Table of 198edo intervals: Difference between revisions

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Remove most unuseful ratios
+marks on diatonic intervals to improve readability
Line 3: Line 3:
Intervals highlighted in '''bold''' are prime harmonics or subharmonics. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank. 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 729 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. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank. 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 729 are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.  


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2 center-3"
|-
|-
! #
! #
! Cents
! Cents
! Marks
! 5 limit
! 5 limit
! 7 limit
! 7 limit
Line 14: Line 15:
| 0
| 0
| 0.00
| 0.00
| P1
| colspan="4" | '''[[1/1]]'''
| colspan="4" | '''[[1/1]]'''
|-
|-
| 1
| 1
| 6.{{overline|06}}
| 6.{{overline|06}}
|
|  
|  
|  
|  
Line 25: Line 28:
| 2
| 2
| 12.{{overline|12}}
| 12.{{overline|12}}
|
| ?
| ?
| [[126/125]]
| [[126/125]]
Line 32: Line 36:
| 3
| 3
| 18.{{overline|18}}
| 18.{{overline|18}}
|
|  
|  
|  
|  
Line 39: Line 44:
| 4
| 4
| 24.{{overline|24}}
| 24.{{overline|24}}
|
| [[81/80]]
| [[81/80]]
| [[64/63]]
| [[64/63]]
Line 46: Line 52:
| 5
| 5
| 30.{{overline|30}}
| 30.{{overline|30}}
|
|  
|  
|  
|  
Line 53: Line 60:
| 6
| 6
| 36.{{overline|36}}
| 36.{{overline|36}}
|
| ''[[128/125]]''
| ''[[128/125]]''
| [[49/48]], [[50/49]]
| [[49/48]], [[50/49]]
Line 60: Line 68:
| 7
| 7
| 42.{{overline|42}}
| 42.{{overline|42}}
|
|  
|  
|  
|  
Line 67: Line 76:
| 8
| 8
| 48.{{overline|48}}
| 48.{{overline|48}}
|
| [[250/243]]
| [[250/243]]
| [[36/35]]
| [[36/35]]
Line 74: Line 84:
| 9
| 9
| 54.{{overline|54}}
| 54.{{overline|54}}
|
|  
|  
|  
|  
Line 81: Line 92:
| 10
| 10
| 60.{{overline|60}}
| 60.{{overline|60}}
|
| [[648/625]]
| [[648/625]]
| [[28/27]]
| [[28/27]]
Line 88: Line 100:
| 11
| 11
| 66.{{overline|66}}
| 66.{{overline|66}}
|
|  
|  
|  
|  
Line 95: Line 108:
| 12
| 12
| 72.{{overline|72}}
| 72.{{overline|72}}
|
| [[25/24]]
| [[25/24]]
| "
| "
Line 102: Line 116:
| 13
| 13
| 78.{{overline|78}}
| 78.{{overline|78}}
|
|  
|  
|  
|  
Line 109: Line 124:
| 14
| 14
| 84.{{overline|84}}
| 84.{{overline|84}}
| m2
| ''[[256/243]]''
| ''[[256/243]]''
| [[21/20]]
| [[21/20]]
Line 116: Line 132:
| 15
| 15
| 90.{{overline|90}}
| 90.{{overline|90}}
|
|  
|  
|  
|  
Line 123: Line 140:
| 16
| 16
| 96.{{overline|96}}
| 96.{{overline|96}}
|
| ''[[135/128]]''
| ''[[135/128]]''
| 200/189
| 200/189
Line 130: Line 148:
| 17
| 17
| 103.{{overline|03}}
| 103.{{overline|03}}
|
|  
|  
|  
|  
Line 137: Line 156:
| 18
| 18
| 109.{{overline|09}}
| 109.{{overline|09}}
|
| [[16/15]]
| [[16/15]]
| "
| "
Line 144: Line 164:
| 19
| 19
| 115.{{overline|15}}
| 115.{{overline|15}}
|
|  
|  
|  
|  
Line 151: Line 172:
| 20
| 20
| 121.{{overline|21}}
| 121.{{overline|21}}
|
| ?
| ?
| [[15/14]]
| [[15/14]]
Line 158: Line 180:
| 21
| 21
| 127.{{overline|27}}
| 127.{{overline|27}}
|
|  
|  
|  
|  
Line 165: Line 188:
| 22
| 22
| 133.{{overline|33}}
| 133.{{overline|33}}
|
| [[27/25]]
| [[27/25]]
| "
| "
Line 172: Line 196:
| 23
| 23
| 139.{{overline|39}}
| 139.{{overline|39}}
|
|  
|  
|  
|  
Line 179: Line 204:
| 24
| 24
| 145.{{overline|45}}
| 145.{{overline|45}}
|
| ''625/576''
| ''625/576''
| [[49/45]]
| [[49/45]]
Line 186: Line 212:
| 25
| 25
| 151.{{overline|51}}
| 151.{{overline|51}}
|
|  
|  
|  
|  
Line 193: Line 220:
| 26
| 26
| 157.{{overline|57}}
| 157.{{overline|57}}
|
| ''800/729''
| ''800/729''
| [[35/32]]
| [[35/32]]
Line 200: Line 228:
| 27
| 27
| 163.{{overline|63}}
| 163.{{overline|63}}
|
|  
|  
|  
|  
Line 207: Line 236:
| 28
| 28
| 169.{{overline|69}}
| 169.{{overline|69}}
|
| ?
| ?
