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>
<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. 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.  
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.  
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|-
| 0
| 0
| 0.0000
| 0.00
| colspan="4" | '''[[1/1]]'''
| colspan="4" | '''[[1/1]]'''
|-
|-
| 1
| 1
| 6.0606
| 6.{{overline|06}}
|  
|  
|  
|  
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|-
| 2
| 2
| 12.1212
| 12.{{overline|12}}
| ?
| ?
| [[126/125]], [[245/243]]
| [[126/125]], [[245/243]]
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|-
| 3
| 3
| 18.1818
| 18.{{overline|18}}
|  
|  
|  
|  
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|-
| 4
| 4
| 24.2424
| 24.{{overline|24}}
| [[81/80]]
| [[81/80]]
| [[64/63]]
| [[64/63]]
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| 5
| 5
| 30.3030
| 30.{{overline|30}}
|  
|  
|  
|  
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|-
| 6
| 6
| 36.3636
| 36.{{overline|36}}
| ?
| ?
| [[49/48]], [[50/49]]
| [[49/48]], [[50/49]]
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| 7
| 7
| 42.4242
| 42.{{overline|42}}
|  
|  
|  
|  
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| 8
| 8
| 48.4848
| 48.{{overline|48}}
| [[250/243]]
| [[250/243]]
| [[36/35]]
| [[36/35]]
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| 9
| 9
| 54.5455
| 54.{{overline|54}}
|  
|  
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|  
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| 10
| 10
| 60.6061
| 60.{{overline|60}}
| [[648/625]]
| [[648/625]]
| [[28/27]]
| [[28/27]]
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| 11
| 11
| 66.6667
| 66.{{overline|66}}
|  
|  
|  
|  
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|-
|-
| 12
| 12
| 72.7273
| 72.{{overline|72}}
| [[25/24]]
| [[25/24]]
| ?
| ?
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| 13
| 13
| 78.7879
| 78.{{overline|78}}
|  
|  
|  
|  
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| 14
| 14
| 84.8485
| 84.{{overline|84}}
| ?
| ?
| [[21/20]]
| [[21/20]]
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| 15
| 15
| 90.9091
| 90.{{overline|90}}
|  
|  
|  
|  
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| 16
| 16
| 96.9697
| 96.{{overline|96}}
| ?
| ?
| 200/189, 343/324
| 200/189, 343/324
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| 17
| 17
| 103.0303
| 103.{{overline|03}}
|  
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| 18
| 18
| 109.0909
| 109.{{overline|09}}
| [[16/15]]
| [[16/15]]
| ?
| ?
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| 19
| 19
| 115.1515
| 115.{{overline|15}}
|  
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|  
|  
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| 20
| 20
| 121.2121
| 121.{{overline|21}}
| ?
| ?
| [[15/14]]
| [[15/14]]
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| 21
| 21
| 127.2727
| 127.{{overline|27}}
|  
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|  
|  
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| 22
| 22
| 133.3333
| 133.{{overline|33}}
| [[27/25]]
| [[27/25]]
| 175/162
| 175/162
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| 23
| 23
| 139.3939
| 139.{{overline|39}}
|  
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|  
|  
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| 24
| 24
| 145.4545
| 145.{{overline|45}}
| ?
| ?
| [[49/45]], 160/147
| [[49/45]], 160/147
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| 25
| 25
| 151.5152
| 151.{{overline|51}}
|  
|  
|  
|  
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| 26
| 26
| 157.5758
| 157.{{overline|57}}
| ?
| ?
| [[35/32]]
| [[35/32]]
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| 27
| 27
| 163.6364
| 163.{{overline|63}}
|  
|  
|  
|  
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| 28
| 28
| 169.6970
| 169.{{overline|69}}
| ?
| ?
| [[54/49]], 441/400
| [[54/49]], 441/400
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| 29
| 29
| 175.7576
| 175.{{overline|75}}
|  
|  
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| 30
| 30
| 181.8182
| 181.{{overline|81}}
| [[10/9]]
| [[10/9]]
| ?
| ?
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| 31
| 31
| 187.8788
| 187.{{overline|87}}
|  
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| 32
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| 193.9394
| 193.{{overline|93}}
| ?
| ?
| [[28/25]], 384/343
| [[28/25]], 384/343
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| 33
| 33
| 200.0000
| 200.00
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| 206.0606
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| [[9/8]]
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| 212.1212
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| 36
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| 218.1818
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| ?
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| ?
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| 37
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| 224.2424
| 224.{{overline|24}}
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| 38
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| 230.3030
| 230.{{overline|30}}
| ?
