Table of 167edo intervals: Difference between revisions

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Let's start with the basics -- get the diatonic marks and prime harmonics right
Line 1: Line 1:
This '''table of [[167edo]] intervals''' assumes [[13-limit]] [[patent val]] {{val|167 265 388 469 578 618}}.  
This '''table of 167edo intervals''' assumes [[13-limit]] [[patent val]] {{val|167 265 388 469 578 618}} of [[167edo]].  


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% or with odd limit over 800 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% or with odd limit over 800 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 center-3"
Line 13: Line 13:
! 13-limit
! 13-limit
|-
|-
|0
| 0
|0.00
| 0.00
|P1
| P1
|colspan="4" | '''[[1/1]]'''
| colspan="4" | '''[[1/1]]'''
|-
|-
|1
| 1
|7.186
| 7.186
|
|  
|
|  
|''[[126/125]]'', [[225/224]]
|  
|''[[121/120]]'', [[176/175]], [[243/242]]
|  
|''[[144/143]]'', [[169/168]], [[196/195]]
|  
|-
|-
|2
| 2
|14.371
| 14.371
|
|  
|''[[81/80]]''
|  
|
|  
|[[99/98]], [[100/99]], [[121/120]]
|  
|''[[91/90]]'', [[105/104]]
|  
|-
|-
|3
| 3
|21.557
| 21.557
|
|  
|81/80
|  
|''[[64/63]]''
|  
|
|  
|''[[65/64]]'', ''[[66/65]]'', [[78/77]]
|  
|-
|-
|4
| 4
|28.743
| 28.743
|
|  
|
|  
|''[[49/48]]'', ''[[50/49]]'', 64/63, [[686/675]]
|  
|[[55/54]], [[56/55]]
|  
|[[648/637]]
|  
|-
|-
|5
| 5
|35.928
| 35.928
|
|  
|
|  
|49/48
|  
|[[45/44]]
|  
|
|
|-
|-
|6
| 6
|43.114
| 43.114
|
|  
|
|  
|''[[36/35]]'', [[525/512]]
|  
|
|  
|[[40/39]], [[693/676]]
|  
|-
|-
|7
| 7
|50.299
| 50.299
|
|  
|[[250/243]]
|  
|36/35
|  
|[[33/32]], [[605/588]]
|  
|
|
|-
|-
|8
| 8
|57.485
| 57.485
|
|  
|
|  
|''[[28/27]]''
|  
|''33/32''
|  
|[[65/63]], [[91/88]], [[336/325]]
|  
|-
|-
|9
| 9
|64.671
| 64.671
|
|  
|''[[25/24]]''
|  
|
|  
|
|  
|[[26/25]], [[27/26]]
|  
|-
|-
|10
| 10
|71.856
| 71.856
|
|  
|25/24
|  
|
|  
|[[704/675]]
|  
|[[715/686]]
|  
|-
|-
|11
| 11
|79.042
| 79.042
|
| m2
|
|  
|''[[21/20]]''
|  
|[[22/21]]
|  
|[[245/234]]
|  
|-
|-
|12
| 12
|86.228
| 86.228
|
|  
|
|  
|21/20
|  
|[[81/77]]
|  
|[[104/99]]
|  
|-
|-
|13
| 13
|93.413
| 93.413
|m2
|  
|
|  
|
|  
|
|  
|''[[55/52]]'', [[96/91]], [[325/308]], [[343/325]]
|  
|-
|-
|14
| 14
|100.599
| 100.599
|
|  
|
|  
|
|  
|[[35/33]]
|  
|[[143/135]], [[441/416]], [[675/637]]
|  
|-
|-
|15
| 15
|107.784
| 107.784
|
|  
|''[[16/15]]''
|  
|
|  
|
|  
|[[117/110]], [[484/455]], [[715/672]]
|  
|-
|-
|16
| 16
|114.970
| 114.970
|
|  
|16/15
|  
|''[[15/14]]''
|  
|[[77/72]], [[576/539]]
|  
|[[125/117]]
|  
|-
|-
|17
| 17
|122.156
| 122.156
|
|  
|
|  
|15/14
|  