| [[54/49]]
| [[54/49]]
Line 214: Line 244:
| 29
| 29
| 175.{{overline|75}}
| 175.{{overline|75}}
|
|  
|  
|  
|  
Line 221: Line 252:
| 30
| 30
| 181.{{overline|81}}
| 181.{{overline|81}}
|
| [[10/9]]
| [[10/9]]
| "
| "
Line 228: Line 260:
| 31
| 31
| 187.{{overline|87}}
| 187.{{overline|87}}
|
|  
|  
|  
|  
Line 235: Line 268:
| 32
| 32
| 193.{{overline|93}}
| 193.{{overline|93}}
|
| ?
| ?
| [[28/25]]
| [[28/25]]
Line 242: Line 276:
| 33
| 33
| 200.00
| 200.00
|
|  
|  
|  
|  
Line 249: Line 284:
| 34
| 34
| 206.{{overline|06}}
| 206.{{overline|06}}
| M2
| [[9/8]]
| [[9/8]]
| "
| "
Line 256: Line 292:
| 35
| 35
| 212.{{overline|12}}
| 212.{{overline|12}}
|
|  
|  
|  
|  
Line 263: Line 300:
| 36
| 36
| 218.{{overline|18}}
| 218.{{overline|18}}
|
| ''[[256/225]]''
| ''[[256/225]]''
| 245/216
| 245/216
Line 270: Line 308:
| 37
| 37
| 224.{{overline|24}}
| 224.{{overline|24}}
|
|  
|  
|  
|  
Line 277: Line 316:
| 38
| 38
| 230.{{overline|30}}
| 230.{{overline|30}}
|
| ''729/640''
| ''729/640''
| '''[[8/7]]'''
| '''[[8/7]]'''
Line 284: Line 324:
| 39
| 39
| 236.{{overline|36}}
| 236.{{overline|36}}
|
|  
|  
|  
|  
Line 291: Line 332:
| 40
| 40
| 242.{{overline|42}}
| 242.{{overline|42}}
|
| [[144/125]]
| [[144/125]]
| "
| "
Line 298: Line 340:
| 41
| 41
| 248.{{overline|48}}
| 248.{{overline|48}}
|
|  
|  
|  
|  
Line 305: Line 348:
| 42
| 42
| 254.{{overline|54}}
| 254.{{overline|54}}
|
| 125/108
| 125/108
| [[81/70]]
| [[81/70]]
Line 312: Line 356:
| 43
| 43
| 260.{{overline|60}}
| 260.{{overline|60}}
|
|  
|  
|  
|  
Line 319: Line 364:
| 44
| 44
| 266.{{overline|66}}
| 266.{{overline|66}}
|
| ?
| ?
| [[7/6]]
| [[7/6]]
Line 326: Line 372:
| 45
| 45
| 272.{{overline|72}}
| 272.{{overline|72}}
|
|  
|  
|  
|  
Line 333: Line 380:
| 46
| 46
| 278.{{overline|78}}
| 278.{{overline|78}}
|
| ''[[75/64]]''
| ''[[75/64]]''
| 147/125, 288/245
| 147/125, 288/245
Line 340: Line 388:
| 47
| 47
| 284.{{overline|84}}
| 284.{{overline|84}}
|
|  
|  
|  
|  
Line 347: Line 396:
| 48
| 48
| 290.{{overline|90}}
| 290.{{overline|90}}
| m3
| ''[[32/27]]''
| ''[[32/27]]''
| [[189/160]]
| [[189/160]]
Line 354: Line 404:
| 49
| 49
| 296.{{overline|96}}
| 296.{{overline|96}}
|
|  
|  
|  
|  
Line 361: Line 412:
| 50
| 50
| 303.{{overline|03}}
| 303.{{overline|03}}
|
| ?
| ?
| [[25/21]]
| [[25/21]]
Line 368: Line 420:
| 51
| 51
| 309.{{overline|09}}
| 309.{{overline|09}}
|
|  
|  
|  
|  
Line 375: Line 428:
| 52
| 52
| 315.{{overline|15}}
| 315.{{overline|15}}
|
| [[6/5]]
| [[6/5]]
| "
| "
Line 382: Line 436:
| 53
| 53
| 321.{{overline|21}}
| 321.{{overline|21}}
|
|  
|  
|  
|  
Line 389: Line 444:
| 54
| 54
| 327.{{overline|27}}
| 327.{{overline|27}}
|
| ?
| ?
| 98/81
| 98/81
Line 396: Line 452:
| 55
| 55
| 333.{{overline|33}}
| 333.{{overline|33}}
|
|  
|  
|  
|  
Line 403: Line 460:
| 56
| 56
| 339.{{overline|39}}
| 339.{{overline|39}}
|
| 243/200
| 243/200
| 175/144
| 175/144
Line 410: Line 468:
| 57
| 57
| 345.{{overline|45}}
| 345.{{overline|45}}
|
|  
|  
|  
|  
Line 417: Line 476:
| 58
| 58
| 351.{{overline|51}}
| 351.{{overline|51}}
|
| ''768/625''
| ''768/625''
| [[49/40]], [[60/49]]
| [[49/40]], [[60/49]]
Line 424: Line 484:
| 59
| 59
| 357.{{overline|57}}
| 357.{{overline|57}}
|
|  
|  
|  
|  
Line 431: Line 492:
| 60
| 60
| 363.{{overline|63}}
| 363.{{overline|63}}
|
| 100/81
| 100/81
| 216/175
| 216/175
Line 438: Line 500:
| 61
| 61
| 369.{{overline|69}}
| 369.{{overline|69}}
|
|  
|  
|  
|  
Line 445: Line 508:
| 62
| 62
| 375.{{overline|75}}
| 375.{{overline|75}}
|
| ?