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| '''[[8/7]]'''
| '''[[8/7]]'''
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| 39
| 39
| 236.3636
| 236.{{overline|36}}
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| 40
| 40
| 242.4242
| 242.{{overline|42}}
| 144/125
| 144/125
| 147/128, 280/243
| 147/128, 280/243
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| 41
| 41
| 248.4848
| 248.{{overline|48}}
|  
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| 42
| 42
| 254.5455
| 254.{{overline|54}}
| 125/108
| 125/108
| [[81/70]]
| [[81/70]]
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| 43
| 43
| 260.6061
| 260.{{overline|60}}
|  
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| 44
| 44
| 266.6667
| 266.{{overline|66}}
| ?
| ?
| [[7/6]]
| [[7/6]]
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| 45
| 45
| 272.7273
| 272.{{overline|72}}
|  
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| 46
| 46
| 278.7879
| 278.{{overline|78}}
| ?
| ?
| ?
| ?
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| 47
| 47
| 284.8485
| 284.{{overline|84}}
|  
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| 48
| 48
| 290.9091
| 290.{{overline|90}}
| ?
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| [[189/160]]
| [[189/160]]
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| 49
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| 296.9697
| 296.{{overline|96}}
|  
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| 50
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| 303.{{overline|03}}
| ?
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| [[25/21]], 343/288
| [[25/21]], 343/288
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| 309.0909
| 309.{{overline|09}}
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| 52
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| 315.1515
| 315.{{overline|15}}
| [[6/5]]
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| 53
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| 321.2121
| 321.{{overline|21}}
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| 54
| 54
| 327.2727
| 327.{{overline|27}}
| ?
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| [[98/81]]
| [[98/81]]
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| 55
| 55
| 333.3333
| 333.{{overline|33}}
|  
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| 56
| 56
| 339.3939
| 339.{{overline|39}}
| 243/200
| 243/200
| ?
| ?
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| 57
| 57
| 345.4545
| 345.{{overline|45}}
|  
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| 58
| 58
| 351.5152
| 351.{{overline|51}}
| ?
| ?
| [[49/40]], [[60/49]]
| [[49/40]], [[60/49]]
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| 59
| 59
| 357.5757
| 357.{{overline|57}}
|  
|  
|  
|  
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| 60
| 60
| 363.6364
| 363.{{overline|63}}
| 100/81
| 100/81
| ?
| ?
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| 61
| 61
| 369.6970
| 369.{{overline|69}}
|  
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| 62
| 62
| 375.7576
| 375.{{overline|75}}
| ?
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| [[56/45]]
| [[56/45]]
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| 63
| 63
| 381.8182
| 381.{{overline|81}}
|  
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|-
| 64
| 64
| 387.8788
| 387.{{overline|87}}
| '''[[5/4]]'''
| '''[[5/4]]'''
| ?
| ?
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|-
| 65
| 65
| 393.9394
| 393.{{overline|93}}
|  
|  
|  
|  
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|-
| 66
| 66
| 400.0000
| 400.00
| ?
| ?
| [[63/50]], 432/343
| [[63/50]], 432/343
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|-
| 67
| 67
| 406.0606
| 406.{{overline|06}}
|  
|  
|  
|  
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|-
|-
| 68
| 68
| 412.1212
| 412.{{overline|12}}
| ?
| ?
| [[80/63]]
| [[80/63]]
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|-
|-
| 69
| 69
| 418.1818
| 418.{{overline|18}}
|  
|  
|  
|  
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|-
|-
| 70
| 70
| 424.2424
| 424.{{overline|24}}
| ?
| ?
| ?
| ?
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|-
|-
| 71
| 71
| 430.3030
| 430.{{overline|30}}
|  
|  
|  
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|-
| 72
| 72
| 436.3636
| 436.{{overline|36}}
| 625/486
| 625/486
| [[9/7]]
| [[9/7]]
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| 73
| 73
| 442.4242
| 442.{{overline|42}}
|  
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| 74
| 74
| 448.4848
| 448.{{overline|48}}
| 162/125
| 162/125
| [[35/27]]
| [[35/27]]
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| 75
| 75
| 454.5455
| 454.{{overline|54}}
|  
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| 76
| 76
| 460.6061
| 460.{{overline|60}}
| ?
| ?
| [[64/49]], 98/75
| [[64/49]], 98/75
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| 77
| 77
| 466.6667
| 466.{{overline|66}}
|  
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| 78
| 78
| 472.7273
| 472.{{overline|72}}
| ?
| ?
| [[21/16]]
| [[21/16]]
Line 565: Line 565:
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| 79
| 79
| 478.7879
| 478.{{overline|78}}
|  
|  
|  
|  
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| 80
| 80
| 484.8485
| 484.{{overline|84}}
| ?
| ?
| ?
| ?
