Table of 198edo intervals: Difference between revisions

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<div style="background: aliceblue; color: darkslategray; font-style: italic; border: 1px solid lightblue; margin: 15px; padding: 4px; text-align: center;">This article is a work in progress.</div>
This '''table of [[198edo]] intervals''' assumes [[13-limit]] [[patent val]] {{val| 198 314 460 556 685 733 }}.  


This '''table of [[198edo]] intervals''' assumes 13-limit patent val {{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.  


Intervals highlighted in '''bold''' are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50% or intervals with odd limit over 729 are not shown. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank.
{| class="wikitable center-1 right-2 center-3"
 
{| class="wikitable center-1 right-2"
|-
|-
! #
! #
! Cents
! Cents
! 5 limit
! Marks
! 7 limit
! 5-limit
! 11 limit
! 7-limit
! 13 limit
! 11-limit
! 13-limit
|-
|-
| 0
| 0
| 0.0000
| 0.00
| colspan="4"| '''[[1/1]]'''
| P1
| colspan="4" | '''[[1/1]]'''
|-
|-
| 1
| 1
| 6.0606
| 6.{{overline|06}}
|
|  
|  
|  
|  
| [[385/384]], [[441/440]], [[540/539]]
| [[385/384]], [[441/440]], [[540/539]]
| [[196/195]], [[325/324]], [[351/350]], [[364/363]]
| [[196/195]], [[325/324]], [[364/363]]
|-
|-
| 2
| 2
| 12.1212
| 12.{{overline|12}}
|
| ?
| ?
| [[126/125]], [[245/243]]
| [[126/125]]
| [[121/120]]
| [[121/120]], [[176/175]]
| [[144/143]], [[169/168]]
| [[144/143]]
|-
|-
| 3
| 3
| 18.1818
| 18.{{overline|18}}
|
|  
|  
|  
|  
| [[99/98]], [[100/99]]
| [[99/98]], [[100/99]]
| ?
| [[91/90]], [[105/104]]
|-
|-
| 4
| 4
| 24.2424
| 24.{{overline|24}}
|
| [[81/80]]
| [[81/80]]
| [[64/63]]
| [[64/63]]
| ?
| "
| [[66/65]], [[78/77]]
| [[66/65]], [[78/77]]
|-
|-
| 5
| 5
| 30.3030
| 30.{{overline|30}}
|
|  
|  
|  
|  
| [[55/54]], [[56/55]]
| [[55/54]], [[56/55]]
| ?
| "
|-
|-
| 6
| 6
| 36.3636
| 36.{{overline|36}}
| ?
|
| ''[[128/125]]''
| [[49/48]], [[50/49]]
| [[49/48]], [[50/49]]
| ?
| "
| ?
| "
|-
|-
| 7
| 7
| 42.4242
| 42.{{overline|42}}
|
|  
|  
|  
|  
| ?
| ''[[45/44]]''
| [[40/39]]
| [[40/39]]
|-
|-
| 8
| 8
| 48.4848
| 48.{{overline|48}}
| ?
|
| [[250/243]]
| [[36/35]]
| [[36/35]]
| ?
| "
| ?
| "
|-
|-
| 9
| 9
| 54.5455
| 54.{{overline|54}}
|
|  
|  
|  
|  
| [[33/32]]
| [[33/32]]
| [[65/63]]
| "
|-
|-
| 10
| 10
| 60.6061
| 60.{{overline|60}}
| ?
|
| [[648/625]]
| [[28/27]]
| [[28/27]]
| ?
| "
| ?
| "
|-
|-
| 11
| 11
| 66.6667
| 66.{{overline|66}}
|
|  
|  
|  
|  
Line 96: Line 107:
|-
|-
| 12
| 12
| 72.7273
| 72.{{overline|72}}
|
| [[25/24]]
| [[25/24]]
| ?
| "
| [[126/121]]
| "
| ?
| "
|-
|-
| 13
| 13
| 78.7879
| 78.{{overline|78}}
|
|  
|  
|  
|  
| [[22/21]]
| [[22/21]]
| ?
| "
|-
|-
| 14
| 14
| 84.8485
| 84.{{overline|84}}
| ?
| m2
| ''[[256/243]]''
| [[21/20]]
| [[21/20]]
| ?
| "
| ?
| "
|-
|-
| 15
| 15
| 90.9091
| 90.{{overline|90}}
|
|  
|  
|  
|  
| ?
| 539/512
| [[96/91]]
| 96/91
|-
|-
| 16
| 16
| 96.9697
| 96.{{overline|96}}
| ?
|
| [[200/189]]
| ''[[135/128]]''
| 200/189
| [[128/121]]
| [[128/121]]
| ?
| [[55/52]]
|-
|-
| 17
| 17
| 103.0303
| 103.{{overline|03}}
|
|  
|  
|  
|  
| [[35/33]]
| [[35/33]]
| ?
