Xenharmonic Wiki

Table of 99edo intervals: Difference between revisions

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Overhaul to accommodate higher limit extensions and the variable mappings for 11 and 13
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Assuming the 13-limit patent val {{val|99 157 230 278 342 366}}.  
This table of [[99edo]] intervals assumes the 99ef val {{val| 99 157 230 278 '''343 367''' 405 421 448 481 }} as tending sharp and 99 patent val {{val| 99 157 230 278 '''342 366''' 405 421 448 481 }} as tending flat. Prime harmonics and subharmonics are labeled in '''bold'''.  


{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
|-
! Step
! #
! Cents
! Cents
! Five limit
! 5-limit
! Seven limit
! 7-limit
! Eleven limit
! 13-limit Extension<br>(Tending Sharp)
! Thirteen limit
! 13-limit Extension<br>(Tending Flat)
! Higher Limit Extension
|-
|-
| | 1
| 0
|12.121
| 0.00
| | 2048/2025
| colspan="5" | '''1/1'''
| | 126/125
| | 99/98
| | 91/90
|-
|-
| | 2
| 1
|24.242
| 12.{{overline|12}}
| | 81/80
| 2048/2025
| | 64/63
| 126/125
| colspan="2" | 55/54
|  
|  
|  
|-
|-
| | 3
| 2
|36.364
| 24.{{overline|24}}
| | 128/125
| 81/80
| colspan="3" | 49/48
| 64/63
| 56/55, 66/65, 78/77
| 55/54, 66/65, 78/77
| 58/57, 69/68, 70/69, 76/75
|-
|-
| | 4
| 3
|48.485
| 36.{{overline|36}}
| | 250/243
| 128/125
| | 36/35
| 49/48, 50/49
| colspan="2" | 33/32
| 40/39, 45/44, 55/54
| 56/55
| 46/45, 51/50, 57/56
|-
|-
| | 5
| 4
|60.606
| 48.{{overline|48}}
| | 648/625
| 250/243
| colspan="2" | 28/27
| 36/35
| | 26/25
|  
| 33/32, 40/39, 45/44
| 35/34
|-
|-
| | 6
| 5
|72.727
| 60.{{overline|60}}
| colspan="2"| 25/24
| 648/625
| colspan="2" | 22/21
| 28/27
| 27/26, 33/32
| 26/25
| 29/28, 30/29
|-
|-
| | 7
| 6
|84.848
| 72.{{overline|72}}
| | 256/243
| 25/24
| colspan="3" | 21/20
| 26/25
|  
| 22/21, 27/26
| 24/23
|-
|-
| | 8
| 7
|96.970
| 84.{{overline|84}}
| colspan="2" | 135/128
| 256/243
| | 81/77
| 21/20
| | 52/49
| 22/21
|  
| 20/19
|-
|-
| | 9
| 8
|109.091
| 96.{{overline|96}}
| colspan="4" | 16/15
| 135/128
| "
|
|
| 18/17, 19/18
|-
|-
| | 10
| 9
|121.212
| 109.{{overline|09}}
| | 2187/2048
| 16/15
| colspan="3" | 15/14
| "
|
|
| '''17/16'''
|-
|-
| | 11
| 10
|133.333
| 121.{{overline|21}}
| colspan="3" | 27/25
| 2187/2048
| | 13/12
| 15/14
| 14/13
|  
| 29/27
|-
|-
| | 12
| 11
|145.455
| 133.{{overline|33}}
| | 625/576
| 27/25
| colspan="3" | 49/45
| "
|
| 13/12, 14/13
|
|-
|-
| | 13
| 12
|157.576
| 145.{{overline|45}}
| | 800/729
| 625/576
| | 35/32
| 49/45
| colspan="2" | 11/10
| 12/11, 13/12
|  
|  
|-
|-
| | 14
| 13
|169.697
| 157.{{overline|57}}
| | 1125/1024
| 800/729