| ?
| [[56/45]]
| [[56/45]]
Line 452: Line 516:
| 63
| 63
| 381.{{overline|81}}
| 381.{{overline|81}}
|
|  
|  
|  
|  
Line 459: Line 524:
| 64
| 64
| 387.{{overline|87}}
| 387.{{overline|87}}
|
| '''[[5/4]]'''
| '''[[5/4]]'''
| "
| "
Line 466: Line 532:
| 65
| 65
| 393.{{overline|93}}
| 393.{{overline|93}}
|
|  
|  
|  
|  
Line 473: Line 540:
| 66
| 66
| 400.00
| 400.00
|
| ''512/405''
| ''512/405''
| [[63/50]]
| [[63/50]]
Line 480: Line 548:
| 67
| 67
| 406.{{overline|06}}
| 406.{{overline|06}}
|
|  
|  
|  
|  
Line 487: Line 556:
| 68
| 68
| 412.{{overline|12}}
| 412.{{overline|12}}
| M3
| ''[[81/64]]''
| ''[[81/64]]''
| [[80/63]]
| [[80/63]]
Line 494: Line 564:
| 69
| 69
| 418.{{overline|18}}
| 418.{{overline|18}}
|
|  
|  
|  
|  
Line 501: Line 572:
| 70
| 70
| 424.{{overline|24}}
| 424.{{overline|24}}
|
| ''[[32/25]]''
| ''[[32/25]]''
| 125/98
| 125/98
Line 508: Line 580:
| 71
| 71
| 430.{{overline|30}}
| 430.{{overline|30}}
|
|  
|  
|  
|  
Line 515: Line 588:
| 72
| 72
| 436.{{overline|36}}
| 436.{{overline|36}}
|
| 625/486
| 625/486
| [[9/7]]
| [[9/7]]
Line 522: Line 596:
| 73
| 73
| 442.{{overline|42}}
| 442.{{overline|42}}
|
|  
|  
|  
|  
Line 529: Line 604:
| 74
| 74
| 448.{{overline|48}}
| 448.{{overline|48}}
|
| 162/125
| 162/125
| [[35/27]]
| [[35/27]]
Line 536: Line 612:
| 75
| 75
| 454.{{overline|54}}
| 454.{{overline|54}}
|
|  
|  
|  
|  
Line 543: Line 620:
| 76
| 76
| 460.{{overline|60}}
| 460.{{overline|60}}
|
| ''125/96''
| ''125/96''
| [[64/49]]
| [[64/49]]
Line 550: Line 628:
| 77
| 77
| 466.{{overline|66}}
| 466.{{overline|66}}
|
|  
|  
|  
|  
Line 557: Line 636:
| 78
| 78
| 472.{{overline|72}}
| 472.{{overline|72}}
|
| ''320/243''
| ''320/243''
| [[21/16]]
| [[21/16]]
Line 564: Line 644:
| 79
| 79
| 478.{{overline|78}}
| 478.{{overline|78}}
|
|  
|  
|  
|  
Line 571: Line 652:
| 80
| 80
| 484.{{overline|84}}
| 484.{{overline|84}}
|
| ?
| ?
| 250/189
| 250/189
Line 578: Line 660:
| 81
| 81
| 490.{{overline|90}}
| 490.{{overline|90}}
|
|  
|  
|  
|  
Line 585: Line 668:
| 82
| 82
| 496.{{overline|96}}
| 496.{{overline|96}}
| P4
| '''[[4/3]]'''
| '''[[4/3]]'''
| "
| "
Line 592: Line 676:
| 83
| 83
| 503.{{overline|03}}
| 503.{{overline|03}}
|
|  
|  
|  
|  
Line 599: Line 684:
| 84
| 84
| 509.{{overline|09}}
| 509.{{overline|09}}
|
| ?
| ?
| ''[[75/56]]'', 168/125
| ''[[75/56]]'', 168/125
Line 606: Line 692:
| 85
| 85
| 515.{{overline|15}}
| 515.{{overline|15}}
|
|  
|  
|  
|  
Line 613: Line 700:
| 86
| 86
| 521.{{overline|21}}
| 521.{{overline|21}}
|
| [[27/20]]
| [[27/20]]
| "
| "
Line 620: Line 708:
| 87
| 87
| 527.{{overline|27}}
| 527.{{overline|27}}
|
|  
|  
|  
|  
Line 627: Line 716:
| 88
| 88
| 533.{{overline|33}}
| 533.{{overline|33}}
|
| ''512/375''
| ''512/375''
| [[49/36]]
| [[49/36]]
Line 634: Line 724:
| 89
| 89
| 539.{{overline|39}}
| 539.{{overline|39}}
|
|  
|  
|  
|  
Line 641: Line 732:
| 90
| 90
| 545.{{overline|45}}
| 545.{{overline|45}}
|
| 1000/729
| 1000/729
| [[48/35]]
| [[48/35]]
Line 648: Line 740:
| 91
| 91
| 551.{{overline|51}}
| 551.{{overline|51}}
|
|  
|  
|  
|  
Line 655: Line 748:
| 92
| 92
| 557.{{overline|57}}
| 557.{{overline|57}}
|
| ''864/625''
| ''864/625''
| ''[[112/81]]''
| ''[[112/81]]''
Line 662: Line 756:
| 93
| 93
| 563.{{overline|63}}
| 563.{{overline|63}}
|
|  
|  
|  
|  
Line 669: Line 764:
| 94
| 94
| 569.{{overline|69}}
| 569.{{overline|69}}
|
| [[25/18]]
| [[25/18]]
| "
| "
Line 676: Line 772:
| 95
| 95
| 575.{{overline|75}}
| 575.{{overline|75}}
|
|  
|  
|  
|  
Line 683: Line 780:
| 96
| 96
| 581.{{overline|81}}
| 581.{{overline|81}}
| d5
| ?