| [[52/49]]
|-
|-
| 18
| 18
| 109.0909
| 109.{{overline|09}}
|
| [[16/15]]
| [[16/15]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 19
| 19
| 115.1515
| 115.{{overline|15}}
|
|  
|  
|  
|  
| ?
| [[77/72]]
| ?
| "
|-
|-
| 20
| 20
| 121.2121
| 121.{{overline|21}}
|
| ?
| ?
| [[15/14]]
| [[15/14]]
| ?
| "
| ?
| "
|-
|-
| 21
| 21
| 127.2727
| 127.{{overline|27}}
|
|  
|  
|  
|  
| ?
| 264/245, 320/297
| [[14/13]]
| [[14/13]]
|-
|-
| 22
| 22
| 133.3333
| 133.{{overline|33}}
|
| [[27/25]]
| [[27/25]]
| [[175/162]]
| "
| ?
| "
| ?
| "
|-
|-
| 23
| 23
| 139.3939
| 139.{{overline|39}}
|
|  
|  
|  
|  
| ?
| ''[[88/81]]''
| [[13/12]]
| [[13/12]]
|-
|-
| 24
| 24
| 145.4545
| 145.{{overline|45}}
| ?
|
| [[49/45]], [[160/147]]
| ''625/576''
| ?
| [[49/45]]
| ?
| "
| "
|-
|-
| 25
| 25
| 151.5152
| 151.{{overline|51}}
|
|  
|  
|  
|  
| [[12/11]]
| [[12/11]]
| ?
| "
|-
|-
| 26
| 26
| 157.5758
| 157.{{overline|57}}
| ?
|
| ''800/729''
| [[35/32]]
| [[35/32]]
| ?
| "
| ?
| "
|-
|-
| 27
| 27
| 163.6364
| 163.{{overline|63}}
|
|  
|  
|  
|  
| [[11/10]]
| [[11/10]]
| ?
| "
|-
|-
| 28
| 28
| 169.6970
| 169.{{overline|69}}
|
| ?
| ?
| [[54/49]]
| [[54/49]]
| ?
| "
| ?
| "
|-
|-
| 29
| 29
| 175.7576
| 175.{{overline|75}}
|
|  
|  
|  
|  
| ?
| 256/231
| ?
| 72/65
|-
|-
| 30
| 30
| 181.8182
| 181.{{overline|81}}
|
| [[10/9]]
| [[10/9]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 31
| 31
| 187.8788
| 187.{{overline|87}}
|
|  
|  
|  
|  
| ?
| 49/44
| ?
| 39/35
|-
|-
| 32
| 32
| 193.9394
| 193.{{overline|93}}
|
| ?
| ?
| [[28/25]]
| [[28/25]]
| [[121/108]]
| "
| ?
| "
|-
|-
| 33
| 33
| 200.0000
| 200.00
|
|  
|  
|  
|  
| ?
| [[55/49]]
| [[91/81]]
| "
|-
|-
| 34
| 34
| 206.0606
| 206.{{overline|06}}
| M2
| [[9/8]]
| [[9/8]]
| ?
| "
| ?
| "
| [[44/39]]
| "
|-
|-
| 35
| 35
| 212.1212
| 212.{{overline|12}}
|
|  
|  
|  
|  
| ?
| 112/99
| ?
| "
|-
|-
| 36
| 36
| 218.1818
| 218.{{overline|18}}
| ?
|
| ?
| ''[[256/225]]''
| ?
| 245/216
| ?
| "
| 143/126, 162/143
|-
|-
| 37
| 37
| 224.2424
| 224.{{overline|24}}
|
|  
|  
|  
|  
| ?
| [[25/22]]
| [[91/80]]
| "
|-
|-
| 38
| 38
| 230.3030
| 230.{{overline|30}}
| ?
|
| ''729/640''
| '''[[8/7]]'''
| '''[[8/7]]'''
| ?
| "
| ?
| "
|-
|-
| 39
| 39
| 236.3636
| 236.{{overline|36}}
|
|  
|  
|  
|  
| [[55/48]]
| [[55/48]]
| ?
| "
|-  
|-  
| 40
| 40
| 242.4242
| 242.{{overline|42}}
| ?
|
| [[280/243]]
| [[144/125]]
| ?
| "
| ?
| "
| "
|-
|-
| 41
| 41
| 248.4848
| 248.{{overline|48}}
|
|  
|  
|  
|  
| ?
| 231/200
| [[15/13]]
| [[15/13]]
|-
|-
| 42
| 42
| 254.5455
| 254.{{overline|54}}
| ?
|
| 125/108
| [[81/70]]
| [[81/70]]
| [[140/121]]
| "
| ?
| "
|-
|-
| 43
| 43
| 260.6061
| 260.{{overline|60}}
|
|  
|  
|  
|  
| [[64/55]]
| [[64/55]]
| ?