| colspan="3" | 54/49
| 35/32
|  
| 11/10, 12/11
| 23/21
|-
|-
| | 15
| 14
|181.818
| 169.{{overline|69}}
| colspan="4" | 10/9
| 1125/1024
| 54/49
| 11/10
|
| 21/19, '''32/29'''
|-
|-
| | 16
| 15
|193.939
| 181.{{overline|81}}
| | 4096/3645
| 10/9
| colspan="3" | 28/25
| "
|
|
|  
|-
|-
| | 17
| 16
|206.061
| 193.{{overline|93}}
| colspan="4" | 9/8
| 4096/3645
| 28/25
|  
|  
| 19/17
|-
|-
| | 18
| 17
|218.182
| 206.{{overline|06}}
| | 256/225
| 9/8
| | 245/216
| "
| | 112/99
|  
| | 91/80
|  
|  
|-
|-
| | 19
| 18
|230.303
| 218.{{overline|18}}
| | 729/640
| 256/225
| colspan="3" | 8/7
| 245/216
| 25/22
|  
| 17/15
|-
|-
| | 20
| 19
|242.424
| 230.{{overline|30}}
| | 144/125
| 729/640
| | 144/125
| '''8/7'''
| | 63/55
|  
| | 52/45
| 25/22
|  
|-
|-
| | 21
| 20
|254.545
| 242.{{overline|42}}
| | 125/108
| 144/125
| colspan="2" | 81/70
| "
| | 15/13
| 15/13
|  
| 23/20
|-
|-
| | 22
| 21
|266.667
| 254.{{overline|54}}
| | 729/625
| 125/108
| colspan="3" | 7/6
| 81/70
|  
| 15/13
|
|-
|-
| | 23
| 22
|278.788
| 266.{{overline|66}}
| colspan="2" | 75/64
| 729/625
| colspan="2" | 33/28
| 7/6
|
|  
|  
|-
|-
| | 24
| 23
|290.909
| 278.{{overline|78}}
| colspan="3" | 32/27
| 75/64
| | 13/11
| "
|
| 33/28
| 20/17, 27/23, 34/29
|-
|-
| | 25
| 24
|303.030
| 290.{{overline|90}}
| | 1215/1024
| 32/27
| colspan="3" | 25/21
| "
| 13/11, 33/28
| 13/11
|
|-
|-
| | 26
| 25
|315.152
| 303.{{overline|03}}
| colspan="4" | 6/5
| 1215/1024
| 25/21
|  
|  
| '''19/16'''
|-
|-
| | 27
| 26
|327.273
| 315.{{overline|15}}
| | 3125/2592
| 6/5
| colspan="2" | 98/81
| "
| | 91/75
|  
|  
|  
|-
|-
| | 28
| 27
|339.394
| 327.{{overline|27}}
| | 243/200
| 3125/2592
| | 128/105
| 98/81
| colspan="2" | 11/9
| 40/33
|  
| 23/19, 29/24
|-
|-
| | 29
| 28
|351.515
| 339.{{overline|39}}
| | 625/512
| 243/200
| colspan="3" | 49/40
| 128/105
|  
| 11/9, 39/32, 40/33
| 17/14, 28/23
|-
|-
| | 30
| 29
|363.636
| 351.{{overline|51}}
| | 100/81
| 625/512
| | 100/81
| 49/40, 60/49
| | 27/22
| 11/9, '''16/13''', 27/22, 39/32
| | 16/13
|  
|  
|-
|-
| | 31
| 30
|375.758
| 363.{{overline|63}}
| | 3888/3125
| 100/81
| colspan="3" | 56/45
| "
|
| '''16/13''', 26/21, 27/22
| 21/17
|-
|-
| | 32
| 31
|387.879
| 375.{{overline|75}}
| colspan="4" | 5/4
| 3888/3125
| 56/45
| 26/21
|  
| 36/29
|-
|-
| | 33
| 32
|400
| 387.{{overline|87}}
| | 512/405
| '''5/4'''
| colspan="2" | 63/50
| "
| | 49/39
|  
|  
|  
|-
|-
| | 34
| 33
|412.121
| 400.00
| | 81/64
| 512/405
| | 80/63
| 63/50
| | 80/63
|  
| | 33/26
|  
| 24/19, 29/23
|-
|-
| | 35
| 34
|424.242
| 412.{{overline|12}}
| | 32/25
| 81/64
| | 32/25
| 80/63
| colspan="2" | 14/11
| 14/11, 33/26
| 33/26
| 19/15
|-
|-