|[[189/176]]
|  
|''[[14/13]]'', [[130/121]], [[338/315]]
|  
|-
|-
|18
| 18
|129.341
| 129.341
|
|  
|
|  
|
|  
|[[264/245]]
|  
|14/13
|  
|-
|-
|19
| 19
|136.527
| 136.527
|
|  
|
|  
|
|  
|[[250/231]]
|  
|[[13/12]], [[225/208]]
|  
|-
|-
|20
| 20
|143.713
| 143.713
|
|  
|
|  
|''[[49/45]]''
|  
|''[[12/11]]'', [[88/81]]
|  
|''[[13/12]]''
|  
|-
|-
|21
| 21
|150.898
| 150.898
|
|  
|
|  
|
|  
|12/11
|  
|
|  
|-
|-
|22
| 22
|158.084
| 158.084
|
|  
|
|  
|[[35/32]], [[192/175]]
|  
|''[[11/10]]'', [[675/616]]
|  
|[[128/117]], [[325/297]], [[351/320]], [[385/351]], [[429/392]]
|  
|-
|-
|23
| 23
|165.269
| 165.269
|
|  
|
|  
|
|  
|11/10
|  
|[[845/768]]
|  
|-
|-
|24
| 24
|172.455
| 172.455
|
|  
|
|  
|''[[54/49]]''
|  
|[[243/220]], [[495/448]], [[875/792]]
|  
|[[182/165]]
|  
|-
|-
|25
| 25
|179.641
| 179.641
|
|  
|[[10/9]]
|  
|
|  
|[[256/231]]
|  
|[[72/65]], [[195/176]], [[231/208]], [[375/338]], [[416/375]]
|  
|-
|-
|26
| 26
|186.826
| 186.826
|
|  
|''10/9''
|  
|
|  
|[[49/44]], [[891/800]]
|  
|[[39/35]]
|  
|-
|-
|27
| 27
|194.012
| 194.012
|
|  
|
|  
|[[28/25]]
|  
|
|  
|[[143/128]], [[160/143]], [[189/169]]
|  
|-
|-
|28
| 28
|201.198
| 201.198
|M2
|[[9/8]]
|
|
|[[55/49]]
|  
|[[91/81]], [[702/625]]
|  
|
|
|-
|-
|29
| 29
|208.383
| 208.383
|
| M2
|''9/8''
|  
|
|  
|
|  
|[[44/39]], [[273/242]]
|  
|-
|-
|30
| 30
|215.569
| 215.569
|
|  
|
|  
|
|  
|''[[25/22]]'', [[112/99]]
|  
|[[162/143]]
|  
|-
|-
|31
| 31
|222.754
| 222.754
|
|  
|
|  
|
|  
|25/22
|  
|[[91/80]]
|  
|-
|-
|32
| 32
|229.940
| 229.940
|
|  
|
|  
|'''[[8/7]]'''
| '''[[8/7]]'''
|
|  
|[[297/260]], [[490/429]]
|  
|-
|-
|33
| 33
|237.126
| 237.126
|
|  
|
|  
|'''''8/7'''''
|  
|[[55/48]]
|  
|[[416/363]], [[650/567]]
|  
|-
|-
|34
| 34
|244.311
| 244.311
|
|  
|[[144/125]]
|  
|
|  
|[[121/105]]
|  
|[[15/13]], [[539/468]]
|  
|-
|-
|35
| 35
|251.497
| 251.497
|
|  
|
|  
|[[81/70]]
|  
|[[140/121]]
|  
|''15/13'', [[52/45]]
|  
|-
|-
|36
| 36
|258.683
| 258.683
|
|  
|
|  
|[[512/441]]
|  
|''[[64/55]]''
|  
|[[65/56]]
|  
|-
|-
|37
| 37
|265.868
| 265.868
|
|  
|
|  
|[[7/6]], [[400/343]]
|  
|
|  
|
|  
|-
|-
|38
| 38
|273.054
| 273.054
|
|  
|[[75/64]]
|  
|''7/6''
|  
|
|  
|[[117/100]]
|  
|-
|-
|39
| 39
|280.240
| 280.240
|
|  
|
|  
|[[147/125]], [[288/245]]
|  
|''[[33/28]]'', [[88/75]]
|  
|
|
|-
|-
|40
| 40
|287.425
| 287.425
|
| m3
|
|  
|[[189/160]], [[405/343]]
|  
|
|  
|[[13/11]]
|  
|-
|-
|41
| 41
|294.611
| 294.611
|m3
|[[32/27]]
|
|
|
|  
|''13/11''
|  
|
|
|-
|-
|42
| 42
|301.796
| 301.796
|
|  
|
|  
|[[25/21]]
|  
|
|  
|
|  
|-
|-
|43
| 43
|308.982
| 308.982
|
|  