| "
|-
|-
| 44
| 44
| 266.6667
| 266.{{overline|66}}
|
| ?
| ?
| [[7/6]]
| [[7/6]]
| ?
| "
| ?
| "
|-
|-
| 45
| 45
| 272.7273
| 272.{{overline|72}}
|
|  
|  
|  
|  
| ?
| 90/77
| ?
| "
|-
|-
| 46
| 46
| 278.7879
| 278.{{overline|78}}
| ?
|
| ?
| ''[[75/64]]''
| ?
| 147/125, 288/245
| ?
| "
| 168/143
|-
|-
| 47
| 47
| 284.8485
| 284.{{overline|84}}
|
|  
|  
|  
|  
| [[33/28]]
| [[33/28]]
| ?
| "
|-
|-
| 48
| 48
| 290.9091
| 290.{{overline|90}}
| ?
| m3
| ''[[32/27]]''
| [[189/160]]
| [[189/160]]
| ?
| "
| [[13/11]]
| [[13/11]]
|-
|-
| 49
| 49
| 296.9697
| 296.{{overline|96}}
|
|  
|  
|  
|  
| ?
| 196/165
| ?
| 108/91
|-
|-
| 50
| 50
| 303.0303
| 303.{{overline|03}}
|
| ?
| ?
| [[25/21]]
| [[25/21]]
| [[144/121]]
| "
| ?
| "
|-
|-
| 51
| 51
| 309.0909
| 309.{{overline|09}}
|
|  
|  
|  
|  
| ?
| 176/147
| ?
| 117/98, 140/117
|-
|-
| 52
| 52
| 315.1515
| 315.{{overline|15}}
|
| [[6/5]]
| [[6/5]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 53
| 53
| 321.2121
| 321.{{overline|21}}
|
|  
|  
|  
|  
| ?
| 77/64
| ?
| 65/54
|-
|-
| 54
| 54
| 327.2727
| 327.{{overline|27}}
| ?
|
| ?
| ?
| ?
| ?
| 98/81
| "
| "
|-
|-
| 55
| 55
| 333.3333
| 333.{{overline|33}}
|
|  
|  
|  
|  
| ?
| [[40/33]]
| [[63/52]]
| [[63/52]]
|-
|-
| 56
| 56
| 339.3939
| 339.{{overline|39}}
| ?
|
| ?
| 243/200
| ?
| 175/144
| ?
| 147/121
| "
|-
|-
| 57
| 57
| 345.4545
| 345.{{overline|45}}
|
|  
|  
|  
|  
Line 418: Line 475:
|-
|-
| 58
| 58
| 351.5152
| 351.{{overline|51}}
| ?
|
| ''768/625''
| [[49/40]], [[60/49]]
| [[49/40]], [[60/49]]
| ?
| "
| ?
| "
|-
|-
| 59
| 59
| 357.5757
| 357.{{overline|57}}
|
|  
|  
|  
|  
Line 432: Line 491:
|-
|-
| 60
| 60
| 363.6364
| 363.{{overline|63}}
| ?
|
| ?
| 100/81
| ?
| 216/175
| ?
| 121/98
| "
|-
|-
| 61
| 61
| 369.6970
| 369.{{overline|69}}
|
|  
|  
|  
|  
| ?
| 99/80
| [[26/21]]
| [[26/21]]
|-
|-
| 62
| 62
| 375.7576
| 375.{{overline|75}}
| ?
|
| ?
| ?
| ?
| ?
| [[56/45]]
| "
| "
|-
|-
| 63
| 63
| 381.8182
| 381.{{overline|81}}
|
|  
|  
|  
|  
| ?
| 96/77
| ?
| 81/65, 125/78
|-
|-
| 64
| 64
| 387.8788
| 387.{{overline|87}}
|
| '''[[5/4]]'''
| '''[[5/4]]'''
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 65
| 65
| 393.9394
| 393.{{overline|93}}
|
|  
|  
|  
|  
| ?
| [[44/35]]
| ?
| 49/39
|-
|-
| 66
| 66
| 400.0000
| 400.00
| ?
|
| ''512/405''
| [[63/50]]
| [[63/50]]
| [[121/96]]
| "
| ?
| "
|-
|-
| 67
| 67
| 406.0606
| 406.{{overline|06}}
|
|  
|  
|  
|  
| ?
| 125/99
| ?
| 91/72
|-
|-
| 68
| 68
| 412.1212
| 412.{{overline|12}}
| ?
| M3
| ''[[81/64]]''
| [[80/63]]
| [[80/63]]
| ?
| "
| [[33/26]]
| [[33/26]]
|-
|-
| 69
| 69
| 418.1818
| 418.{{overline|18}}
|
|  
|  
|  
|  
| [[14/11]]
| [[14/11]]
| ?
| "
|-
|-
| 70
| 70
| 424.2424
| 424.{{overline|24}}
| ?
|
| ?
| ''[[32/25]]''
| ?
| 125/98
| ?
