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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 [[13-limit]] [[patent val]] {{val| 103 163 239 289 356 381 }} 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.


{| class="wikitable center-1 right-2 center-3"
{| class="wikitable center-1 right-2"
|-
|-
! #
! Degree
! Cents
! Cents
! Marks
! Approximate Ratios
! 5-limit
! 7-limit
! 11-limit
! 13-limit
|-
|-
|0
| 1
|0.00
| 11.650
|P1
| 81/80, 126/125
|colspan="4" | '''[[1/1]]'''
|-
|-
|1
| 2
|11.650
| 23.301
|
| 65/64, 66/65, 78/77
|''[[81/80]]''
|[[1029/1024]]
|[[2835/2816]]
|[[512/507]], [[144/143]]
|-
|-
|2
| 3
|23.301
| 34.951
|
| 49/48, 50/49, 64/63
|81/80
|[[64/63]]
|[[8192/8085]]
|[[65/64]], [[78/77]]
|-
|-
|3
| 4
|34.951
| 46.602
|
| 33/32, 35/34, 36/35
|''[[128/125]]''
|''64/63'', [[49/48]], [[50/49]]
|
|
|-
|-
|4
| 5
|46.602
| 58.252
|
| 27/26, 34/33
|128/125
|[[36/35]]
|''[[33/32]]''
|[[40/39]], [[1053/1024]], [[416/405]]
|-
|-
|5
| 6
|58.252
| 69.903
|
| 25/24, 26/25, 28/27
|
|[[28/27]]
|33/32, [[512/495]]
|[[121/117]]
|-
|-
|6
| 7
|69.903
| 81.553
|
| 21/20, 22/21
|[[25/24]]
|
|[[126/121]]
|[[176/169]]
|-
|-
|7
| 8
|81.553
| 93.204
|
| 18/17
|''25/24'', [[16384/15625]]
|[[21/20]]
|[[22/21]]
|
|-
|-
|8
| 9
|93.204
| 104.854
|m2
| 17/16
|[[135/128]]
|''21/20''
|[[128/121]], [[5120/4851]]
|[[96/91]], [[325/308]]
|-
|-
|9
| 10
|104.854
| 116.505
|
| 15/14, 16/15
|''[[16/15]]''
|[[1225/1152]], [[3584/3375]]
|[[1089/1024]]
|''[[273/256]]'', [[52/49]]
|-
|-
|10
| 11
|116.505
| 128.155
|
| 14/13
|16/15
|[[15/14]]
|[[77/72]]
|
|-
|-
|11
| 12
|128.155
| 139.806
|
| 13/12
|
|
|
|''[[13/12]]'', [[14/13]]
|-
|-
|12
| 13
|139.806
| 151.456
|
| 12/11
|
|[[1024/945]]
|''[[12/11]]''
|[[13/12]]
|-
|-
|13
| 14
|151.456
| 163.107
|
| 11/10
|
|
|12/11, [[275/252]]
|[[16384/15015]]
|-
|-
|14
| 15
|163.107
| 174.757
|
| 72/65
|[[1125/1024]]
|''[[35/32]]''
|[[11/10]]
|[[100/91]]
|-
|-
|15
| 16
|174.757
| 186.408
|
| 10/9
|''[[10/9]]''
|[[567/512]], [[448/405]]
|[[256/231]]
|
|-
|-
|16
| 17
|186.408
| 198.058
|
| 9/8
|10/9
|
|[[49/44]]
|
|-
|-
|17
| 18
|198.058
| 209.708
|
|  
|''[[9/8]]''
|[[28/25]], [[18375/16384]]
|[[121/108]]
|[[175/156]]
|-
|-
|18
| 19
|209.709
| 221.359
|M2
| 17/15, 25/22
|9/8
|[[640/567]]
|[[2048/1815]]
|[[44/39]]
|-
|-
|19
| 20
|221.359
| 233.010
|
| 8/7
|[[256/225]]