| | 36
| 35
|436.364
| 424.{{overline|24}}
| | 625/486
| 32/25
| colspan="3" | 9/7
| "
|
| 14/11
| 23/18
|-
|-
| | 37
| 36
|448.485
| 436.{{overline|36}}
| | 162/125
| 625/486
| colspan="2" | 35/27
| 9/7
| | 13/10
|  
|  
|  
|-
|-
| | 38
| 37
|460.606
| 448.{{overline|48}}
| | 125/96
| 162/125
| | 64/49
| 35/27
| colspan="2" | 55/42
|  
| 13/10
|  
|-
|-
| | 39
| 38
|472.727
| 460.{{overline|60}}
| | 320/243
| 125/96
| colspan="3" | 21/16
| 64/49
| 13/10
|  
| 30/23
|-
|-
| | 40
| 39
|484.848
| 472.{{overline|72}}
| | 675/512
| 320/243
| colspan="2" | 250/189
| 21/16
| | 65/49
|  
| 33/25
| 38/29
|-
|-
| | 41
| 40
|496.970
| 484.{{overline|84}}
| colspan="4" | 4/3
| 675/512
| 250/189
| 33/25
|
|
|-
|-
| | 42
| 41
|509.091
| 496.{{overline|96}}
| | 8192/6075
| '''4/3'''
| | 75/56
| "
| colspan="2" | 66/49
|  
|  
|  
|-
|-
| | 43
| 42
|521.212
| 509.{{overline|09}}
| colspan="4" | 27/20
| 8192/6075
| 75/56
|  
|  
| 51/38
|-
|-
| | 44
| 43
|533.333
| 521.{{overline|21}}
| | 512/375
| 27/20
| colspan="3" | 49/36
| "
|
|
| 23/17
|-
|-
| | 45
| 44
|545.455
| 533.{{overline|33}}
| | 1000/729
| 512/375
| | 48/35
| 49/36
| colspan="2" | 11/8
| 15/11
|  
|  
|-
|-
| | 46
| 45
|557.576
| 545.{{overline|45}}
| | 864/625
| 1000/729
| colspan="2" | 112/81
| 48/35
| | 91/66
|  
| '''11/8''', 15/11
|  
|-
|-
| | 47
| 46
|569.697
| 557.{{overline|57}}
| colspan="3" | 25/18
| 864/625
| | 18/13
| 112/81
| '''11/8''', 18/13
|  
| 29/21, 40/29
|-
|-
| | 48
| 47
|581.818
| 569.{{overline|69}}
| | 1024/729
| 25/18
| colspan="3" | 7/5
| "
|
| 18/13
| '''32/23'''
|-
|-
| | 49
| 48
|593.939
| 581.{{overline|81}}
| colspan="4" | 45/32
| 1024/729
| 7/5
|
|
|
|-
|-
| | 50
| 49
|606.061
| 593.{{overline|93}}
| colspan="4" | 64/45
| 45/32
| "
|
|
| 24/17, 38/27
|-
|-
| | 51
| 50
|618.182
| 606.{{overline|06}}
| | 729/512
| 64/45
| colspan="3" | 10/7
| "
|
|
| 17/12, 27/19
|-
|-
| | 52
| 51
|630.303
| 618.{{overline|18}}
| colspan="3" | 36/25
| 729/512
| | 13/9
| 10/7
|
|  
|  
|-
|-
| | 53
| 52
|642.424
| 630.{{overline|30}}
| | 625/432
| 36/25
| colspan="2" | 81/56
| "
| | 75/52
|
| 13/9
| '''23/16'''
|-
|-
| | 54
| 53
|654.545
| 642.{{overline|42}}
| | 729/500
| 625/432
| | 35/24
| 81/56
| colspan="2" | 16/11
| '''16/11'''
|  
| 29/20, 42/29
|-
|-
| | 55
| 54
|666.667
| 654.{{overline|54}}
| | 375/256
| 729/500
| colspan="3" | 72/49
| 35/24
|  
| '''16/11''', 22/15
|
|-
|-
| | 56
| 55
|678.788
| 666.{{overline|66}}
| colspan="4" | 40/27
| 375/256
| 72/49
| 22/15
|
|
|-
|-
| | 57
| 56
|690.909
| 678.{{overline|78}}
| | 6075/4096
| 40/27
| | 112/75
| "
| colspan="2" | 49/33
|  
|  
| 34/23
|-
|-
| | 58
| 57
|703.030