| "
| "
|-
|-
| 71
| 71
| 430.3030
| 430.{{overline|30}}
|
|  
|  
|  
|  
| ?
| 77/60
| ?
| 50/39
|-
|-
| 72
| 72
| 436.3636
| 436.{{overline|36}}
| ?
|
| 625/486
| [[9/7]]
| [[9/7]]
| ?
| "
| ?
| "
|-
|-
| 73
| 73
| 442.4242
| 442.{{overline|42}}
|
|  
|  
|  
|  
| [[128/99]]
| [[128/99]]
| ?
| 84/65
|-
|-
| 74
| 74
| 448.4848
| 448.{{overline|48}}
| ?
|
| 162/125
| [[35/27]]
| [[35/27]]
| ?
| "
| ?
| "
|-
|-
| 75
| 75
| 454.5455
| 454.{{overline|54}}
|
|  
|  
|  
|  
| ?
| 100/77
| [[13/10]]
| [[13/10]]
|-
|-
| 76
| 76
| 460.6061
| 460.{{overline|60}}
| ?
|
| ?
| ''125/96''
| ?
| [[64/49]]
| ?
| "
| "
|-
|-
| 77
| 77
| 466.6667
| 466.{{overline|66}}
|
|  
|  
|  
|  
| ?
| 55/42, 72/55
| ?
| "
|-
|-
| 78
| 78
| 472.7273
| 472.{{overline|72}}
| ?
|
| ''320/243''
| [[21/16]]
| [[21/16]]
| ?
| "
| ?
| "
|-
|-
| 79
| 79
| 478.7879
| 478.{{overline|78}}
|
|  
|  
|  
|  
| ?
| [[33/25]]
| ?
| "
|-
|-
| 80
| 80
| 484.8485
| 484.{{overline|84}}
| ?
|
| ?
| ?
| ?
| ?
| 250/189
| 160/121
| 143/108, 189/143, 224/169
|-
|-
| 81
| 81
| 490.9091
| 490.{{overline|90}}
|
|  
|  
|  
|  
| ?
| 175/132
| ?
| 65/49
|-
|-
| 82
| 82
| 496.9697
| 496.{{overline|96}}
| P4
| '''[[4/3]]'''
| '''[[4/3]]'''
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 83
| 83
| 503.0303
| 503.{{overline|03}}
|
|  
|  
|  
|  
| ?
| 147/110
| ?
| 234/175
|-
|-
| 84
| 84
| 509.0909
| 509.{{overline|09}}
| ?
|
| ?
| ?
| ?
| ?
| ''[[75/56]]'', 168/125
| "
| "
|-
|-
| 85
| 85
| 515.1515
| 515.{{overline|15}}
|
|  
|  
|  
|  
| ?
| 66/49
| ?
| 35/26
|-
|-
| 86
| 86
| 521.2121
| 521.{{overline|21}}
|
| [[27/20]]
| [[27/20]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 87
| 87
| 527.2727
| 527.{{overline|27}}
|
|  
|  
|  
|  
| ?
| 110/81
| ?
| 65/48
|-
|-
| 88
| 88
| 533.3333
| 533.{{overline|33}}
| ?
|
| ''512/375''
| [[49/36]]
| [[49/36]]
| ?
| "
| ?
| "
|-
|-
| 89
| 89
| 539.3939
| 539.{{overline|39}}
|
|  
|  
|  
|  
| [[15/11]]
| [[15/11]]
| ?
| "
|-
|-
| 90
| 90
| 545.4545
| 545.{{overline|45}}
| ?
|
| 1000/729
| [[48/35]]
| [[48/35]]
| ?
| "
| ?
| "
|-
|-
| 91
| 91
| 551.5152
| 551.{{overline|51}}
|
|  
|  
|  
|  
| '''[[11/8]]'''
| '''[[11/8]]'''
| ?
| "
|-
|-
| 92
| 92
| 557.5758
| 557.{{overline|57}}
| ?
|
| [[441/320]]
| ''864/625''
| ?
| ''[[112/81]]''
| ?
| "
| 91/66
|-
|-
| 93
| 93
| 563.6364
| 563.{{overline|63}}
|
|  
|  
|  
|  
| ?
| 320/231
| [[18/13]]
| [[18/13]]
|-
|-
| 94
| 94
| 569.6970
| 569.{{overline|69}}
|
| [[25/18]]
| [[25/18]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 95
| 95
| 575.7576
| 575.{{overline|75}}
|
|  
|  
|  
|  
| ?
| 88/63
| ?
| 39/28
|-
|-
| 96
| 96
| 581.8182
| 581.{{overline|81}}
| d5
| ?
| ?
| [[7/5]]
| [[7/5]]
| ?
| "
| ?
| "
|-
|-
| 97
| 97
| 587.8788
| 587.{{overline|87}}
|
|  
|  
|  
|  
| ?
| 108/77
| ?