|''[[6/5]]''
|  
|[[448/375]]
|  
|[[105/88]], [[484/405]]
|  
|[[117/98]], [[140/117]]
|  
|-
|-
|44
| 44
|316.168
| 316.168
|
|  
|6/5
|  
|
|  
|[[605/504]]
|  
|
|  
|-
|-
|45
| 45
|323.353
| 323.353
|
|  
|
|  
|[[135/112]]
|  
|
|  
|[[65/54]]
|  
|-
|-
|46
| 46
|330.539
| 330.539
|
|  
|
|  
|[[98/81]]
|  
|[[40/33]], [[121/100]]
|  
|[[63/52]]
|  
|-
|-
|47
| 47
|337.725
| 337.725
|
|  
|
|  
|[[175/144]]
|  
|''[[40/33]]'', [[147/121]]
|  
|''[[39/32]]'', [[91/75]]
|  
|-
|-
|48
| 48
|344.910
| 344.910
|
|  
|[[625/512]]
|  
|[[128/105]]
|  
|[[11/9]], [[336/275]]
|  
|39/32, [[825/676]]
|  
|-
|-
|49
| 49
|352.096
| 352.096
|
|  
|
|  
|[[49/40]]
|  
|''11/9'', [[27/22]]
|  
|[[364/297]]
|  
|-
|-
|50
| 50
|359.281
| 359.281
|
|  
|
|  
|
|  
|
|  
|'''[[16/13]]'''
| '''[[16/13]]'''
|-
|-
|51
| 51
|366.467
| 366.467
|
|  
|[[100/81]]
|  
|
|  
|[[99/80]], [[121/98]]
|  
|'''''16/13''''', [[26/21]], [[225/182]]
|  
|-
|-
|52
| 52
|373.653
| 373.653
|
|  
|
|  
|
|  
|[[150/121]]
|  
|''26/21'', [[242/195]], [[273/220]]
|  
|-
|-
|53
| 53
|380.838
| 380.838
|
|  
|'''''[[5/4]]'''''
|  
|[[56/45]]
|  
|
|  
|[[81/65]]
|  
|-
|-
|54
| 54
|388.024
| 388.024
|
|  
|'''5/4'''
| '''[[5/4]]'''
|
|  
|
|  
|[[169/135]], [[429/343]], [[1001/800]]
|  
|-
|-
|55
| 55
|395.210
| 395.210
|
|  
|
|  
|
|  
|[[44/35]]
|  
|[[49/39]]
|  
|-
|-
|56
| 56
|402.395
| 402.395
|
|  
|
|  
|[[63/50]]
|  
|[[44/35]], [[121/96]], [[125/99]], [[486/385]]
|  
|[[525/416]]
|  
|-
|-
|57
| 57
|409.581
| 409.581
|M3
|[[81/64]]
|
|
|[[308/243]], [[792/625]]
|  
|[[33/26]], [[195/154]]
|  
|
|
|-
|-
|58
| 58
|416.766
| 416.766
|
| M3
|
|  
|
|  
|[[14/11]]
|  
|
|
|-
|-
|59
| 59
|423.952
| 423.952
|
|  
|[[32/25]]
|  
|[[125/98]]
|  
|''14/11''
|  
|[[143/112]], [[216/169]]
|  
|-
|-
|60
| 60
|431.138
| 431.138
|
|  
|''32/25''
|  
|''[[9/7]]''
|  
|[[77/60]], [[440/343]]
|  
|[[50/39]]
|  
|-
|-
|61
| 61
|438.323
| 438.323
|
|  
|
|  
|9/7
|  
|[[165/128]], [[567/440]]
|  
|[[156/121]], [[676/525]]
|  
|-
|-
|62
| 62
|445.509
| 445.509
|
|  
|
|  
|''[[35/27]]''
|  
|[[128/99]]
|  
|[[84/65]], [[507/392]]
|  
|-
|-
|63
| 63
|452.695
| 452.695
|
|  
|
|  
|
|  
|[[100/77]], [[891/686]]
|  
|[[13/10]]
|  
|-
|-
|64
| 64
|459.880
| 459.880
|
|  
|
|  
|[[64/49]]
|  
|[[176/135]]
|  
|''13/10'', [[441/338]], [[845/648]]
|  
|-
|-
|65
| 65
|467.066
| 467.066
|
|  
|
|  
|[[21/16]]
|  
|[[55/42]]
|  
|
|  
|-
|-
|66
| 66
|474.251
| 474.251
|
|  
|
|  
|21/16
|  
|[[405/308]]
|  
|[[130/99]], [[154/117]]
|  
|-
|-
|67
| 67
|481.437
| 481.437
|
|  
|
|  
|
|  
|[[33/25]]
|  
|[[169/128]], [[416/315]]
|  
|-
|-
|68