|'''''[[8/7]]'''''
|[[25/22]]
|
|-
|-
|20
| 21
|233.010
| 244.660
|
| 15/13
|[[9375/8192]]
|'''8/7'''
|
|[[143/125]]
|-
|-
|21
| 22
|244.660
| 256.311
|
|  
|[[144/125]]
|[[147/128]]
|
|[[15/13]]
|-
|-
|22
| 23
|256.311
| 267.961
|
| 7/6
|
|''[[7/6]]''
|''[[64/55]]'', [[297/256]]
|[[196/169]]
|-
|-
|23
| 24
|267.961
| 279.712
|
| 20/17
|
|7/6
|
|[[2048/1755]]
|-
|-
|24
| 25
|279.612
| 291.262
|
| 13/11
|[[75/64]]
|[[288/245]]
|[[33/28]], [[88/75]], [[1280/1089]]
|[[169/144]], [[1053/896]]
|-
|-
|25
| 26
|291.262
| 303.013
|m3
| 25/21
|[[32/27]]
|
|[[4096/3465]]
|[[13/11]], [[200/169]]
|-
|-
|26
| 27
|302.913
| 314.563
|
| 6/5
|''32/27''
|[[25/21]], [[343/288]]
|
|[[512/429]], [[143/120]]
|-
|-
|27
| 28
|314.563
| 326.214
|
| 63/52, 65/54
|[[6/5]]
|
|
|[[2457/2048]]
|-
|-
|28
| 29
|326.214
| 337.864
|
| 17/14, 39/32
|''6/5''
|
|''[[77/64]]'', [[1024/847]], [[2475/2048]]
|''[[63/52]]'', [[169/140]]
|-
|-
|29
| 30
|337.864
| 349.615
|
| 11/9, 27/22
|
|[[175/144]]
|
|[[39/32]], [[1280/1053]]
|-
|-
|30
| 31
|349.515
| 361.165
|
| 16/13, 21/17
|
|[[49/40]], [[60/49]]
|[[11/9]]
|'''''[[16/13]]''''', ''39/32'', [[175/143]]
|-
|-
|31
| 32
|361.165
| 372.816
|
| 26/21, 81/65
|
|
|[[8192/6655]], [[154/125]]
|'''16/13''', [[832/675]]
|-
|-
|32
| 33
|372.816
| 384.466
|
| 5/4
|
|
|''[[96/77]]'', [[1024/825]], [[2541/2048]], [[32768/26411]]
|[[26/21]]
|-
|-
|33
| 34
|384.466
| 396.117
|
| 44/35
|'''[[5/4]]''', [[8192/6561]]
|
|
|[[156/125]]
|-
|-
|34
| 35
|396.117
| 407.767
|
| 33/26
|'''''5/4'''''
|
|[[121/96]], [[44/35]]
|
|-
|-
|35
| 36
|407.767
| 419.417
|M3
| 14/11
|[[81/64]]
|
|''[[14/11]]''
|
|-
|-
|36
| 37
|419.417
| 431.068
|
| 9/7
|''[[32/25]]''
|[[125/98]], [[32768/25725]]
|14/11, [[275/216]]
|[[8192/6435]], [[312/245]]
|-
|-
|37
| 38
|431.068
| 442.708
|
| 22/17
|32/25
|
|[[77/60]], [[440/343]]
|[[50/39]]
|-
|-
|38
| 39
|442.718
| 454.369
|
| 13/10
|
|''[[9/7]]'', [[1323/1024]]
|[[128/99]]
|
|-
|-
|39
| 40
|454.369
| 466.019
|
| 17/13, 21/16
|
|''[[64/49]]''
|
|[[13/10]]
|-
|-
|40
| 41
|466.019
| 477.670
|
|  
|
|[[21/16]], [[64/49]]
|[[72/55]]
|[[1089/832]]
|-
|-
|41
| 42
|477.670
| 489.320
|
| 65/49
|[[675/512]]
|''21/16''
|
|[[169/128]]
|-
|-
|42
| 43
|489.320
| 500.971
|
| 4/3
|'''''[[4/3]]'''''
|[[4096/3087]]
|[[512/385]], [[297/224]]
|''169/128'', [[224/169]], [[65/49]]
|-
|-
|43
| 44
|500.971
| 512.621