| ?
| [[7/5]]
| [[7/5]]
Line 690: Line 788:
| 97
| 97
| 587.{{overline|87}}
| 587.{{overline|87}}
|
|  
|  
|  
|  
Line 697: Line 796:
| 98
| 98
| 593.{{overline|93}}
| 593.{{overline|93}}
|
| ''[[45/32]]''
| ''[[45/32]]''
| 343/243
| 343/243
Line 704: Line 804:
| 99
| 99
| 600.00
| 600.00
|
|  
|  
|  
|  
Line 711: Line 812:
| 100
| 100
| 606.{{overline|06}}
| 606.{{overline|06}}
|
| ''[[64/45]]''
| ''[[64/45]]''
| 486/343
| 486/343
Line 718: Line 820:
| 101
| 101
| 612.{{overline|12}}
| 612.{{overline|12}}
|
|  
|  
|  
|  
Line 725: Line 828:
| 102
| 102
| 618.{{overline|18}}
| 618.{{overline|18}}
| A4
| ?
| ?
| [[10/7]]
| [[10/7]]
Line 732: Line 836:
| 103
| 103
| 624.{{overline|24}}
| 624.{{overline|24}}
|
|  
|  
|  
|  
Line 739: Line 844:
| 104
| 104
| 630.{{overline|30}}
| 630.{{overline|30}}
|
| [[36/25]]
| [[36/25]]
| "
| "
Line 746: Line 852:
| 105
| 105
| 636.{{overline|36}}
| 636.{{overline|36}}
|
|  
|  
|  
|  
Line 753: Line 860:
| 106
| 106
| 642.{{overline|42}}
| 642.{{overline|42}}
|
| ''625/432''
| ''625/432''
| ''[[81/56]]''
| ''[[81/56]]''
Line 760: Line 868:
| 107
| 107
| 648.{{overline|48}}
| 648.{{overline|48}}
|
|  
|  
|  
|  
Line 767: Line 876:
| 108
| 108
| 654.{{overline|54}}
| 654.{{overline|54}}
|
| 729/500
| 729/500
| [[35/24]]
| [[35/24]]
Line 774: Line 884:
| 109
| 109
| 660.{{overline|60}}
| 660.{{overline|60}}
|
|  
|  
|  
|  
Line 781: Line 892:
| 110
| 110
| 666.{{overline|66}}
| 666.{{overline|66}}
|
| ''375/256''
| ''375/256''
| [[72/49]]
| [[72/49]]
Line 788: Line 900:
| 111
| 111
| 672.{{overline|72}}
| 672.{{overline|72}}
|
|  
|  
|  
|  
Line 795: Line 908:
| 112
| 112
| 678.{{overline|78}}
| 678.{{overline|78}}
|
| [[40/27]]
| [[40/27]]
| "
| "
Line 802: Line 916:
| 113
| 113
| 684.{{overline|84}}
| 684.{{overline|84}}
|
|  
|  
|  
|  
Line 809: Line 924:
| 114
| 114
| 690.{{overline|90}}
| 690.{{overline|90}}
|
| ?
| ?
| ''[[112/75]]'', 125/84
| ''[[112/75]]'', 125/84
Line 816: Line 932:
| 115
| 115
| 696.{{overline|96}}
| 696.{{overline|96}}
|
|  
|  
|  
|  
Line 823: Line 940:
| 116
| 116
| 703.{{overline|03}}
| 703.{{overline|03}}
| P5
| '''[[3/2]]'''
| '''[[3/2]]'''
| "
| "
Line 830: Line 948:
| 117
| 117
| 709.{{overline|09}}
| 709.{{overline|09}}
|
|  
|  
|  
|  
Line 837: Line 956:
| 118
| 118
| 715.{{overline|15}}
| 715.{{overline|15}}
|
| ?
| ?