| 68
|488.623
| 488.623
|
|  
|
|  
|
|  
|[[175/132]], [[297/224]]
|  
|[[65/49]]
|  
|-
|-
|69
| 69
|495.808
| 495.808
|P4
| P4
|'''[[4/3]]'''
| '''[[4/3]]'''
|
|  
|
|  
|[[225/169]]
|  
|-
|-
|70
| 70
|502.994
| 502.994
|
|  
|'''''4/3'''''
|  
|[[75/56]]
|  
|[[147/110]]
|  
|[[234/175]]
|  
|-
|-
|71
| 71
|510.180
| 510.180
|
|  
|
|  
|''75/56'', [[168/125]]
|  
|[[121/90]]
|  
|''[[35/26]]'', [[192/143]]
|  
|-
|-
|72
| 72
|517.365
| 517.365
|
|  
|[[27/20]]
|  
|
|  
|[[66/49]]
|  
|[[182/135]]
|  
|-
|-
|73
| 73
|524.551
| 524.551
|
|  
|''27/20''
|  
|
|  
|
|  
|[[65/48]], [[88/65]]
|  
|-
|-
|74
| 74
|531.737
| 531.737
|
|  
|
|  
|[[49/36]], [[200/147]]
|  
|''[[15/11]]'', [[110/81]]
|  
|[[495/364]], [[972/715]]
|  
|-
|-
|75
| 75
|538.922
| 538.922
|
|  
|[[512/375]]
|  
|
|  
|15/11
|  
|[[273/200]]
|  
|-
|-
|76
| 76
|546.108
| 546.108
|
|  
|
|  
|[[48/35]]
|  
|'''''[[11/8]]'''''
|  
|[[196/143]], [[351/256]], [[891/650]]
|  
|-
|-
|77
| 77
|553.293
| 553.293
|
|  
|
|  
|[[135/98]]
|  
|'''11/8''', [[500/363]]
| '''[[11/8]]'''
|[[260/189]]
|  
|-
|-
|78
| 78
|560.479
| 560.479
|
|  
|[[864/625]]
|  
|[[112/81]]
|  
|
|  
|[[18/13]], [[539/390]]
|  
|-
|-
|79
| 79
|567.665
| 567.665
|
|  
|[[25/18]]
|  
|
|  
|[[168/121]]
|  
|''18/13''
|  
|-
|-
|80
| 80
|574.850
| 574.850
|
| d5
|''25/18''
|  
|[[1024/735]]
|  
|[[675/484]]
|  
|[[39/28]]
|  
|-
|-
|81
| 81
|582.036
| 582.036
|
|  
|
|  
|[[7/5]], [[480/343]]
|  
|
|  
|
|  
|-
|-
|82
| 82
|589.222
| 589.222
|d5
|  
|[[45/32]], [[1024/729]]
|  
|''7/5''
|  
|
|  
|
|  
|-
|-
|83
| 83
|596.407
| 596.407
|
|  
|''45/32''
|  
|[[343/243]], [[882/625]]
|  
|[[484/343]]
|  
|[[55/39]]
|  
|-
|-
|84
| 84
|603.593
| 603.593
|
|  
|''[[64/45]]''
|  
|[[625/441]]
|  
|[[343/242]]
|  
|[[78/55]]
|  
|-
|-
|85
| 85
|610.778
| 610.778
|A4
|  
|64/45, [[729/512]]
|  
|''[[10/7]]''
|  
|
|  
|[[845/594]]
|  
|-
|-
|86
| 86
|617.964
| 617.964
|
|  
|
|  
|10/7, [[343/240]]
|  
|
|  
|
|  
|-
|-
|87
| 87
|625.150
| 625.150
|
| A4
|''[[36/25]]''
|  
|[[735/512]], [[1125/784]]
|  
|
|  
|[[56/39]]
|  
|-
|-
|88
| 88
|632.335
| 632.335
|
|  
|36/25
|  
|
|  
|[[121/84]]
|  
|''[[13/9]]''
|  
|-
|-
|89
| 89
|639.521
| 639.521
|
|  
|[[625/432]]
|  
|[[81/56]]
|  
|
|
|13/9
|  
|-
|-
|90
| 90
|646.707
| 646.707
|
|  
|
|  
|
|  
|'''[[16/11]]''', [[363/250]]
| '''[[16/11]]'''
|[[189/130]]
|  
|-
|-
|91
| 91
|653.892
| 653.892
|
|  
|
|  
|[[35/24]]
|  
|'''''16/11'''''
|  
|[[143/98]], [[512/351]]
|  
|-
|-
|92
| 92
|661.078
| 661.078
|
|  
|[[375/256]]
|  
|
|  
|[[22/15]]
|  
|[[343/234]]
|  
|-
|-
|93
| 93
|668.263
| 668.263
|
|  