|P4
| 27/20
|'''4/3''', [[10935/8192]]
|[[21875/16384]]
|[[385/288]], [[147/110]], [[720/539]]
|[[243/182]]
|-
|-
|44
| 45
|512.621
| 524.272
|
| 65/48
|''[[27/20]]''
|''[[343/256]]'', [[168/125]]
|[[121/90]]
|[[192/143]], [[35/26]], [[3328/2475]]
|-
|-
|45
| 46
|524.272
| 535.922
|
| 15/11
|27/20
|[[256/189]]
|[[693/512]]
|[[65/48]], [[88/65]]
|-
|-
|46
| 47
|535.922
| 547.573
|
| 11/8
|
|''[[48/35]]''
|[[15/11]]
|[[567/416]]
|-
|-
|47
| 48
|547.573
| 559.223
|
| 18/13
|
|48/35
|'''[[11/8]]'''
|
|-
|-
|48
| 49
|559.223
| 570.874
|
| 25/18
|
|[[112/81]]
|'''''11/8''''', [[243/176]], [[8192/5929]], [[2475/1792]]
|[[18/13]]
|-
|-
|49
| 50
|570.874
| 582.524
|
| 7/5
|[[25/18]]
|''[[7/5]]''
|[[245/176]], [[2816/2025]]
|''18/13''
|-
|-
|50
| 51
|582.524
| 594.175
|d5
| 24/17
|
|[[7/5]]
|
|
|-
|-
|51
| …
|594.175
| …
|
| …
|[[45/32]]
|
|[[512/363]], [[5775/4096]]
|[[128/91]], [[55/39]]
|-
|52
|605.825
|A4
|[[64/45]]
|
|[[363/256]], [[78/55]], [[8192/5775]]
|[[91/64]]
|-
|53
|617.476
|
|
|[[10/7]]
|
|
|-
|54
|629.126
|
|[[36/25]]
|''10/7''
|[[352/245]], [[2025/1408]]
|''[[13/9]]''
|-
|55
|640.777
|
|
|[[81/56]]
|'''''[[16/11]]''''', [[352/243]], [[5929/4096]], [[3584/2475]]
|13/9
|-
|56
|652.427
|
|
|[[35/24]]
|'''16/11'''
|
|-
|57
|664.078
|
|
|''35/24''
|[[22/15]]
|[[832/567]]
|-
|58
|675.728
|
|[[40/27]]
|[[189/128]]
|[[1024/693]]
|[[96/65]], [[65/44]]
|-
|59
|687.379
|
|''40/27''
|''[[512/343]]'', [[125/84]]
|[[180/121]]
|[[143/96]], [[52/35]], [[2475/1664]]
|-
|60
|699.029
|P5
|'''[[3/2]]''', [[16384/10935]]
|[[32768/21875]]
|[[576/385]], [[220/147]], [[539/360]]
|[[364/243]]
|-
|61
|710.680
|
|'''''3/2'''''
|[[3087/2048]]
|[[385/256]], [[448/297]]
|''[[256/169]]'', [[169/112]], [[98/65]]
|-
|62
|722.330
|
|[[1024/675]]
|''[[32/21]]''
|
|256/169
|-
|63
|733.981
|
|
|32/21, [[49/32]]
|[[55/36]]
|[[1664/1089]]
|-
|64
|745.631
|
|
|''49/32''
|
|[[20/13]]
|-
|65
|757.282
|
|
|''[[14/9]]'', [[2048/1323]]
|[[99/64]]
|
|-
|66
|768.932
|
|[[25/16]]
|
|[[120/77]], [[343/220]]
|[[39/25]]
|-
|67
|780.583
|
|''25/16''
|[[196/125]], [[25725/16384]]
|[[11/7]], [[432/275]]
|[[6435/4096]], [[245/156]]
|-
|68
|792.233
|m6
|[[128/81]]
|
|''11/7''
|
|-
|69
|803.883
|
|'''''[[8/5]]'''''
|
|[[192/121]], [[35/22]]
|
|-
|70
|815.534
|
|'''8/5''', [[6561/4096]]
|
|
|[[125/78]]
|-
|71
|827.184
|
|
|