| 189/125
| 189/125
Line 844: Line 964:
| 119
| 119
| 721.{{overline|21}}
| 721.{{overline|21}}
|
|  
|  
|  
|  
Line 851: Line 972:
| 120
| 120
| 727.{{overline|27}}
| 727.{{overline|27}}
|
| ''243/160''
| ''243/160''
| [[32/21]]
| [[32/21]]
Line 858: Line 980:
| 121
| 121
| 733.{{overline|33}}
| 733.{{overline|33}}
|
|  
|  
|  
|  
Line 865: Line 988:
| 122
| 122
| 739.{{overline|39}}
| 739.{{overline|39}}
|
| ''192/125''
| ''192/125''
| [[49/32]]
| [[49/32]]
Line 872: Line 996:
| 123
| 123
| 745.{{overline|45}}
| 745.{{overline|45}}
|
|  
|  
|  
|  
Line 879: Line 1,004:
| 124
| 124
| 751.{{overline|51}}
| 751.{{overline|51}}
|
| 125/81
| 125/81
| [[54/35]]
| [[54/35]]
Line 886: Line 1,012:
| 125
| 125
| 757.{{overline|57}}
| 757.{{overline|57}}
|
|  
|  
|  
|  
Line 893: Line 1,020:
| 126
| 126
| 763.{{overline|63}}
| 763.{{overline|63}}
|
| 972/625
| 972/625
| [[14/9]]
| [[14/9]]
Line 900: Line 1,028:
| 127
| 127
| 769.{{overline|69}}
| 769.{{overline|69}}
|
|  
|  
|  
|  
Line 907: Line 1,036:
| 128
| 128
| 775.{{overline|75}}
| 775.{{overline|75}}
|
| ''[[25/16]]''
| ''[[25/16]]''
| 196/125
| 196/125
Line 914: Line 1,044:
| 129
| 129
| 781.{{overline|81}}
| 781.{{overline|81}}
|
|  
|  
|  
|  
Line 921: Line 1,052:
| 130
| 130
| 787.{{overline|87}}
| 787.{{overline|87}}
| m6
| ''[[128/81]]''
| ''[[128/81]]''
| [[63/40]]
| [[63/40]]
Line 928: Line 1,060:
| 131
| 131
| 793.{{overline|93}}
| 793.{{overline|93}}
|
|  
|  
|  
|  
Line 935: Line 1,068:
| 132
| 132
| 800.00
| 800.00
|
| ''405/256''
| ''405/256''
| [[100/63]]
| [[100/63]]
Line 942: Line 1,076:
| 133
| 133
| 806.{{overline|06}}
| 806.{{overline|06}}
|
|  
|  
|  
|  
Line 949: Line 1,084:
| 134
| 134
| 812.{{overline|12}}
| 812.{{overline|12}}
|
| '''[[8/5]]'''
| '''[[8/5]]'''
| "
| "
Line 956: Line 1,092:
| 135
| 135
| 818.{{overline|18}}
| 818.{{overline|18}}
|
|  
|  
|  
|  
Line 963: Line 1,100:
| 136
| 136
| 824.{{overline|24}}
| 824.{{overline|24}}
|
| ?
| ?
| [[45/28]]
| [[45/28]]
Line 970: Line 1,108:
| 137
| 137
| 830.{{overline|30}}
| 830.{{overline|30}}
|
|  
|  
|  
|  
Line 977: Line 1,116:
| 138
| 138
| 836.{{overline|36}}
| 836.{{overline|36}}
|
| 81/50
| 81/50
| 175/108
| 175/108
Line 984: Line 1,124:
| 139
| 139
| 842.{{overline|42}}
| 842.{{overline|42}}
|
|  
|  
|  
|  
Line 991: Line 1,132:
| 140
| 140
| 848.{{overline|48}}
| 848.{{overline|48}}
|
| ''625/384''
| ''625/384''
| [[49/30]], [[80/49]]
| [[49/30]], [[80/49]]
Line 998: Line 1,140:
| 141
| 141
| 854.{{overline|54}}
| 854.{{overline|54}}
|
|  
|  
|  
|  
Line 1,005: Line 1,148:
| 142
| 142
| 860.{{overline|60}}
| 860.{{overline|60}}
|
| 400/243
| 400/243
| 288/175
| 288/175
Line 1,012: Line 1,156:
| 143
| 143
| 866.{{overline|66}}
| 866.{{overline|66}}
|
|  
|  
|  
|  
Line 1,019: Line 1,164:
| 144
| 144
| 872.{{overline|72}}
| 872.{{overline|72}}
|
| ?
| ?
| [[81/49]]
| [[81/49]]
Line 1,026: Line 1,172:
| 145
| 145
| 878.{{overline|78}}
| 878.{{overline|78}}
|
|  
|  
|  
|  
Line 1,033: Line 1,180:
| 146
| 146
| 884.{{overline|84}}
| 884.{{overline|84}}
|
| [[5/3]]
| [[5/3]]
| "
| "
Line 1,040: Line 1,188:
| 147
| 147
| 890.{{overline|90}}
| 890.{{overline|90}}
|
|  
|  
|  
|  
Line 1,047: Line 1,196:
| 148
| 148
| 896.{{overline|96}}
| 896.{{overline|96}}
|
| ?
| ?
| [[42/25]]
| [[42/25]]
Line 1,054: Line 1,204:
| 149
| 149
| 903.{{overline|03}}
| 903.{{overline|03}}
|
|  
|  
|  
|  
Line 1,061: Line 1,212:
| 150
| 150
| 909.{{overline|09}}
| 909.{{overline|09}}
| M6
| ''[[27/16]]''
| ''[[27/16]]''
| [[320/189]]
| [[320/189]]
Line 1,068: Line 1,220:
| 151
| 151
| 915.{{overline|15}}
| 915.{{overline|15}}
|
|  
|  
|  
|  
Line 1,075: Line 1,228:
| 152
| 152
| 921.{{overline|21}}
| 921.{{overline|21}}
|
| ''[[128/75]]''
| ''[[128/75]]''
| 245/144, 250/147
| 245/144, 250/147
Line 1,082: Line 1,236:
| 153
| 153
| 927.{{overline|27}}
| 927.{{overline|27}}
|
|  
|  
|  
|  
Line 1,089: Line 1,244:
| 154
| 154
| 933.{{overline|33}}
| 933.{{overline|33}}
|
| ?
| ?