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| 81
| 81
| 490.9091
| 490.{{overline|90}}
|  
|  
|  
|  
Line 586: Line 586:
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|-
| 82
| 82
| 496.9697
| 496.{{overline|96}}
| '''[[4/3]]'''
| '''[[4/3]]'''
| ?
| ?
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| 83
| 83
| 503.0303
| 503.{{overline|03}}
|  
|  
|  
|  
Line 600: Line 600:
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|-
| 84
| 84
| 509.0909
| 509.{{overline|09}}
| ?
| ?
| 343/256
| 343/256
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|-
| 85
| 85
| 515.1515
| 515.{{overline|15}}
|  
|  
|  
|  
Line 614: Line 614:
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|-
| 86
| 86
| 521.2121
| 521.{{overline|21}}
| [[27/20]]
| [[27/20]]
| ?
| ?
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|-
| 87
| 87
| 527.2727
| 527.{{overline|27}}
|  
|  
|  
|  
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| 88
| 88
| 533.3333
| 533.{{overline|33}}
| ?
| ?
| [[49/36]], 200/147
| [[49/36]], 200/147
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| 89
| 89
| 539.3939
| 539.{{overline|39}}
|  
|  
|  
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| 90
| 90
| 545.4545
| 545.{{overline|45}}
| 1000/729
| 1000/729
| [[48/35]]
| [[48/35]]
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| 91
| 91
| 551.5152
| 551.{{overline|51}}
|  
|  
|  
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| 92
| 92
| 557.5758
| 557.{{overline|57}}
| ?
| ?
| 441/320
| 441/320
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| 93
| 93
| 563.6364
| 563.{{overline|63}}
|  
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| 94
| 94
| 569.6970
| 569.{{overline|69}}
| [[25/18]]
| [[25/18]]
| ?
| ?
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| 95
| 95
| 575.7576
| 575.{{overline|75}}
|  
|  
|  
|  
Line 684: Line 684:
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|-
| 96
| 96
| 581.8182
| 581.{{overline|81}}
| ?
| ?
| [[7/5]]
| [[7/5]]
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| 97
| 97
| 587.8788
| 587.{{overline|87}}
|  
|  
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| 98
| 98
| 593.9394
| 593.{{overline|93}}
| ?
| ?
| 343/243, 800/567
| 343/243, 800/567
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| 99
| 99
| 600.0000
| 600.00
|  
|  
|  
|  
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| 100
| 100
| 606.0606
| 606.{{overline|06}}
| ?
| ?
| 486/343, 567/400
| 486/343, 567/400
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| 101
| 101
| 612.1212
| 612.{{overline|12}}
|  
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| 102
| 102
| 618.1818
| 618.{{overline|18}}
| ?
| ?
| [[10/7]]
| [[10/7]]
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| 103
| 103
| 624.2424
| 624.{{overline|24}}
|  
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| 104
| 104
| 630.3030
| 630.{{overline|30}}
| [[36/25]]
| [[36/25]]
| ?
| ?
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| 105
| 105
| 636.3636
| 636.{{overline|36}}
|  
|  
|  
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| 106
| 106
| 642.4242
| 642.{{overline|42}}
| ?
| ?
| 640/441
| 640/441
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| 107
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| 648.4848
| 648.{{overline|48}}
|  
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| 108
| 108
| 654.5455
| 654.{{overline|54}}
| 729/500
| 729/500
| [[35/24]]
| [[35/24]]
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| 109
| 109
| 660.6061
| 660.{{overline|60}}
|  
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|  
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| 110
| 110
| 666.6667
| 666.{{overline|66}}
| ?
| ?
| [[72/49]], 147/100
| [[72/49]], 147/100
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| 111
| 111
| 672.7273
| 672.{{overline|72}}
|  
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| 112
| 112
| 678.7879
| 678.{{overline|78}}
| [[40/27]]
| [[40/27]]
| ?
| ?
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| 113
| 113
| 684.8485
| 684.{{overline|84}}
|  
|  
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Line 810: Line 810:
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| 114
| 114
| 690.9091
| 690.{{overline|90}}
| ?
| ?
| 512/343
| 512/343
Line 817: Line 817:
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| 115
| 115
| 696.9697
| 696.{{overline|96}}
|  
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Line 824: Line 824:
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|-
| 116
| 116
| 703.0303
| 703.{{overline|03}}
| '''[[3/2]]'''
| '''[[3/2]]'''
| ?
| ?