| "
|-
|-
| 98
| 98
| 593.9394
| 593.{{overline|93}}
| ?
|
| ?
| ''[[45/32]]''
| ?
| 343/243
| ?
| 484/343
| 55/39
|-
|-
| 99
| 99
| 600.0000
| 600.00
|
|  
|  
|  
|  
| [[99/70]], [[140/99]]
| [[99/70]], [[140/99]]
| ?
| "
|-
|-
| 100
| 100
| 606.0606
| 606.{{overline|06}}
| ?
|
| ?
| ''[[64/45]]''
| ?
| 486/343
| ?
| 343/242
| 78/55
|-
|-
| 101
| 101
| 612.1212
| 612.{{overline|12}}
|
|  
|  
|  
|  
| ?
| 77/54
| ?
| "
|-
|-
| 102
| 102
| 618.1818
| 618.{{overline|18}}
| A4
| ?
| ?
| [[10/7]]
| [[10/7]]
| ?
| "
| ?
| "
|-
|-
| 103
| 103
| 624.2424
| 624.{{overline|24}}
|
|  
|  
|  
|  
| ?
| 63/44
| ?
| 56/39
|-
|-
| 104
| 104
| 630.3030
| 630.{{overline|30}}
|
| [[36/25]]
| [[36/25]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 105
| 105
| 636.3636
| 636.{{overline|36}}
|
|  
|  
|  
|  
| ?
| 231/160
| [[13/9]]
| [[13/9]]
|-
|-
| 106
| 106
| 642.4242
| 642.{{overline|42}}
| ?
|
| ?
| ''625/432''
| ?
| ''[[81/56]]''
| ?
| "
| 132/91
|-
|-
| 107
| 107
| 648.4848
| 648.{{overline|48}}
|
|  
|  
|  
|  
| '''[[16/11]]'''
| '''[[16/11]]'''
| ?
| "
|-
|-
| 108
| 108
| 654.5455
| 654.{{overline|54}}
| ?
|
| [[640/441]]
| 729/500
| ?
| [[35/24]]
| ?
| "
| "
|-
|-
| 109
| 109
| 660.6061
| 660.{{overline|60}}
|
|  
|  
|  
|  
| [[22/15]]
| [[22/15]]
| ?
| "
|-
|-
| 110
| 110
| 666.6667
| 666.{{overline|66}}
| ?
|
| ?
| ''375/256''
| ?
| [[72/49]]
| ?
| "
| "
|-
|-
| 111
| 111
| 672.7273
| 672.{{overline|72}}
|
|  
|  
|  
|  
| ?
| 81/55
| ?
| 96/65
|-
|-
| 112
| 112
| 678.7879
| 678.{{overline|78}}
|
| [[40/27]]
| [[40/27]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 113
| 113
| 684.8485
| 684.{{overline|84}}
|
|  
|  
|  
|  
| ?
| 49/33
| ?
| 52/35
|-
|-
| 114
| 114
| 690.9091
| 690.{{overline|90}}
| ?
|
| ?
| ?
| ?
| ?
| ''[[112/75]]'', 125/84
| "
| "
|-
|-
| 115
| 115
| 696.9697
| 696.{{overline|96}}
|
|  
|  
|  
|  
| ?
| 220/147
| ?
| 175/117
|-
|-
| 116
| 116
| 703.0303
| 703.{{overline|03}}
| [[3/2]]
| P5
| ?
| '''[[3/2]]'''
| ?
| "
| ?
| "
| "
|-
|-
| 117
| 117
| 709.0909
| 709.{{overline|09}}
|
|  
|  
|  
|  
| ?
| 264/175
| ?
| 98/65
|-
|-
| 118
| 118
| 715.1515
| 715.{{overline|15}}
| ?
|
| ?
| ?
| ?
| ?
| 189/125
| 121/80
| 169/112, 216/143, 286/189
|-
|-
| 119
| 119
| 721.2121
| 721.{{overline|21}}
|
|  
|  
|  
|  
| ?
| [[50/33]]
| ?
| "
|-
|-
| 120
| 120
| 727.2727
| 727.{{overline|27}}
|  
|
| ''243/160''
| [[32/21]]
| [[32/21]]
| ?
| "
| ?
| "
|-
|-
| 121
| 121
| 733.3333
| 733.{{overline|33}}
|
|  
|  
|  
|  
| ?
| 55/36, 84/55
| ?
| "
|-
|-
| 122
| 122
| 739.3939
| 739.{{overline|39}}
| ?
|
| ?
| ''192/125''
| ?
| [[49/32]]
| ?
| "
| "
|-
|-
| 123
| 123
| 745.4545
| 745.{{overline|45}}
|
|  
|  
|  
|  
| ?
| 77/50
| [[20/13]]
| [[20/13]]
|-
|-
| 124
| 124
| 751.5152
| 751.{{overline|51}}
| ?
|
| 125/81
| [[54/35]]
| [[54/35]]
| ?