| [[12/7]]
| [[12/7]]
Line 1,096: Line 1,252:
| 155
| 155
| 939.{{overline|39}}
| 939.{{overline|39}}
|
|  
|  
|  
|  
Line 1,103: Line 1,260:
| 156
| 156
| 945.{{overline|45}}
| 945.{{overline|45}}
|
| 216/125
| 216/125
| [[140/81]]
| [[140/81]]
Line 1,110: Line 1,268:
| 157
| 157
| 951.{{overline|51}}
| 951.{{overline|51}}
|
|  
|  
|  
|  
Line 1,117: Line 1,276:
| 158
| 158
| 957.{{overline|57}}
| 957.{{overline|57}}
|
| [[125/72]]
| [[125/72]]
| "
| "
Line 1,124: Line 1,284:
| 159
| 159
| 963.{{overline|63}}
| 963.{{overline|63}}
|
|  
|  
|  
|  
Line 1,131: Line 1,292:
| 160
| 160
| 969.{{overline|69}}
| 969.{{overline|69}}
|
| ''1280/729''
| ''1280/729''
| '''[[7/4]]'''
| '''[[7/4]]'''
Line 1,138: Line 1,300:
| 161
| 161
| 975.{{overline|75}}
| 975.{{overline|75}}
|
|  
|  
|  
|  
Line 1,145: Line 1,308:
| 162
| 162
| 981.{{overline|81}}
| 981.{{overline|81}}
|
| ''[[225/128]]''
| ''[[225/128]]''
| 432/245
| 432/245
Line 1,152: Line 1,316:
| 163
| 163
| 987.{{overline|87}}
| 987.{{overline|87}}
|
|  
|  
|  
|  
Line 1,159: Line 1,324:
| 164
| 164
| 993.{{overline|93}}
| 993.{{overline|93}}
| m7
| [[16/9]]
| [[16/9]]
| "
| "
Line 1,166: Line 1,332:
| 165
| 165
| 1000.00
| 1000.00
|
|  
|  
|  
|  
Line 1,173: Line 1,340:
| 166
| 166
| 1006.{{overline|06}}
| 1006.{{overline|06}}
|
| ?
| ?
| [[25/14]]
| [[25/14]]
Line 1,180: Line 1,348:
| 167
| 167
| 1012.{{overline|12}}
| 1012.{{overline|12}}
|
|  
|  
|  
|  
Line 1,187: Line 1,356:
| 168
| 168
| 1018.{{overline|18}}
| 1018.{{overline|18}}
|
| [[9/5]]
| [[9/5]]
| "
| "
Line 1,194: Line 1,364:
| 169
| 169
| 1024.{{overline|24}}
| 1024.{{overline|24}}
|
|  
|  
|  
|  
Line 1,201: Line 1,372:
| 170
| 170
| 1030.{{overline|30}}
| 1030.{{overline|30}}
|
| ?
| ?
| [[49/27]]
| [[49/27]]
Line 1,208: Line 1,380:
| 171
| 171
| 1036.{{overline|36}}
| 1036.{{overline|36}}
|
|  
|  
|  
|  
Line 1,215: Line 1,388:
| 172
| 172
| 1042.{{overline|42}}
| 1042.{{overline|42}}
|
| ''729/400''
| ''729/400''
| [[64/35]]
| [[64/35]]
Line 1,222: Line 1,396:
| 173
| 173
| 1048.{{overline|48}}
| 1048.{{overline|48}}
|
|  
|  
|  
|  
Line 1,229: Line 1,404:
| 174
| 174
| 1054.{{overline|54}}
| 1054.{{overline|54}}
|
| ''1152/625''
| ''1152/625''
| [[90/49]]
| [[90/49]]
Line 1,236: Line 1,412:
| 175
| 175
| 1060.{{overline|60}}
| 1060.{{overline|60}}
|
|  
|  
|  
|  
Line 1,243: Line 1,420:
| 176
| 176
| 1066.{{overline|66}}
| 1066.{{overline|66}}
|
| [[50/27]]
| [[50/27]]
| "
| "
Line 1,250: Line 1,428:
| 177
| 177
| 1072.{{overline|72}}
| 1072.{{overline|72}}
|
|  
|  
|  
|  
Line 1,257: Line 1,436:
| 178
| 178
| 1078.{{overline|78}}
| 1078.{{overline|78}}
|
| ?
| ?