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| 117
| 117
| 709.0909
| 709.{{overline|09}}
|  
|  
|  
|  
Line 838: Line 838:
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| 118
| 118
| 715.1515
| 715.{{overline|15}}
| ?
| ?
| ?
| ?
Line 845: Line 845:
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| 119
| 119
| 721.2121
| 721.{{overline|21}}
|  
|  
|  
|  
Line 852: Line 852:
|-
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| 120
| 120
| 727.2727
| 727.{{overline|27}}
|  
|  
| [[32/21]]
| [[32/21]]
Line 859: Line 859:
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| 121
| 121
| 733.3333
| 733.{{overline|33}}
|  
|  
|  
|  
Line 866: Line 866:
|-
|-
| 122
| 122
| 739.3939
| 739.{{overline|39}}
| ?
| ?
| [[49/32]], 75/49
| [[49/32]], 75/49
Line 873: Line 873:
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| 123
| 123
| 745.4545
| 745.{{overline|45}}
|  
|  
|  
|  
Line 880: Line 880:
|-
|-
| 124
| 124
| 751.5152
| 751.{{overline|51}}
| 125/81
| 125/81
| [[54/35]]
| [[54/35]]
Line 887: Line 887:
|-
|-
| 125
| 125
| 757.5758
| 757.{{overline|57}}
|  
|  
|  
|  
Line 894: Line 894:
|-
|-
| 126
| 126
| 763.6364
| 763.{{overline|63}}
| 972/625
| 972/625
| [[14/9]]
| [[14/9]]
Line 901: Line 901:
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| 127
| 127
| 769.6970
| 769.{{overline|69}}
|  
|  
|  
|  
Line 908: Line 908:
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| 128
| 128
| 775.7576
| 775.{{overline|75}}
| ?
| ?
| ?
| ?
Line 915: Line 915:
|-
|-
| 129
| 129
| 781.8182
| 781.{{overline|81}}
|  
|  
|  
|  
Line 922: Line 922:
|-
|-
| 130
| 130
| 787.8788
| 787.{{overline|87}}
| ?
| ?
| [[63/40]]
| [[63/40]]
Line 929: Line 929:
|-
|-
| 131
| 131
| 793.9394
| 793.{{overline|93}}
|  
|  
|  
|  
Line 936: Line 936:
|-
|-
| 132
| 132
| 800.0000
| 800.00
| ?
| ?
| [[100/63]], 343/216
| [[100/63]], 343/216
Line 943: Line 943:
|-
|-
| 133
| 133
| 806.0606
| 806.{{overline|06}}
|  
|  
|  
|  
Line 950: Line 950:
|-
|-
| 134
| 134
| 812.1212
| 812.{{overline|12}}
| '''[[8/5]]'''
| '''[[8/5]]'''
| ?
| ?
Line 957: Line 957:
|-
|-
| 135
| 135
| 818.1818
| 818.{{overline|18}}
|  
|  
|  
|  
Line 964: Line 964:
|-
|-
| 136
| 136
| 824.2424
| 824.{{overline|24}}
| ?
| ?
| [[45/28]]
| [[45/28]]
Line 971: Line 971:
|-
|-
| 137
| 137
| 830.3030
| 830.{{overline|30}}
|  
|  
|  
|  
Line 978: Line 978:
|-
|-
| 138
| 138
| 836.3636
| 836.{{overline|36}}
| 81/50
| 81/50
| ?
| ?
Line 985: Line 985:
|-
|-
| 139
| 139
| 842.4242
| 842.{{overline|42}}
|  
|  
|  
|  
Line 992: Line 992:
|-
|-
| 140
| 140
| 848.4848
| 848.{{overline|48}}
| ?
| ?
| [[49/30]], [[80/49]]
| [[49/30]], [[80/49]]
Line 999: Line 999:
|-
|-
| 141
| 141
| 854.5455
| 854.{{overline|54}}
|  
|  
|  
|  
Line 1,006: Line 1,006:
|-
|-
| 142
| 142
| 860.6061
| 860.{{overline|60}}
| 400/243
| 400/243
| ?
| ?
