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]]

Revision as of 04:22, 29 January 2024

This table of 103edo intervals assumes 13-limit patent 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.

Degree Cents Approximate Ratios
1 11.650 81/80, 126/125
2 23.301 65/64, 66/65, 78/77
3 34.951 49/48, 50/49, 64/63
4 46.602 33/32, 35/34, 36/35
5 58.252 27/26, 34/33
6 69.903 25/24, 26/25, 28/27
7 81.553 21/20, 22/21
8 93.204 18/17
9 104.854 17/16
10 116.505 15/14, 16/15
11 128.155 14/13
12 139.806 13/12
13 151.456 12/11
14 163.107 11/10
15 174.757 72/65
16 186.408 10/9
17 198.058 9/8
18 209.708
19 221.359 17/15, 25/22
20 233.010 8/7
21 244.660 15/13
22 256.311
23 267.961 7/6
24 279.712 20/17
25 291.262 13/11
26 303.013 25/21
27 314.563 6/5
28 326.214 63/52, 65/54
29 337.864 17/14, 39/32
30 349.615 11/9, 27/22
31 361.165 16/13, 21/17
32 372.816 26/21, 81/65
33 384.466 5/4
34 396.117 44/35
35 407.767 33/26
36 419.417 14/11
37 431.068 9/7
38 442.708 22/17
39 454.369 13/10
40 466.019 17/13, 21/16
41 477.670
42 489.320 65/49
43 500.971 4/3
44 512.621 27/20
45 524.272 65/48
46 535.922 15/11
47 547.573 11/8
48 559.223 18/13
49 570.874 25/18
50 582.524 7/5
51 594.175 24/17
… … …
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