| "
| ?
| "
|-
|-
| 125
| 125
| 757.5758
| 757.{{overline|57}}
|
|  
|  
|  
|  
| ?
| [[99/64]]
| ?
| 65/42
|-
|-
| 126
| 126
| 763.6364
| 763.{{overline|63}}
| ?
|
| 972/625
| [[14/9]]
| [[14/9]]
| ?
| "
| ?
| "
|-
|-
| 127
| 127
| 769.6970
| 769.{{overline|69}}
|
|  
|  
|  
|  
| ?
| 120/77
| ?
| 39/25
|-
|-
| 128
| 128
| 775.7576
| 775.{{overline|75}}
| ?
|
| ?
| ''[[25/16]]''
| ?
| 196/125
| ?
| "
| "
|-
|-
| 129
| 129
| 781.8182
| 781.{{overline|81}}
|
|  
|  
|  
|  
| [[11/7]]
| [[11/7]]
| ?
| "
|-
|-
| 130
| 130
| 787.8788
| 787.{{overline|87}}
| ?
| m6
| ''[[128/81]]''
| [[63/40]]
| [[63/40]]
| ?
| "
| [[52/33]]
| [[52/33]]
|-
|-
| 131
| 131
| 793.9394
| 793.{{overline|93}}
|
|  
|  
|  
|  
| ?
| 198/125
| ?
| 144/91
|-
|-
| 132
| 132
| 800.0000
| 800.00
| ?
|
| ''405/256''
| [[100/63]]
| [[100/63]]
| [[192/121]]
| "
| ?
| "
|-
|-
| 133
| 133
| 806.0606
| 806.{{overline|06}}
|
|  
|  
|  
|  
| ?
| [[35/22]]
| ?
| "
|-
|-
| 134
| 134
| 812.1212
| 812.{{overline|12}}
|
| '''[[8/5]]'''
| '''[[8/5]]'''
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 135
| 135
| 818.1818
| 818.{{overline|18}}
|
|  
|  
|  
|  
| ?
| 77/48
| ?
| 125/78, 130/81
|-
|-
| 136
| 136
| 824.2424
| 824.{{overline|24}}
| ?
|
| ?
| ?
| ?
| ?
| [[45/28]]
| "
| "
|-
|-
| 137
| 137
| 830.3030
| 830.{{overline|30}}
|
|  
|  
|  
|  
| ?
| [[160/99]]
| [[21/13]]
| [[21/13]]
|-
|-
| 138
| 138
| 836.3636
| 836.{{overline|36}}
| ?
|
| ?
| 81/50
| ?
| 175/108
| ?
| 196/121
| "
|-
|-
| 139
| 139
| 842.4242
| 842.{{overline|42}}
|
|  
|  
|  
|  
Line 992: Line 1,131:
|-
|-
| 140
| 140
| 848.4848
| 848.{{overline|48}}
| ?
|
| ''625/384''
| [[49/30]], [[80/49]]
| [[49/30]], [[80/49]]
| ?
| "
| ?
| "
|-
|-
| 141
| 141
| 854.5455
| 854.{{overline|54}}
|
|  
|  
|  
|  
Line 1,006: Line 1,147:
|-
|-
| 142
| 142
| 860.6061
| 860.{{overline|60}}
| ?
|
| ?
| 400/243
| ?
| 288/175
| ?
| 242/147
| "
|-
|-
| 143
| 143
| 866.6667
| 866.{{overline|66}}
|
|  
|  
|  
|  
| ?
| [[33/20]]
| [[104/63]]
| [[104/63]]
|-
|-
| 144
| 144
| 872.7273
| 872.{{overline|72}}
| ?
|
| ?
| ?
| ?
| ?
| [[81/49]]
| "
| "
|-
|-
| 145
| 145
| 878.7879
| 878.{{overline|78}}
|
|  
|  
|  
|  
| ?
| 128/77
| ?
| 108/65
|-
|-
| 146
| 146
| 884.8485
| 884.{{overline|84}}
|
| [[5/3]]
| [[5/3]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 147
| 147
| 890.9091
| 890.{{overline|90}}
|
|  
|  
|  
|  
| ?
| 147/88
| ?
| 117/70, 196/117
|-
|-
| 148
| 148
| 896.9697
| 896.{{overline|96}}
|
| ?
| ?
| [[42/25]]
| [[42/25]]
| ?
| "
| ?
| "
|-
|-
| 149
| 149
| 903.0303
| 903.{{overline|03}}
|
|  
|  
|  
|  
| ?
| 165/98
| ?
| 91/54
|-
|-
| 150
| 150
| 909.0909
| 909.{{overline|09}}
| ?
| M6
| ''[[27/16]]''
| [[320/189]]
| [[320/189]]
| ?
| "
| [[22/13]]
| [[22/13]]
|-
|-
| 151
| 151
| 915.1515
| 915.{{overline|15}}
|
|  
|  
|  
|  
| ?