Line 1,013: Line 1,013:
|-
|-
| 143
| 143
| 866.6667
| 866.{{overline|66}}
|  
|  
|  
|  
Line 1,020: Line 1,020:
|-
|-
| 144
| 144
| 872.7273
| 872.{{overline|72}}
| ?
| ?
| [[81/49]]
| [[81/49]]
Line 1,027: Line 1,027:
|-
|-
| 145
| 145
| 878.7879
| 878.{{overline|78}}
|  
|  
|  
|  
Line 1,034: Line 1,034:
|-
|-
| 146
| 146
| 884.8485
| 884.{{overline|84}}
| [[5/3]]
| [[5/3]]
| ?
| ?
Line 1,041: Line 1,041:
|-
|-
| 147
| 147
| 890.9091
| 890.{{overline|90}}
|  
|  
|  
|  
Line 1,048: Line 1,048:
|-
|-
| 148
| 148
| 896.9697
| 896.{{overline|96}}
| ?
| ?
| [[42/25]], 576/343
| [[42/25]], 576/343
Line 1,055: Line 1,055:
|-
|-
| 149
| 149
| 903.0303
| 903.{{overline|03}}
|  
|  
|  
|  
Line 1,062: Line 1,062:
|-
|-
| 150
| 150
| 909.0909
| 909.{{overline|09}}
| ?
| ?
| [[320/189]]
| [[320/189]]
Line 1,069: Line 1,069:
|-
|-
| 151
| 151
| 915.1515
| 915.{{overline|15}}
|  
|  
|  
|  
Line 1,076: Line 1,076:
|-
|-
| 152
| 152
| 921.2121
| 921.{{overline|21}}
| ?
| ?
| ?
| ?
Line 1,083: Line 1,083:
|-
|-
| 153
| 153
| 927.2727
| 927.{{overline|27}}
|  
|  
|  
|  
Line 1,090: Line 1,090:
|-
|-
| 154
| 154
| 933.3333
| 933.{{overline|33}}
| ?
| ?
| [[12/7]]
| [[12/7]]
Line 1,097: Line 1,097:
|-
|-
| 155
| 155
| 939.3939
| 939.{{overline|39}}
|  
|  
|  
|  
Line 1,104: Line 1,104:
|-
|-
| 156
| 156
| 945.4545
| 945.{{overline|45}}
| 216/125
| 216/125
| [[140/81]]
| [[140/81]]
Line 1,111: Line 1,111:
|-
|-
| 157
| 157
| 951.5152
| 951.{{overline|51}}
|  
|  
|  
|  
Line 1,118: Line 1,118:
|-
|-
| 158
| 158
| 957.5758
| 957.{{overline|57}}
| 125/72
| 125/72
| 243/140, 256/147
| 243/140, 256/147
Line 1,125: Line 1,125:
|-
|-
| 159
| 159
| 963.6364
| 963.{{overline|63}}
|  
|  
|  
|  
Line 1,132: Line 1,132:
|-
|-
| 160
| 160
| 969.6970
| 969.{{overline|69}}
| ?
| ?
| '''[[7/4]]'''
| '''[[7/4]]'''
Line 1,139: Line 1,139:
|-
|-
| 161
| 161
| 975.7576
| 975.{{overline|75}}
|  
|  
|  
|  
Line 1,146: Line 1,146:
|-
|-
| 162
| 162
| 981.8182
| 981.{{overline|81}}
| ?
| ?
| ?
| ?
Line 1,153: Line 1,153:
|-
|-
| 163
| 163
| 987.8788
| 987.{{overline|87}}
|  
|  
|  
|  
Line 1,160: Line 1,160:
|-
|-
| 164
| 164
| 993.9394
| 993.{{overline|93}}
| [[16/9]]
| [[16/9]]
| ?
| ?
Line 1,167: Line 1,167:
|-
|-
| 165
| 165
| 1000.0000
| 1000.00
|  
|  
|  
|  
Line 1,174: Line 1,174:
|-
|-
| 166
| 166
| 1006.0606
| 1006.{{overline|06}}
| ?
| ?
| [[25/14]], 343/192
| [[25/14]], 343/192
Line 1,181: Line 1,181:
|-
|-
| 167
| 167
| 1012.1212
| 1012.{{overline|12}}
|  
|  
|  
|  
Line 1,188: Line 1,188:
|-
|-
| 168
| 168
| 1018.1818
| 1018.{{overline|18}}
| [[9/5]]
| [[9/5]]
| ?
| ?
