [[169/100]]
| 22/13
| "
|-
|-
|79
| 79
|920.388
| 920.388
|
|  
|[[128/75]]
|  
|[[245/144]]
|  
|[[56/33]], [[75/44]], [[1089/640]]
|  
|[[288/169]], [[1792/1053]]
|  
| 17/10
|-
|-
|80
| 80
|932.039
| 932.039
|
|  
|
|  
|[[12/7]]
| 12/7
|
| "
|[[1755/1024]]
| "
| "
|-
|-
|81
| 81
|943.689
| 943.689
|
|  
|
|  
|''12/7''
|  
|''[[55/32]]'', [[512/297]]
| 45/26
|[[169/98]]
| "
| "
|-
|-
|82
| 82
|955.340
| 955.340
|
|  
|[[125/72]]
|  
|[[256/147]]
|  
|
| 26/15
|[[26/15]]
| "
| "
|-
|-
|83
| 83
|966.990
| 966.990
|
|  
|[[16384/9375]]
|  
|'''[[7/4]]'''
| '''7/4'''
|
| "
|[[250/143]]
| "
| "
|-
|-
|84
| 84
|978.641
| 978.641
|
|  
|[[225/128]]
|  
|'''''7/4'''''
|  
|[[44/25]]
| 44/25
|
| "
| 30/17
|-
|-
|85
| 85
|990.291
| 990.291
|m7
|  
|[[16/9]]
|  
|[[567/320]]
|  
|[[1815/1024]]
|  
|[[39/22]]
| 39/22
| "
|-
|-
|86
| 86
|1001.942
| 1001.942
|
| m7
|''16/9''
| ''16/9''
|[[25/14]], [[32768/18375]]
| "
|[[216/121]]
| "
|[[312/175]]
| "
| "
|-
|-
|87
| 87
|1013.592
| 1013.592
|
|  
|[[9/5]]
| 9/5
|
| "
|[[88/49]]
| "
|
| "
| "
|-
|-
|88
| 88
|1025.243
| 1025.243
|
|  
|''9/5''
|  
|[[1024/567]], [[405/224]]
|  
|[[231/128]]
|  
|
| 65/36
| "
|-
|-
|89
| 89
|1036.893
| 1036.893
|
|  
|[[2048/1125]]
|  
|''[[64/35]]''
|  
|[[20/11]]
| 20/11
|[[91/50]]
| "
| "
|-
|-
|90
| 90
|1048.544
| 1048.544
|
|  
|
|  
|
|  
|[[11/6]], [[504/275]]
| 11/6
|[[15015/8192]]
| "
| "
|-
|-
|91
| 91
|1060.194
| 1060.194
|
|  
|
|  
|[[945/512]]
|  
|''11/6''
|  
|[[24/13]]
| 24/13
| "
|-
|-
|92
| 92
|1071.845
| 1071.845
|
|  
|
|  
|
|  
|
|  
|''24/13'', [[13/7]]
| 13/7
| "
|-
|-
|93
| 93
|1083.495
| 1083.495
|
|  
|[[15/8]]
| 15/8
|[[28/15]]
| 28/15
|[[144/77]]
| "
|
| "
| "
|-
|-
|94
| 94
|1095.146
| 1095.146
|
| M7
|''15/8''
| "
|[[2304/1225]], [[3375/1792]]
| "
|[[2048/1089]]
| "
|''[[512/273]]'', [[49/26]]
| "
| '''32/17'''
|-
|-
|95
| 95
|1106.796
| 1106.796
|M7
|  
|[[256/135]]
|  
|''[[40/21]]''
|  
|[[121/64]], [[4851/2560]]
|  
|[[91/48]], [[616/325]]
|  
| 17/9
|-
|-
|96
| 96
|1118.447
| 1118.447
|
|  
|''[[48/25]]'', [[15625/8192]]
|  
|[[40/21]]
| 40/21
|[[21/11]]
| 21/11
|
| "
| "
|-
|-
|97
| 97
|1130.097
| 1130.097
|
|  
|48/25
| 48/25
|
| ''27/14''
|[[121/63]]
| "
|[[169/88]]
| 25/13
| "
|-
|-
|98
| 98
|1141.748
| 1141.748
|
|  
|
|  
|[[27/14]]
|  
|[[64/33]], [[495/256]]
|  
|[[234/121]]
| ''52/27''
| ''33/17''
|-
|-
|99
| 99
|1153.398
| 1153.398
|
|  
|[[125/64]]
|  
|[[35/18]]
| 35/18
|''64/33''
| ''64/33''
|[[39/20]], [[2048/1053]], [[405/208]]
| "
| 68/35
|-
|-
|100
| 100
|1165.049
| 1165.049
|
|  
|''125/64''
|  
|''[[63/32]]'', [[96/49]], [[49/25]]
| 49/25, ''63/32'', 96/49
|
| "
|
| "
| "
|-
|-
|101
| 101
|1176.699
| 1176.699
|
|  
|[[160/81]]
|  
|63/32
|  
|[[8085/4096]]
|  
|[[128/65]], [[77/39]]
| 65/33, 77/39, 128/65
| "
|-
|-
|102
| 102
|1188.350
| 1188.350
|
|  
|''160/81''
| ''160/81''
|[[2048/1029]]
| 125/63
|[[5632/2835]]
| "
|[[507/256]], [[143/72]]
| "
| "
|-
|-
|103
| 103
|1200.000
| 1200.000
|P8
| P8
|colspan="4" | '''[[2/1]]'''
| colspan="5" | '''2/1'''
|}
|}


[[Category:103edo]]
[[Category:103edo]]
[[Category:Tables of edo intervals]]
[[Category:Tables of edo intervals]]
Retrieved from "https://en.xen.wiki/w/Table_of_103edo_intervals"