|
|  
|[72/49]], [[147/100]]
|  
|''22/15'', [[81/55]]
|  
|[[715/486]]
|  
|-
|-
|94
| 94
|675.449
| 675.449
|
|  
|''[[40/27]]''
|  
|
|  
|
|  
|[[65/44]]
|  
|-
|-
|95
| 95
|682.635
| 682.635
|
|  
|40/27
|  
|
|  
|[[49/33]]
|  
|[[135/91]]
|  
|-
|-
|96
| 96
|689.820
| 689.820
|
|  
|
|  
|''[[112/75]]'', [[125/84]]
|  
|''49/33''
|  
|''[[52/35]]'', [[143/96]]
|  
|-
|-
|97
| 97
|697.006
| 697.006
|
|  
|'''''[[3/2]]'''''
|  
|112/75
|  
|[[121/81]]
|  
|[[175/117]]
|  
|-
|-
|98
| 98
|704.192
| 704.192
|P5
| P5
|'''3/2'''
| '''[[3/2]]'''
|
|  
|
|  
|[[338/225]]
|  
|-
|-
|99
| 99
|711.377
| 711.377
|
|  
|
|  
|
|  
|[[264/175]], [[448/297]]
|  
|[[98/65]]
|  
|-
|-
|100
| 100
|718.563
| 718.563
|
|  
|
|  
|[[50/33]]
|  
|[[256/169]], [[315/208]]
|  
|
|-
|-
|101
| 101
|725.749
| 725.749
|
|  
|
|  
|[[32/21]]
|  
|[[616/405]]
|  
|[[99/65]], [[117/77]]
|  
|-
|-
|102
| 102
|732.934
| 732.934
|
|  
|
|  
|''32/21''
|  
|[[55/36]], [[84/55]]
|  
|
|  
|-
|-
|103
| 103
|740.120
| 740.120
|
|  
|
|  
|[[49/32]]
|  
|[[135/88]]
|  
|''[[20/13]]'', [[676/441]]
|  
|-
|-
|104
| 104
|747.305
| 747.305
|
|  
|
|  
|
|  
|[[77/50]]
|  
|20/13
|  
|-
|-
|105
| 105
|754.491
| 754.491
|
|  
|
|  
|''[[54/35]]''
|  
|[[99/64]]
|  
|[[65/42]], [[784/507]]
|  
|-
|-
|106
| 106
|761.677
| 761.677
|
|  
|
|  
|[[14/9]]
|  
|[[256/165]]
|  
|[[121/78]], [[525/338]]
|  
|-
|-
|107
| 107
|768.862
| 768.862
|
|  
|''[[25/16]]''
|  
|''14/9''
|  
|[[120/77]], [[343/220]]
|  
|[[39/25]]
|  
|-
|-
|108
| 108
|776.048
| 776.048
|
|  
|25/16
|  
|
|  
|''[[11/7]]''
|  
|[[169/108]]
|  
|-
|-
|109
| 109
|783.234
| 783.234
|
| m6
|
|  
|
|  
|11/7
|  
|
|  
|-
|-
|110
| 110
|790.419
| 790.419
|m6
|  
|[[128/81]]
|  
|
|  
|[[243/154]], [[625/396]]
|  
|[[52/33]]
|  
|-
|-
|111
| 111
|797.605
| 797.605
|
|  
|
|  
|[[100/63]]
|  
|''[[35/22]]'', [[198/125]], [[385/243]]
|  
|[[165/104]], [[507/320]], [[832/525]]
|  
|-
|-
|112
| 112
|804.790
| 804.790
|
|  
|
|  
|
|  
|35/22
|  
|[[78/49]]
|  
|-
|-
|113
| 113
|811.976
| 811.976
|
|  
|'''[[8/5]]'''
| '''[[8/5]]'''
|
|  
|[[1125/704]]
|  
|[[270/169]], [[686/429]]
|  
|-
|-
|114
| 114
|819.162
| 819.162
|
|  
|'''''8/5'''''
|  
|[[45/28]]
|  
|[[77/48]]
|  
|[[130/81]]
|  
|-
|-
|115
| 115
|826.347
| 826.347
|
|  
|
|  
|
|  
|[[121/75]]
|  
|''[[21/13]]'', [[195/121]], [[440/273]]
|  
|-
|-
|116
| 116
|833.533
| 833.533
|
|  
|[[81/50]]
|  
|
|  
|[[196/121]]
|  
|'''''[[13/8]]''''', 21/13, [[364/225]]
|  
|-
|-
|117
| 117
|840.719
| 840.719
|
|  
|
|  
|
|  
|
|  
|'''13/8'''
| '''[[13/8]]'''
|-
|-
|118
| 118
|847.904
| 847.904
|
|  
|
|  