| [[56/33]]
| ?
| "
|-
|-
| 152
| 152
| 921.2121
| 921.{{overline|21}}
| ?
|
| ?
| ''[[128/75]]''
| ?
| 245/144, 250/147
| ?
| "
| 143/84
|-
|-
| 153
| 153
| 927.2727
| 927.{{overline|27}}
|
|  
|  
|  
|  
| ?
| 77/45
| ?
| "
|-
|-
| 154
| 154
| 933.3333
| 933.{{overline|33}}
|
| ?
| ?
| [[12/7]]
| [[12/7]]
| ?
| "
| ?
| "
|-
|-
| 155
| 155
| 939.3939
| 939.{{overline|39}}
|
|  
|  
|  
|  
| [[55/32]]
| [[55/32]]
| ?
| "
|-
|-
| 156
| 156
| 945.4545
| 945.{{overline|45}}
| ?
|
| 216/125
| [[140/81]]
| [[140/81]]
| [[121/70]]
| [[121/70]]
| ?
| "
|-
|-
| 157
| 157
| 951.5152
| 951.{{overline|51}}
|
|  
|  
|  
|  
| ?
| 343/198, 400/231
| [[26/15]]
| [[26/15]]
|-
|-
| 158
| 158
| 957.5758
| 957.{{overline|57}}
| ?
|
| [[243/140]]
| [[125/72]]
| ?
| "
| ?
| "
| "
|-
|-
| 159
| 159
| 963.6364
| 963.{{overline|63}}
|
|  
|  
|  
|  
| [[96/55]]
| [[96/55]]
| ?
| "
|-
|-
| 160
| 160
| 969.6970
| 969.{{overline|69}}
| ?
|
| ''1280/729''
| '''[[7/4]]'''
| '''[[7/4]]'''
| ?
| "
| ?
| "
|-
|-
| 161
| 161
| 975.7576
| 975.{{overline|75}}
|
|  
|  
|  
|  
| ?
| [[44/25]]
| [[160/91]]
| "
|-
|-
| 162
| 162
| 981.8182
| 981.{{overline|81}}
| ?
|
| ?
| ''[[225/128]]''
| ?
| 432/245
| ?
| "
| 143/81, 252/143
|-
|-
| 163
| 163
| 987.8788
| 987.{{overline|87}}
|
|  
|  
|  
|  
| ?
| 99/56
| ?
| "
|-
|-
| 164
| 164
| 993.9394
| 993.{{overline|93}}
| m7
| [[16/9]]
| [[16/9]]
| ?
| "
| ?
| "
| [[39/22]]
| "
|-
|-
| 165
| 165
| 1000.0000
| 1000.00
|
|  
|  
|  
|  
| ?
| [[98/55]]
| [[162/91]]
| "
|-
|-
| 166
| 166
| 1006.0606
| 1006.{{overline|06}}
| ?
|
| ?
| ?
| ?
| ?
| [[25/14]]
| "
| "
|-
|-
| 167
| 167
| 1012.1212
| 1012.{{overline|12}}
|
|  
|  
|  
|  
| ?
| 88/49
| ?
| 70/39
|-
|-
| 168
| 168
| 1018.1818
| 1018.{{overline|18}}
|
| [[9/5]]
| [[9/5]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 169
| 169
| 1024.2424
| 1024.{{overline|24}}
|
|  
|  
|  
|  
| ?
| 231/128
| ?
| 65/36
|-
|-
| 170
| 170
| 1030.3030
| 1030.{{overline|30}}
| ?
|
| ?
| ?
| ?
| ?
| [[49/27]]
| "
| "
|-
|-
| 171
| 171
| 1036.3636
| 1036.{{overline|36}}
|
|  
|  
|  
|  
| [[20/11]]
| [[20/11]]
| ?
| "
|-
|-
| 172
| 172
| 1042.4242
| 1042.{{overline|42}}
| ?
|
| ?
| ''729/400''
| ?
| [[64/35]]
| ?
| "
| "
|-
|-
| 173
| 173
| 1048.4848
| 1048.{{overline|48}}
|
|  
|  
|  
|  
| [[11/6]]
| [[11/6]]
| ?
| "
|-
|-
| 174
| 174
| 1054.5455
| 1054.{{overline|54}}
| ?
|
| ?
| ''1152/625''
| ?
| [[90/49]]
| ?
| "
| "
|-
|-
| 175
| 175
| 1060.6061
| 1060.{{overline|60}}
|
|  
|  
|  
|  
| ?
| 231/125
| [[24/13]]
| [[24/13]]
|-
|-
| 176
| 176
| 1066.6667
| 1066.{{overline|66}}
|
| [[50/27]]
| [[50/27]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 177
| 177
| 1072.7273
| 1072.{{overline|72}}
|
|  
|  
|  
|  
| ?