| 690.{{overline|90}}
| colspan="4" | 3/2
| 6075/4096
| 112/75
|  
|  
| 76/51
|-
|-
| | 59
| 58
|715.152
| 703.{{overline|03}}
| | 1024/675
| '''3/2'''
| colspan="2" | 189/125
| "
| | 91/60
|  
|  
|  
|-
|-
| | 60
| 59
|727.273
| 715.{{overline|15}}
| | 243/160
| 1024/675
| colspan="3" | 32/21
| 189/125
| 50/33
|
|  
|-
|-
| | 61
| 60
|739.394
| 727.{{overline|27}}
| | 192/125
| 243/160
| colspan="3" | 49/32
| 32/21
|  
| 50/33
| 29/19
|-
|-
| | 62
| 61
|751.515
| 739.{{overline|39}}
| | 125/81
| 192/125
| colspan="2" | 54/35
| 49/32
| | 20/13
| 20/13
|  
| 23/15
|-
|-
| | 63
| 62
|763.636
| 751.{{overline|51}}
| | 972/625
| 125/81
| colspan="3" | 14/9
| 54/35
|  
| 20/13
|
|-
|-
| | 64
| 63
|775.758
| 763.{{overline|63}}
| colspan="2" | 25/16
| 972/625
| colspan="2" | 11/7
| 14/9
|
|  
|  
|-
|-
| | 65
| 64
|787.879
| 775.{{overline|75}}
| | 128/81
| 25/16
| colspan="2" | 63/40
| "
| | 52/33
|
| 11/7
| 36/23
|-
|-
| | 66
| 65
|800
| 787.{{overline|87}}
| | 405/256
| 128/81
| colspan="2" | 100/63
| 63/40
| | 78/49
| 11/7, 52/33
| 52/33
|  
|-
|-
| | 67
| 66
|812.121
| 800.00
| colspan="4" | 8/5
| 405/256
| 100/63
|  
|  
| 27/17, 46/29
|-
|-
| | 68
| 67
|824.242
| 812.{{overline|12}}
| | 3125/1944
| '''8/5'''
| colspan="3" | 45/28
| "
|
|
|  
|-
|-
| | 69
| 68
|836.364
| 824.{{overline|24}}
| colspan="2" | 81/50
| 3125/1944
| | 44/27
| 45/28
| | 13/8
| 21/13
|  
| 29/18
|-
|-
| | 70
| 69
|848.485
| 836.{{overline|36}}
| | 625/384
| 81/50
| colspan="3" | 49/30
| "
|
| '''13/8''', 21/13, 44/27
| 34/21
|-
|-
| | 71
| 70
|860.606
| 848.{{overline|48}}
| | 400/243
| 625/384
| | 105/64
| 49/30, 80/49
| colspan="2" | 18/11
| '''13/8''', 18/11, 44/27, 64/39
|  
|  
|-
|-
| | 72
| 71
|872.727
| 860.{{overline|60}}
| | 3375/2048
| 400/243
| colspan="3" | 81/49
| 105/64
|  
| 18/11, 33/20, 64/39
| 28/17, 23/14
|-
|-
| | 73
| 72
|884.848
| 872.{{overline|72}}
| colspan="4" | 5/3
| 3375/2048
| 81/49
| 33/20
|  
| 38/23, 48/29
|-
|-
| | 74
| 73
|896.970
| 884.{{overline|84}}
| | 2048/1215
| 5/3
| colspan="3" | 42/25
| "
|
|
|  
|-
|-
| | 75
| 74
|909.091
| 896.{{overline|96}}
| colspan="3" | 27/16
| 2048/1215
| | 22/13
| 42/25
|  
|
| '''32/19'''
|-
|-
| | 76
| 75
|921.212
| 909.{{overline|09}}
| colspan="2" | 128/75
| 27/16
| colspan="2" | 56/33
| "
| 22/13, 56/33
| 22/13
|
|-
|-
| | 77
| 76
|933.333
| 921.{{overline|21}}
| | 1250/729
| 128/75
| colspan="3" | 12/7
| "
|
| 56/33
| 17/10, 29/17, 46/27
|-
|-
| | 78
| 77
|945.455
| 933.{{overline|33}}
| | 216/125
| 1250/729
| colspan="2" | 140/81
| 12/7
| | 26/15
|  
|  
|  
|-
|-
| | 79
| 78
|957.576
| 945.{{overline|45}}
| colspan="2" | 125/72
| 216/125
| | 110/63