|[[49/30]], [[80/49]]
|  
|''[[18/11]]'', [[44/27]]
|  
|[[297/182]]
|  
|-
|-
|119
| 119
|855.090
| 855.090
|
|  
|[[1024/625]]
|  
|[[105/64]]
|  
|18/11, [[275/168]]
|  
|[[64/39]], [[819/500]]
|  
|-
|-
|120
| 120
|862.275
| 862.275
|
|  
|
|  
|[[288/175]]
|  
|''[[33/20]]'', [[242/147]]
|  
|[[150/91]]
|  
|-
|-
|121
| 121
|869.461
| 869.461
|
|  
|
|  
|[[81/49]]
|  
|33/20, [[200/121]]
|  
|[[945/572]]
|  
|-
|-
|122
| 122
|876.647
| 876.647
|
|  
|
|  
|''81/49'', [[224/135]]
|  
|
|  
|''[[91/55]]'', [[108/65]]
|  
|-
|-
|123
| 123
|883.832
| 883.832
|
|  
|[[5/3]]
|  
|
|  
|[[1008/605]]
|  
|[[693/416]]
|  
|-
|-
|124
| 124
|891.018
| 891.018
|
|  
|''5/3''
|  
|[[375/224]]
|  
|[[405/242]]
|  
|[[117/70]]
|  
|-
|-
|125
| 125
|898.204
| 898.204
|
|  
|
|  
|[[42/25]]
|  
|
|  
|
|  
|-
|-
|126
| 126
|905.389
| 905.389
|M6
|  
|[[27/16]]
|  
|
|  
|[[1225/726]]
|  
|''[[22/13]]''
|  
|-
|-
|127
| 127
|912.575
| 912.575
|
| M6
|
|  
|[[320/189]], [[686/405]]
|  
|[[847/500]]
|  
|22/13
|  
|-
|-
|128
| 128
|919.760
| 919.760
|
|  
|
|  
|[[245/144]]
|  
|''[[56/33]]'', [[75/44]], [[1029/605]]
|  
|[[143/84]]
|  
|-
|-
|129
| 129
|926.946
| 926.946
|
|  
|[[128/75]]
|  
|''[[12/7]]'', [[875/512]]
|  
|''75/44'', [[77/45]]
|  
|[[169/99]], [[1155/676]]
|  
|-
|-
|130
| 130
|934.132
| 934.132
|
|  
|
|  
|12/7, [[343/200]]
|  
|
|  
|
|  
|-
|-
|131
| 131
|941.317
| 941.317
|
|  
|
|  
|[[441/256]]
|  
|''[[55/32]]''
|  
|[[112/65]]
|  
|-
|-
|132
| 132
|948.503
| 948.503
|
|  
|
|  
|
|  
|[[121/70]]
|  
|[[26/15]], [[45/26]]
|  
|-
|-
|133
| 133
|955.689
| 955.689
|
|  
|[[125/72]]
|  
|
|  
|
|  
|26/15, [[936/539]]
|  
|-
|-
|134
| 134
|962.874
| 962.874
|
|  
|
|  
|'''''[[7/4]]'''''
|  
|[[96/55]]
|  
|[[363/208]], [[567/325]]
|  
|-
|-
|135
| 135
|970.060
| 970.060
|
|  
|
|  
|'''7/4'''
| '''[[7/4]]'''
|
|  
|[[429/245]]
|  
|-
|-
|136
| 136
|977.246
| 977.246
|
|  
|
|  
|
|  
|[[44/25]]
|  
|[[160/91]]
|  
|-
|-
|137
| 137
|984.431
| 984.431
|
|  
|
|  
|
|  
|''44/25'', [[99/56]]
|  
|''[[39/22]]'', [[143/81]], [[1125/637]]
|  
|-
|-
|138
| 138
|991.617
| 991.617
|
| m7
|''[[16/9]]''
|  
|
|  
|
|  
|39/22, [[484/273]]
|  
|-
|-
|139
| 139
|998.802
| 998.802
|m7
|  
|16/9
|  
|
|  
|[[98/55]]
|  
|[[162/91]], [[625/351]]
|  
|-
|-
|140
| 140
|1005.988
| 1005.988
|
|  
|
|  
|[[25/14]]
|  
|
|  
|[[143/80]], [[338/189]]
|  
|-
|-
|141
| 141
|1013.174
| 1013.174
|
|  
|''[[9/5]]''
|  
|
|  
|[[88/49]]
|  
|[[70/39]]
|  
|-
|-
|142
| 142
|1020.359
| 1020.359
|
|  
|9/5
|  
|
|  
|[[231/128]]
|  
|[[65/36]], [[375/208]]
|  
|-
|-
|143
| 143
|1027.545
| 1027.545
|
|  
|
|  