| [[28/15]]
| [[28/15]]
Line 1,264: Line 1,444:
| 179
| 179
| 1084.{{overline|84}}
| 1084.{{overline|84}}
|
|  
|  
|  
|  
Line 1,271: Line 1,452:
| 180
| 180
| 1090.{{overline|90}}
| 1090.{{overline|90}}
|
| [[15/8]]
| [[15/8]]
| "
| "
Line 1,278: Line 1,460:
| 181
| 181
| 1096.{{overline|96}}
| 1096.{{overline|96}}
|
|  
|  
|  
|  
Line 1,285: Line 1,468:
| 182
| 182
| 1103.{{overline|03}}
| 1103.{{overline|03}}
|
| ''256/135''
| ''256/135''
| 189/100
| 189/100
Line 1,292: Line 1,476:
| 183
| 183
| 1109.{{overline|09}}
| 1109.{{overline|09}}
|
|  
|  
|  
|  
Line 1,299: Line 1,484:
| 184
| 184
| 1115.{{overline|15}}
| 1115.{{overline|15}}
| M7
| ''[[243/128]]''
| ''[[243/128]]''
| [[40/21]]
| [[40/21]]
Line 1,306: Line 1,492:
| 185
| 185
| 1121.{{overline|21}}
| 1121.{{overline|21}}
|
|  
|  
|  
|  
Line 1,313: Line 1,500:
| 186
| 186
| 1127.{{overline|27}}
| 1127.{{overline|27}}
|
| [[48/25]]
| [[48/25]]
| "
| "
Line 1,320: Line 1,508:
| 187
| 187
| 1133.{{overline|33}}
| 1133.{{overline|33}}
|
|  
|  
|  
|  
Line 1,327: Line 1,516:
| 188
| 188
| 1139.{{overline|39}}
| 1139.{{overline|39}}
|
| 625/324
| 625/324
| [[27/14]]
| [[27/14]]
Line 1,334: Line 1,524:
| 189
| 189
| 1145.{{overline|45}}
| 1145.{{overline|45}}
|
|  
|  
|  
|  
Line 1,341: Line 1,532:
| 190
| 190
| 1151.{{overline|51}}
| 1151.{{overline|51}}
|
| 243/125
| 243/125
| [[35/18]]
| [[35/18]]
Line 1,348: Line 1,540:
| 191
| 191
| 1157.{{overline|57}}
| 1157.{{overline|57}}
|
|  
|  
|  
|  
Line 1,355: Line 1,548:
| 192
| 192
| 1163.{{overline|63}}
| 1163.{{overline|63}}
|
| ''125/64''
| ''125/64''
| 49/25, 96/49
| 49/25, 96/49
Line 1,362: Line 1,556:
| 193
| 193
| 1169.{{overline|69}}
| 1169.{{overline|69}}
|
|  
|  
|  
|  
Line 1,369: Line 1,564:
| 194
| 194
| 1175.{{overline|75}}
| 1175.{{overline|75}}
|
| 160/81
| 160/81
| 63/32
| 63/32
Line 1,376: Line 1,572:
| 195
| 195
| 1181.{{overline|81}}
| 1181.{{overline|81}}
|
|  
|  
|  
|  
Line 1,383: Line 1,580:
| 196
| 196
| 1187.{{overline|87}}
| 1187.{{overline|87}}
|
| ?
| ?
| 125/63
| 125/63
Line 1,390: Line 1,588:
| 197
| 197
| 1193.{{overline|93}}
| 1193.{{overline|93}}
|
|  
|  
|  
|  
Line 1,397: Line 1,596:
| 198
| 198
| 1200.00
| 1200.00
| P8
| colspan="4" | '''[[2/1]]'''
| colspan="4" | '''[[2/1]]'''
|-
|-

Revision as of 08:31, 2 August 2021

This table of 198edo intervals assumes 13-limit patent val ⟨198 314 460 556 685 733].

Intervals highlighted in bold are prime harmonics or subharmonics. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank. 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 729 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 6.06 385/384, 441/440, 540/539 196/195
2 12.12 ? 126/125 121/120 144/143
3 18.18 99/98, 100/99 91/90, 105/104
4 24.24 81/80 64/63 " 66/65, 78/77
5 30.30 55/54, 56/55 "
6 36.36 128/125 49/48, 50/49 " "
7 42.42 45/44 40/39
8 48.48 250/243 36/35 " "
9 54.54 33/32 "
10 60.60 648/625 28/27 " "
11 66.66 80/77 26/25, 27/26
12 72.72 25/24 " " "
13 78.78 22/21 "
14 84.84 m2 256/243 21/20 " "
15 90.90 539/512 96/91
16 96.96 135/128 200/189 128/121 55/52
17 103.03 35/33 52/49
18 109.09 16/15 " " "
19 115.15 77/72 "
20 121.21 ? 15/14 " "
21 127.27 264/245, 320/297 14/13
22 133.33 27/25 " " "
23 139.39 88/81 13/12
24 145.45 625/576 49/45 " "
25 151.51 12/11 "
26 157.57 800/729 35/32 " "
27 163.63 11/10 "
28 169.69 ? 54/49 " "
29 175.75 256/231 72/65
30 181.81 10/9 " " "
31 187.87 49/44 39/35
32 193.93 ? 28/25 " "
33 200.00 55/49 "
34 206.06 M2 9/8 " " "
35 212.12 112/99 "
36 218.18 256/225 245/216 " 143/126, 162/143
37 224.24 25/22 "
38 230.30 729/640 8/7 " "
39 236.36 55/48 "
40 242.42 144/125 " " "
41 248.48 231/200 15/13
42 254.54 125/108 81/70 " "
43 260.60 64/55 "
44 266.66 ? 7/6 " "
45 272.72 90/77 "
46 278.78 75/64 147/125, 288/245 " 168/143
47 284.84 33/28 "
48 290.90 m3 32/27 189/160 " 13/11
49 296.96 196/165 108/91
50 303.03 ? 25/21 " "
51 309.09 176/147 117/98, 140/117