| 140/81
| | 45/26
|  
| 26/15
|  
|-
|-
| | 80
| 79
|969.697
| 957.{{overline|57}}
| | 1280/729
| 125/72
| colspan="3" | 7/4
| 26/15
|  
|
| 40/23
|-
|-
| | 81
| 80
|981.818
| 969.{{overline|69}}
| colspan="2" | 225/128
| 1280/729
| colspan="2" | 99/56
| '''7/4'''
|  
| 44/25
|
|-
|-
| | 82
| 81
|993.939
| 981.{{overline|81}}
| colspan="4" | 16/9
| 225/128
| "
| 44/25
|
| 30/17
|-
|-
| | 83
| 82
|1006.061
| 993.{{overline|93}}
| | 3645/2048
| 16/9
| colspan="3" | 25/14
| "
|
|
|  
|-
|-
| | 84
| 83
|1018.182
| 1006.{{overline|06}}
| colspan="4" | 9/5
| 3645/2048
| 25/14
|  
|  
| 34/19
|-
|-
| | 85
| 84
|1030.303
| 1018.{{overline|18}}
| | 2048/1125
| 9/5
| colspan="3" | 49/27
| "
|
|
|  
|-
|-
| | 86
| 85
|1042.424
| 1030.{{overline|30}}
| | 729/400
| 2048/1125
| | 64/35
| 49/27
| colspan="2" | 11/6
| 20/11
|  
| '''29/16'''
|-
|-
| | 87
| 86
|1054.545
| 1042.{{overline|42}}
| | 1152/625
| 729/400
| colspan="3" | 90/49
| 64/35
|  
| 11/6, 20/11
| 42/23
|-
|-
| | 88
| 87
|1066.667
| 1054.{{overline|54}}
| colspan="3" | 50/27
| 1152/625
| | 13/7
| 90/49
| 11/6, 24/13
|  
|  
|-
|-
| | 89
| 88
|1078.788
| 1066.{{overline|66}}
| | 4096/2187
| 50/27
| colspan="3" | 28/15
| "
|
| 13/7, 24/13
|
|-
|-
| | 90
| 89
|1090.909
| 1078.{{overline|78}}
| colspan="4" | 15/8
| 4096/2187
| 28/15
| 13/7
|
| 54/29
|-
|-
| | 91
| 90
|1103.030
| 1090.{{overline|90}}
| | 256/135
| 15/8
| | 189/100
| "
| | 154/81
|  
| | 49/26
|  
| '''32/17'''
|-
|-
| | 92
| 91
|1115.152
| 1103.{{overline|03}}
| | 243/128
| 256/135
| colspan="3" | 40/21
| 189/100
|
|  
| 17/9, 36/19
|-
|-
| | 93
| 92
|1127.273
| 1115.{{overline|15}}
| colspan="2" | 48/25
| 243/128
| colspan="2" | 21/11
| 40/21
|  
|
| 19/10
|-
|-
| | 94
| 93
|1139.394
| 1127.{{overline|27}}
| | 625/324
| 48/25
| colspan="2" | 27/14
| "
| | 25/13
| 25/13
| 52/27
| 23/12
|-
|-
| | 95
| 94
|1151.515
| 1139.{{overline|39}}
| | 243/125
| 625/324
| colspan="3" | 35/18
| 27/14
| 52/27, 64/33
| 25/13
| 29/15, 56/29
|-
|-
| | 96
| 95
|1163.636
| 1151.{{overline|51}}
| | 125/64
| 243/125
| colspan="3" | 49/25
| 35/18
|  
| 39/20, 64/33, 88/45
|
|-
|-
| | 97
| 96
|1175.758
| 1163.{{overline|63}}
| | 160/81
| 125/64
| colspan="3" | 63/32
| 49/25, 96/49
| 39/20, 88/45, 108/55
| 55/28
| 45/23, 100/51, 112/57
|-
|-
| | 98
| 97
|1187.879
| 1175.{{overline|75}}
| | 2025/1024
| 160/81
| colspan="3" | 125/63
| 63/32
| 55/28, 65/33, 77/39
| 65/33, 77/39, 108/55
| 57/29, 69/35, 75/38, 136/69
|-
|-
| | 99
| 98
|1200
| 1187.{{overline|87}}
| colspan="4" | 2/1
| 2025/1024
| 125/63
|
|
|
|-
| 99
| 1200.00
| colspan="5" | '''2/1'''
|}
|}


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