Line 1,195: Line 1,195:
|-
|-
| 169
| 169
| 1024.2424
| 1024.{{overline|24}}
|  
|  
|  
|  
Line 1,202: Line 1,202:
|-
|-
| 170
| 170
| 1030.3030
| 1030.{{overline|30}}
| ?
| ?
| [[49/27]], 800/441
| [[49/27]], 800/441
Line 1,209: Line 1,209:
|-
|-
| 171
| 171
| 1036.3636
| 1036.{{overline|36}}
|  
|  
|  
|  
Line 1,216: Line 1,216:
|-
|-
| 172
| 172
| 1042.4242
| 1042.{{overline|42}}
| ?
| ?
| [[64/35]]
| [[64/35]]
Line 1,223: Line 1,223:
|-
|-
| 173
| 173
| 1048.4848
| 1048.{{overline|48}}
|  
|  
|  
|  
Line 1,230: Line 1,230:
|-
|-
| 174
| 174
| 1054.5455
| 1054.{{overline|54}}
| ?
| ?
| [[90/49]], 147/80
| [[90/49]], 147/80
Line 1,237: Line 1,237:
|-
|-
| 175
| 175
| 1060.6061
| 1060.{{overline|60}}
|  
|  
|  
|  
Line 1,244: Line 1,244:
|-
|-
| 176
| 176
| 1066.6667
| 1066.{{overline|66}}
| [[50/27]]
| [[50/27]]
| 384/175
| 384/175
Line 1,251: Line 1,251:
|-
|-
| 177
| 177
| 1072.7273
| 1072.{{overline|72}}
|  
|  
|  
|  
Line 1,258: Line 1,258:
|-
|-
| 178
| 178
| 1078.7879
| 1078.{{overline|78}}
| ?
| ?
| [[28/15]]
| [[28/15]]
Line 1,265: Line 1,265:
|-
|-
| 179
| 179
| 1084.8485
| 1084.{{overline|84}}
|  
|  
|  
|  
Line 1,272: Line 1,272:
|-
|-
| 180
| 180
| 1090.9091
| 1090.{{overline|90}}
| [[15/8]]
| [[15/8]]
| ?
| ?
Line 1,279: Line 1,279:
|-
|-
| 181
| 181
| 1096.9697
| 1096.{{overline|96}}
|  
|  
|  
|  
Line 1,286: Line 1,286:
|-
|-
| 182
| 182
| 1103.0303
| 1103.{{overline|03}}
| ?
| ?
| 189/100, 648/343
| 189/100, 648/343
Line 1,293: Line 1,293:
|-
|-
| 183
| 183
| 1109.0909
| 1109.{{overline|09}}
|  
|  
|  
|  
Line 1,300: Line 1,300:
|-
|-
| 184
| 184
| 1115.1515
| 1115.{{overline|15}}
| ?
| ?
| [[40/21]]
| [[40/21]]
Line 1,307: Line 1,307:
|-
|-
| 185
| 185
| 1121.2121
| 1121.{{overline|21}}
|  
|  
|  
|  
Line 1,314: Line 1,314:
|-
|-
| 186
| 186
| 1127.2727
| 1127.{{overline|27}}
| [[48/25]]
| [[48/25]]
| ?
| ?
Line 1,321: Line 1,321:
|-
|-
| 187
| 187
| 1133.3333
| 1133.{{overline|33}}
|  
|  
|  
|  
Line 1,328: Line 1,328:
|-
|-
| 188
| 188
| 1139.3939
| 1139.{{overline|39}}
| 625/324
| 625/324
| [[27/14]]
| [[27/14]]
Line 1,335: Line 1,335:
|-
|-
| 189
| 189
| 1145.4545
| 1145.{{overline|45}}
|  
|  
|  
|  
Line 1,342: Line 1,342:
|-
|-
| 190
| 190
| 1151.5152
| 1151.{{overline|51}}
| 243/125
| 243/125
| [[35/18]]
| [[35/18]]
Line 1,349: Line 1,349:
|-
|-
| 191
| 191
| 1157.5758
| 1157.{{overline|57}}
|  
|  
|  
|  
Line 1,356: Line 1,356:
|-
|-
| 192
| 192
| 1163.6364
| 1163.{{overline|63}}
| ?
| ?
| 96/49, 49/25
| 96/49, 49/25
Line 1,363: Line 1,363:
|-
|-
| 193
| 193
| 1169.6970
| 1169.{{overline|69}}
|  
|  
|  
|  
Line 1,370: Line 1,370:
|-
|-
| 194
| 194
| 1175.7576
| 1175.{{overline|75}}
| 160/81
| 160/81
| 63/32
| 63/32
Line 1,377: Line 1,377:
|-
|-
| 195
| 195
| 1181.8182
| 1181.{{overline|81}}
|  
|  
|  
|  
Line 1,384: Line 1,384:
|-
|-
| 196
| 196
| 1187.8788
| 1187.{{overline|87}}
| ?