|''[[49/27]]'', [[405/224]]
|  
|[[440/243]], [[896/495]]
|  
|[[165/91]]
|  
|-
|-
|144
| 144
|1034.731
| 1034.731
|
|  
|
|  
|
|  
|[[20/11]]
|  
|
|  
|-
|-
|145
| 145
|1041.916
| 1041.916
|
|  
|
|  
|[[64/35]], [[175/96]]
|  
|''20/11'', [[1125/616]]
|  
|[[117/64]], [[594/325]], [[640/351]], [[702/385]], [[715/392]], [[1183/648]]
|  
|-
|-
|146
| 146
|1049.102
| 1049.102
|
|  
|
|  
|
|  
|[[11/6]]
|  
|
|  
|-
|-
|147
| 147
|1056.287
| 1056.287
|
|  
|
|  
|
|  
|''11/6'', [[81/44]]
|  
|''[[24/13]]''
|  
|-
|-
|148
| 148
|1063.473
| 1063.473
|
|  
|
|  
|
|  
|[[231/125]]
|  
|24/13, [[1183/640]]
|  
|-
|-
|149
| 149
|1070.659
| 1070.659
|
|  
|
|  
|
|  
|[[245/132]]
|  
|[[13/7]]
|  
|-
|-
|150
| 150
|1077.844
| 1077.844
|
|  
|
|  
|[[28/15]]
|  
|
|  
|''13/7'', [[121/65]], [[315/169]]
|  
|-
|-
|151
| 151
|1085.030
| 1085.030
|
|  
|[[15/8]]
|  
|
|  
|[[144/77]], [[539/288]]
|  
|[[234/125]]
|  
|-
|-
|152
| 152
|1092.216
| 1092.216
|
|  
|''15/8''
|  
|
|  
|[[1323/704]]
|  
|[[169/90]], [[220/117]], [[455/242]]
|  
|-
|-
|153
| 153
|1099.401
| 1099.401
|
|  
|
|  
|
|  
|[[66/35]]
|  
|[[49/26]], [[270/143]], [[832/441]], [[1274/675]]
|  
|-
|-
|154
| 154
|1106.587
| 1106.587
|M7
|  
|
|  
|
|  
|
|  
|[[91/48]], [[616/325]], [[650/343]]
|  
|-
|-
|155
| 155
|1113.772
| 1113.772
|
|  
|
|  
|[[40/21]]
|  
|''[[21/11]]''
|  
|[[99/52]]
|  
|-
|-
|156
| 156
|1120.958
| 1120.958
|
| M7
|
|  
|
|  
|21/11, [[275/144]]
|  
|[[468/245]]
|  
|-
|-
|157
| 157
|1128.144
| 1128.144
|
|  
|[[48/25]]
|  
|
|  
|[[675/352]]
|  
|''[[25/13]]'', [[1372/715]]
|  
|-
|-
|158
| 158
|1135.329
| 1135.329
|
|  
|
|  
|[[27/14]]
|  
|
|  
|25/13, [[52/27]]
|  
|-
|-
|159
| 159
|1142.515
| 1142.515
|
|  
|
|  
|''27/14''
|  
|''[[64/33]]''
|  
|[[126/65]], [[176/91]], [[325/168]]
|  
|-
|-
|160
| 160
|1149.701
| 1149.701
|
|  
|[[243/125]]
|  
|[[35/18]]
|  
|[[1176/605]]
|  
|
|  
|-
|-
|161
| 161
|1156.886
| 1156.886
|
|  
|
|  
|''35/18'', [[1024/525]]
|  
|
|  
|[[39/20]], [[1352/693]]
|  
|-
|-
|162
| 162
|1164.072
| 1164.072
|
|  
|
|  
|[[49/25]], [[96/49]]
|  
|
|  
|[[1375/702]]
|  
|-
|-
|163
| 163
|1171.257
| 1171.257
|
|  
|
|  
|''49/25'', [[63/32]], [[675/343]]
|  
|[[55/28]]
|  
|[[637/324]], [[1125/572]]
|  
|-
|-
|164
| 164
|1178.443
| 1178.443
|
|  
|[[160/81]]
|  
|''63/32''
|  
|
|  
|''[[65/33]]'', [[77/39]]
|  
|-
|-
|165
| 165
|1185.629
| 1185.629
|
|  
|
|  
|[[125/63]]
|  
|[[99/50]], [[240/121]]
|  
|
|  
|-
|-
|166
| 166
|1192.814
| 1192.814
|
|  
|
|  
|''125/63'', [[448/225]]
|  
|[[175/88]], [[484/243]]
|  
|''[[143/72]]'', [[195/98]]
|  
|-
|-
|167
| 167
|1200.000