|''[[77/48]]'', [[825/512]], [[4096/2541]], [[26411/16384]]
|[[21/13]]
|-
|72
|838.835
|
|
|
|[[6655/4096]], [[125/77]]
|'''[[13/8]]''', [[675/416]]
|-
|73
|850.485
|
|
|[[80/49]], [[49/30]]
|[[18/11]]
|'''''13/8''''', ''[[64/39]]''
|-
|74
|862.136
|
|
|[[288/175]]
|
|64/39, [[1053/640]]
|-
|75
|873.786
|
|''[[5/3]]''
|
|''[[128/77]]'', [[847/512]], [[4096/2475]]
|''[[104/63]]'', [[280/169]]
|-
|76
|885.437
|
|5/3
|
|
|[[4096/2457]]
|-
|77
|897.087
|
|''[[27/16]]''
|[[42/25]], [[576/343]]
|
|[[429/256]], [[240/143]]
|-
|78
|908.738
|M6
|27/16
|
|[[3465/2048]]
|[[22/13]], [[169/100]]
|-
|79
|920.388
|
|[[128/75]]
|[[245/144]]
|[[56/33]], [[75/44]], [[1089/640]]
|[[288/169]], [[1792/1053]]
|-
|80
|932.039
|
|
|[[12/7]]
|
|[[1755/1024]]
|-
|81
|943.689
|
|
|''12/7''
|''[[55/32]]'', [[512/297]]
|[[169/98]]
|-
|82
|955.340
|
|[[125/72]]
|[[256/147]]
|
|[[26/15]]
|-
|83
|966.990
|
|[[16384/9375]]
|'''[[7/4]]'''
|
|[[250/143]]
|-
|84
|978.641
|
|[[225/128]]
|'''''7/4'''''
|[[44/25]]
|
|-
|85
|990.291
|m7
|[[16/9]]
|[[567/320]]
|[[1815/1024]]
|[[39/22]]
|-
|86
|1001.942
|
|''16/9''
|[[25/14]], [[32768/18375]]
|[[216/121]]
|[[312/175]]
|-
|87
|1013.592
|
|[[9/5]]
|
|[[88/49]]
|
|-
|88
|1025.243
|
|''9/5''
|[[1024/567]], [[405/224]]
|[[231/128]]
|
|-
|89
|1036.893
|
|[[2048/1125]]
|''[[64/35]]''
|[[20/11]]
|[[91/50]]
|-
|90
|1048.544
|
|
|
|[[11/6]], [[504/275]]
|[[15015/8192]]
|-
|91
|1060.194
|
|
|[[945/512]]
|''11/6''
|[[24/13]]
|-
|92
|1071.845
|
|
|
|
|''24/13'', [[13/7]]
|-
|93
|1083.495
|
|[[15/8]]
|[[28/15]]
|[[144/77]]
|
|-
|94
|1095.146
|
|''15/8''
|[[2304/1225]], [[3375/1792]]
|[[2048/1089]]
|''[[512/273]]'', [[49/26]]
|-
|95
|1106.796
|M7
|[[256/135]]
|''[[40/21]]''
|[[121/64]], [[4851/2560]]
|[[91/48]], [[616/325]]
|-
|96
|1118.447
|
|''[[48/25]]'', [[15625/8192]]
|[[40/21]]
|[[21/11]]
|
|-
|97
|1130.097
|
|48/25
|
|[[121/63]]
|[[169/88]]
|-
|98
|1141.748
|
|
|[[27/14]]
|[[64/33]], [[495/256]]
|[[234/121]]
|-
|99
|1153.398
|
|[[125/64]]
|[[35/18]]
|''64/33''
|[[39/20]], [[2048/1053]], [[405/208]]
|-
|100
|1165.049
|
|''125/64''
|''[[63/32]]'', [[96/49]], [[49/25]]
|
|
|-
|101
|1176.699
|
|[[160/81]]
|63/32
|[[8085/4096]]
|[[128/65]], [[77/39]]
|-
|102
|1188.350
|
|''160/81''
|[[2048/1029]]
|[[5632/2835]]
|[[507/256]], [[143/72]]
|-
|103
|1200.000
|P8
|colspan="4" | '''[[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"