| ?
| 125/63, 486/245
| 125/63, 486/245
Line 1,391: Line 1,391:
|-
|-
| 197
| 197
| 1193.9394
| 1193.{{overline|93}}
|  
|  
|  
|  
Line 1,398: Line 1,398:
|-
|-
| 198
| 198
| 1200.0000
| 1200.00
| colspan="4" | '''[[2/1]]'''
| colspan="4" | '''[[2/1]]'''
|-
|-

Revision as of 15:11, 9 November 2020

This article is a work in progress.

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. 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.

# Cents 5 limit 7 limit 11 limit 13 limit
0 0.00 1/1
1 6.06 385/384, 441/440, 540/539 196/195, 325/324, 351/350, 364/363
2 12.12 ? 126/125, 245/243 121/120 144/143, 169/168
3 18.18 99/98, 100/99 ?
4 24.24 81/80 64/63 245/242 66/65, 78/77
5 30.30 55/54, 56/55 ?
6 36.36 ? 49/48, 50/49 ? ?
7 42.42 ? 40/39
8 48.48 250/243 36/35 ? ?
9 54.54 33/32 65/63
10 60.60 648/625 28/27 ? ?
11 66.66 80/77 26/25, 27/26
12 72.72 25/24 ? 126/121 ?
13 78.78 22/21 ?
14 84.84 ? 21/20 ? ?
15 90.90 ? 96/91
16 96.96 ? 200/189, 343/324 128/121 ?
17 103.03 35/33 ?
18 109.09 16/15 ? ? ?
19 115.15 ? ?
20 121.21 ? 15/14 ? ?
21 127.27 ? 14/13
22 133.33 27/25 175/162 ? ?
23 139.39 ? 13/12
24 145.45 ? 49/45, 160/147 ? ?
25 151.51 12/11 ?
26 157.57 ? 35/32 ? ?
27 163.63 11/10 ?
28 169.69 ? 54/49, 441/400 ? ?
29 175.75 ? ?
30 181.81 10/9 ? ? ?
31 187.87 ? ?
32 193.93 ? 28/25, 384/343 121/108 ?
33 200.00 ? 91/81
34 206.06 9/8 ? ? 44/39
35 212.12 ? ?
36 218.18 ? ? ? ?
37 224.24 ? 91/80
38 230.30 ? 8/7 ? ?
39 236.36 55/48 ?
40 242.42 144/125 147/128, 280/243 ? ?
41 248.48 ? 15/13
42 254.54 125/108 81/70 140/121 ?
43 260.60 64/55 ?
44 266.66 ? 7/6 ? ?
45 272.72 ? ?
46 278.78 ? ? ? ?
47 284.84 33/28 ?
48 290.90 ? 189/160 ? 13/11
49 296.96 ? ?
50 303.03 ? 25/21, 343/288 144/121 ?
51 309.09 ? ?
52 315.15 6/5 ? ? ?
53 321.21 ? ?
54 327.27 ? 98/81 ? ?
55 333.33 ? 63/52
56 339.39 243/200 ? ? ?
57 345.45 11/9 39/32
58 351.51 ? 49/40, 60/49 ? ?
59 357.57 27/22 16/13
60 363.63 100/81 ? ? ?
61 369.69 ? 26/21
62 375.75 ? 56/45 ? ?
63 381.81 ? ?
64 387.87 5/4 ? ? ?
65 393.93 ? ?
66 400.00 ? 63/50, 432/343 121/96 ?
67 406.06 ? ?
68 412.12 ? 80/63 ? 33/26
69 418.18 14/11 ?
70 424.24 ? ? ? ?
71 430.30 ? ?
72 436.36 625/486 9/7 ? ?
73 442.42 128/99 ?
74 448.48 162/125 35/27 ? ?
75 454.54 ? 13/10
76 460.60 ? 64/49, 98/75 ? ?
77 466.66 ? ?
78 472.72 ? 21/16 ? ?
79 478.78 ? ?
80 484.84 ? ? ? ?
81 490.90 ? ?
82 496.96 4/3 ? ? ?
83 503.03 ? ?
84 509.09 ? 343/256 ? ?
85 515.15 ? ?
86 521.21 27/20 ? ? ?
87 527.27 ? ?
88 533.33 ? 49/36, 200/147 ? ?
89 539.39 15/11 ?
90 545.45 1000/729 48/35 ? ?