| 245/132
| [[13/7]]
| [[13/7]]
|-
|-
| 178
| 178
| 1078.7879
| 1078.{{overline|78}}
|
| ?
| ?
| [[28/15]]
| [[28/15]]
| ?
| "
| ?
| "
|-
|-
| 179
| 179
| 1084.8485
| 1084.{{overline|84}}
|
|  
|  
|  
|  
| ?
| [[144/77]]
| ?
| "
|-
|-
| 180
| 180
| 1090.9091
| 1090.{{overline|90}}
|
| [[15/8]]
| [[15/8]]
| ?
| "
| ?
| "
| ?
| "
|-
|-
| 181
| 181
| 1096.9697
| 1096.{{overline|96}}
|
|  
|  
|  
|  
| ?
| [[66/35]]
| ?
| 49/26
|-
|-
| 182
| 182
| 1103.0303
| 1103.{{overline|03}}
| ?
|
| ?
| ''256/135''
| ?
| 189/100
| ?
| [[121/64]]
| 104/55
|-
|-
| 183
| 183
| 1109.0909
| 1109.{{overline|09}}
|
|  
|  
|  
|  
| ?
| 1024/539
| ?
| 91/48
|-
|-
| 184
| 184
| 1115.1515
| 1115.{{overline|15}}
| ?
| M7
| ''[[243/128]]''
| [[40/21]]
| [[40/21]]
| ?
| "
| ?
| "
|-
|-
| 185
| 185
| 1121.2121
| 1121.{{overline|21}}
|
|  
|  
|  
|  
| [[21/11]]
| [[21/11]]
| ?
| "
|-
|-
| 186
| 186
| 1127.2727
| 1127.{{overline|27}}
|
| [[48/25]]
| [[48/25]]
| ?
| "
| ?
| "
| [[121/63]]
| "
|-
|-
| 187
| 187
| 1133.3333
| 1133.{{overline|33}}
|
|  
|  
|  
|  
| ?
| 77/40
| [[25/13]], [[52/27]]
| [[25/13]], [[52/27]]
|-
|-
| 188
| 188
| 1139.3939
| 1139.{{overline|39}}
| ?
|
| 625/324
| [[27/14]]
| [[27/14]]
| ?
| "
| ?
| "
|-
|-
| 189
| 189
| 1145.4545
| 1145.{{overline|45}}
|
|  
|  
|  
|  
| [[64/33]]
| [[64/33]]
| [[126/65]]
| "
|-
|-
| 190
| 190
| 1151.5152
| 1151.{{overline|51}}
| ?
|
| 243/125
| [[35/18]]
| [[35/18]]
| ?
| "
| ?
| "
|-
|-
| 191
| 191
| 1157.5758
| 1157.{{overline|57}}
|
|  
|  
|  
|  
| ?
| ''88/45''
| [[39/20]]
| [[39/20]]
|-
|-
| 192
| 192
| 1163.6364
| 1163.{{overline|63}}
| ?
|
| 96/49, 49/25
| ''125/64''
| ?
| 49/25, 96/49
| ?
| "
| "
|-
|-
| 193
| 193
| 1169.6970
| 1169.{{overline|69}}
|
|  
|  
|  
|  
| 108/55, 55/27
| 55/28, 108/55
| ?
| "
|-
|-
| 194
| 194
| 1175.7576
| 1175.{{overline|75}}
|
| 160/81
| 160/81
| 63/32
| 63/32
| ?
| "
| 65/33, 77/39
| 65/33, 77/39
|-
|-
| 195
| 195
| 1181.8182
| 1181.{{overline|81}}
|
|  
|  
|  
|  
| 196/99, 99/50
| 99/50, 196/99
| ?
| 180/91, 208/105
|-
|-
| 196
| 196
| 1187.8788
| 1187.{{overline|87}}
|
| ?
| ?
| 125/63, 486/245
| 125/63
| 240/121
| 175/88, 240/121
| 143/72, 336/169
| 143/72
|-
|-
| 197
| 197
| 1193.9394
| 1193.{{overline|93}}
|
|  
|  
|  
|  
| 768/385, 880/441, 539/270
| 539/270, 768/385, 880/441
| 195/98, 648/325, 700/351, 363/182
| 195/98, 363/182, 648/325
|-
|-
| 198
| 198
| 1200.0000
| 1200.00
| colspan="4"| '''[[2/1]]'''
| P8
| colspan="4" | '''[[2/1]]'''
|-
|-
|}
|}


[[Category:198edo]]
[[Category:198edo]]
[[Category:Interval collection]]
[[Category:Tables of edo intervals]]

Latest revision as of 10:53, 21 January 2024

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, 325/324, 364/363
2 12.12 ? 126/125 121/120, 176/175 144/143
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 ? 125/63 175/88, 240/121 143/72
197 1193.93 539/270, 768/385, 880/441 195/98, 363/182, 648/325
198 1200.00 P8 2/1
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