52 315.15 6/5 " " "
53 321.21 77/64 65/54
54 327.27 ? 98/81 " "
55 333.33 40/33 63/52
56 339.39 243/200 175/144 147/121 "
57 345.45 11/9 39/32
58 351.51 768/625 49/40, 60/49 " "
59 357.57 27/22 16/13
60 363.63 100/81 216/175 121/98 "
61 369.69 99/80 26/21
62 375.75 ? 56/45 " "
63 381.81 96/77 81/65, 125/78
64 387.87 5/4 " " "
65 393.93 44/35 49/39
66 400.00 512/405 63/50 " "
67 406.06 125/99 91/72
68 412.12 M3 81/64 80/63 " 33/26
69 418.18 14/11 "
70 424.24 32/25 125/98 " "
71 430.30 77/60 50/39
72 436.36 625/486 9/7 " "
73 442.42 128/99 84/65
74 448.48 162/125 35/27 " "
75 454.54 100/77 13/10
76 460.60 125/96 64/49 " "
77 466.66 55/42, 72/55 "
78 472.72 320/243 21/16 " "
79 478.78 33/25 "
80 484.84 ? 250/189 160/121 143/108, 189/143, 224/169
81 490.90 175/132 65/49
82 496.96 P4 4/3 " " "
83 503.03 147/110 234/175
84 509.09 ? 75/56, 168/125 " "
85 515.15 66/49 35/26
86 521.21 27/20 " " "
87 527.27 110/81 65/48
88 533.33 512/375 49/36 " "
89 539.39 15/11 "
90 545.45 1000/729 48/35 " "
91 551.51 11/8 "
92 557.57 864/625 112/81 " 91/66
93 563.63 320/231 18/13
94 569.69 25/18 " " "
95 575.75 88/63 39/28
96 581.81 d5 ? 7/5 " "
97 587.87 108/77 "
98 593.93 45/32 343/243 484/343 55/39
99 600.00 99/70, 140/99 "
100 606.06 64/45 486/343 343/242 78/55
101 612.12 77/54 "
102 618.18 A4 ? 10/7 " "
103 624.24 63/44 56/39
104 630.30 36/25 " " "
105 636.36 231/160 13/9
106 642.42 625/432 81/56 " 132/91
107 648.48 16/11 "
108 654.54 729/500 35/24 " "
109 660.60 22/15 "
110 666.66 375/256 72/49 " "
111 672.72 81/55 96/65
112 678.78 40/27 " " "
113 684.84 49/33 52/35
114 690.90 ? 112/75, 125/84 " "
115 696.96 220/147 175/117
116 703.03 P5 3/2 " " "
117 709.09 264/175 98/65
118 715.15 ? 189/125 121/80 169/112, 216/143, 286/189
119 721.21 50/33 "
120 727.27 243/160 32/21 " "
121 733.33 55/36, 84/55 "
122 739.39 192/125 49/32 " "
123 745.45 77/50 20/13
124 751.51 125/81 54/35 " "
125 757.57 99/64 65/42
126 763.63 972/625 14/9 " "
127 769.69 120/77 39/25
128 775.75 25/16 196/125 " "
129 781.81 11/7 "
130 787.87 m6 128/81 63/40 " 52/33
131 793.93 198/125 144/91
132 800.00 405/256 100/63 " "
133 806.06 35/22 "
134 812.12 8/5 " " "
135 818.18 77/48 125/78, 130/81
136 824.24 ? 45/28 " "
137 830.30 160/99 21/13
138 836.36 81/50 175/108 196/121 "
139 842.42 44/27 13/8
140 848.48 625/384 49/30, 80/49 " "
141 854.54 18/11 64/39
142 860.60 400/243 288/175 242/147 "
143 866.66 33/20 104/63
144 872.72 ? 81/49 " "
145 878.78 128/77 108/65
146 884.84 5/3 " " "
147 890.90 147/88 117/70, 196/117
148 896.96 ? 42/25 " "
149 903.03 165/98 91/54
150 909.09 M6 27/16 320/189 " 22/13
151 915.15 56/33 "
152 921.21 128/75 245/144, 250/147 " 143/84
153 927.27 77/45 "
154 933.33 ? 12/7 " "
155 939.39 55/32 "
156 945.45 216/125 140/81 121/70 "
157 951.51 343/198, 400/231 26/15
158 957.57 125/72 " " "
159 963.63 96/55 "
160 969.69 1280/729 7/4 " "
161 975.75 44/25 "
162 981.81 225/128 432/245 " 143/81, 252/143
163 987.87 99/56 "
164 993.93 m7 16/9 " " "
165 1000.00 98/55 "
166 1006.06 ? 25/14 " "
167 1012.12 88/49 70/39
168 1018.18 9/5 " " "
169 1024.24 231/128 65/36
170 1030.30 ? 49/27 " "
171 1036.36 20/11 "
172 1042.42 729/400 64/35 " "
173 1048.48 11/6 "
174 1054.54 1152/625 90/49 " "
175 1060.60 231/125 24/13
176 1066.66 50/27 " " "
177 1072.72 245/132 13/7
178 1078.78 ? 28/15 " "
179 1084.84 144/77 "
180 1090.90 15/8 " " "
181 1096.96 66/35 49/26
182 1103.03 256/135 189/100 121/64 104/55
183 1109.09 1024/539 91/48
184 1115.15 M7 243/128 40/21 " "
185 1121.21 21/11 "
186 1127.27 48/25 " " "
187 1133.33 77/40 25/13, 52/27
188 1139.39 625/324 27/14 " "
189 1145.45 64/33 "
190 1151.51 243/125 35/18 " "
191 1157.57 88/45 39/20
192 1163.63 125/64 49/25, 96/49 " "
193 1169.69 55/28, 108/55 "
194 1175.75 160/81 63/32 " 65/33, 77/39
195 1181.81 99/50, 196/99 180/91, 208/105
196 1187.87 ? 125/63 240/121 143/72
197 1193.93 539/270, 768/385, 880/441 195/98
198 1200.00 P8 2/1
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