91 551.51 11/8 ?
92 557.57 ? 441/320 ? ?
93 563.63 ? 18/13
94 569.69 25/18 ? ? ?
95 575.75 ? ?
96 581.81 ? 7/5 ? ?
97 587.87 ? ?
98 593.93 ? 343/243, 800/567 ? ?
99 600.00 99/70, 140/99 ?
100 606.06 ? 486/343, 567/400 ? ?
101 612.12 ? ?
102 618.18 ? 10/7 ? ?
103 624.24 ? ?
104 630.30 36/25 ? ? ?
105 636.36 ? 13/9
106 642.42 ? 640/441 ? ?
107 648.48 16/11 ?
108 654.54 729/500 35/24 ? ?
109 660.60 22/15 ?
110 666.66 ? 72/49, 147/100 ? ?
111 672.72 ? ?
112 678.78 40/27 ? ? ?
113 684.84 ? ?
114 690.90 ? 512/343 ? ?
115 696.96 ? ?
116 703.03 3/2 ? ? ?
117 709.09 ? ?
118 715.15 ? ? ? ?
119 721.21 ? ?
120 727.27 32/21 ? ?
121 733.33 ? ?
122 739.39 ? 49/32, 75/49 ? ?
123 745.45 ? 20/13
124 751.51 125/81 54/35 ? ?
125 757.57 99/64 ?
126 763.63 972/625 14/9 ? ?
127 769.69 ? ?
128 775.75 ? ? ? ?
129 781.81 11/7 ?
130 787.87 ? 63/40 ? 52/33
131 793.93 ? ?
132 800.00 ? 100/63, 343/216 192/121 ?
133 806.06 ? ?
134 812.12 8/5 ? ? ?
135 818.18 ? ?
136 824.24 ? 45/28 ? ?
137 830.30 ? 21/13
138 836.36 81/50 ? ? ?
139 842.42 44/27 13/8
140 848.48 ? 49/30, 80/49 ? ?
141 854.54 18/11 64/39
142 860.60 400/243 ? ? ?
143 866.66 ? 104/63
144 872.72 ? 81/49 ? ?
145 878.78 ? ?
146 884.84 5/3 ? ? ?
147 890.90 ? ?
148 896.96 ? 42/25, 576/343 121/72 ?
149 903.03 ? ?
150 909.09 ? 320/189 ? 22/13
151 915.15 56/33 ?
152 921.21 ? ? ? ?
153 927.27 ? ?
154 933.33 ? 12/7 ? ?
155 939.39 55/32 ?
156 945.45 216/125 140/81 121/70 ?
157 951.51 ? 26/15
158 957.57 125/72 243/140, 256/147 ? ?
159 963.63 96/55 ?
160 969.69 ? 7/4 ? ?
161 975.75 ? 160/91
162 981.81 ? ? ? ?
163 987.87 ? ?
164 993.93 16/9 ? ? 39/22
165 1000.00 ? 162/91
166 1006.06 ? 25/14, 343/192 216/121 ?
167 1012.12 ? ?
168 1018.18 9/5 ? ? ?
169 1024.24 ? ?
170 1030.30 ? 49/27, 800/441 ? ?
171 1036.36 20/11 ?
172 1042.42 ? 64/35 ? ?
173 1048.48 11/6 ?
174 1054.54 ? 90/49, 147/80 ? ?
175 1060.60 ? 24/13
176 1066.66 50/27 384/175 ? ?
177 1072.72 ? 13/7
178 1078.78 ? 28/15 ? ?
179 1084.84 ? ?
180 1090.90 15/8 ? ? ?
181 1096.96 66/35 ?
182 1103.03 ? 189/100, 648/343 121/64 ?
183 1109.09 ? 91/48
184 1115.15 ? 40/21 ? ?
185 1121.21 21/11 ?
186 1127.27 48/25 ? 121/63 ?
187 1133.33 77/40 25/13, 52/27
188 1139.39 625/324 27/14 ? ?
189 1145.45 64/33 126/65
190 1151.51 243/125 35/18 ? ?
191 1157.57 ? 39/20
192 1163.63 ? 96/49, 49/25 ? ?
193 1169.69 108/55, 55/27 ?
194 1175.75 160/81 63/32 484/245 65/33, 77/39
195 1181.81 196/99, 99/50 ?
196 1187.87 ? 125/63, 486/245 240/121 143/72, 336/169
197 1193.93 768/385, 880/441, 539/270 195/98, 648/325, 700/351, 363/182
198 1200.00 2/1
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