| 1200.000
|P8
| P8
|colspan="4" | '''[[2/1]]'''
| colspan="4" | '''[[2/1]]'''
|}
|}


[[Category:167edo]]
[[Category:167edo]]
[[Category:Tables of edo intervals]]
[[Category:Tables of edo intervals]]

Revision as of 05:10, 29 January 2024

This table of 167edo intervals assumes 13-limit patent val ⟨167 265 388 469 578 618] of 167edo.

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% or with odd limit over 800 are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.

# Cents Marks 5-limit 7-limit 11-limit 13-limit
0 0.00 P1 1/1
1 7.186
2 14.371
3 21.557
4 28.743
5 35.928
6 43.114
7 50.299
8 57.485
9 64.671
10 71.856
11 79.042 m2
12 86.228
13 93.413
14 100.599
15 107.784
16 114.970
17 122.156
18 129.341
19 136.527
20 143.713
21 150.898
22 158.084
23 165.269
24 172.455
25 179.641
26 186.826
27 194.012
28 201.198
29 208.383 M2
30 215.569
31 222.754
32 229.940 8/7
33 237.126
34 244.311
35 251.497
36 258.683
37 265.868
38 273.054
39 280.240
40 287.425 m3
41 294.611
42 301.796
43 308.982
44 316.168
45 323.353
46 330.539
47 337.725
48 344.910
49 352.096
50 359.281 16/13
51 366.467
52 373.653
53 380.838
54 388.024 5/4
55 395.210
56 402.395
57 409.581
58 416.766 M3
59 423.952
60 431.138
61 438.323
62 445.509
63 452.695
64 459.880
65 467.066
66 474.251
67 481.437
68 488.623
69 495.808 P4 4/3
70 502.994
71 510.180
72 517.365
73 524.551
74 531.737
75 538.922
76 546.108
77 553.293 11/8
78 560.479
79 567.665
80 574.850 d5
81 582.036
82 589.222
83 596.407
84 603.593
85 610.778
86 617.964
87 625.150 A4
88 632.335
89 639.521
90 646.707 16/11
91 653.892
92 661.078
93 668.263
94 675.449
95 682.635
96 689.820
97 697.006
98 704.192 P5 3/2
99 711.377
100 718.563
101 725.749
102 732.934
103 740.120
104 747.305
105 754.491
106 761.677
107 768.862
108 776.048
109 783.234 m6
110 790.419
111 797.605
112 804.790
113 811.976 8/5
114 819.162
115 826.347
116 833.533
117 840.719 13/8
118 847.904
119 855.090
120 862.275
121 869.461
122 876.647
123 883.832
124 891.018
125 898.204
126 905.389
127 912.575 M6
128 919.760
129 926.946
130 934.132
131 941.317
132 948.503
133 955.689
134 962.874
135 970.060 7/4
136 977.246
137 984.431
138 991.617 m7
139 998.802
140 1005.988
141 1013.174
142 1020.359
143 1027.545
144 1034.731
145 1041.916
146 1049.102
147 1056.287
148 1063.473
149 1070.659
150 1077.844
151 1085.030
152 1092.216
153 1099.401
154 1106.587
155 1113.772
156 1120.958 M7
157 1128.144
158 1135.329
159 1142.515
160 1149.701
161 1156.886
162 1164.072
163 1171.257
164 1178.443
165 1185.629
166 1192.814
167 1200.000 P8 2/1
Retrieved from "https://en.xen.wiki/index.php?title=Table_of_167edo_intervals&oldid=133441"