Xenharmonic Wiki

Table of 198edo intervals: Difference between revisions

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VisualWikitext
7-limit is done
11-limit is done
Line 2: Line 2:
This article is a work in progress.
This article is a work in progress.


7-limit is done.  
11-limit is done.  
</div>
</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. Note that no 7-limit interval can be represented by odd degrees, so those entries are left blank. 7-limit intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in ''italic'', for they are consistent under the criterion of 99edo. Intervals otherwise that differ by more than 50%, with odd limit over 729, or with two more simpler mapped to the same degree, are not shown. 


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
Line 26: Line 26:
|  
|  
|  
|  
| [[385/384]], [[441/440]], [[540/539]]
| [[385/384]], [[441/440]]
| [[196/195]], [[325/324]], [[351/350]], [[364/363]]
| [[196/195]], [[325/324]]
|-
|-
| 2
| 2
| 12.{{overline|12}}
| 12.{{overline|12}}
| ?
| ?
| [[126/125]], [[245/243]]
| [[126/125]], [[225/224|''225/224'']]
| [[121/120]]
| [[121/120]]
| [[144/143]], [[169/168]]
| [[144/143]], [[169/168]]
Line 59: Line 59:
| 6
| 6
| 36.{{overline|36}}
| 36.{{overline|36}}
| ?
| [[128/125|''128/125'']]
| [[49/48]], [[50/49]]
| [[49/48]], [[50/49]]
| ?
| ?
Line 68: Line 68:
|  
|  
|  
|  
| ?
| 352/343
| [[40/39]]
| [[40/39]]
|-
|-
Line 82: Line 82:
|  
|  
|  
|  
| [[33/32]]
| [[33/32]], 567/550
| [[65/63]]
| [[65/63]]
|-
|-
Line 89: Line 89:
| [[648/625]]
| [[648/625]]
| [[28/27]]
| [[28/27]]
| ?
| 363/350
| ?
| ?
|-
|-
Line 96: Line 96:
|  
|  
|  
|  
| [[80/77]]
| [[80/77]], 343/330
| [[26/25]], [[27/26]]
| [[26/25]], [[27/26]]
|-
|-
Line 115: Line 115:
| 14
| 14
| 84.{{overline|84}}
| 84.{{overline|84}}
| ?
| [[256/243|''256/243'']]
| [[21/20]], 360/343
| [[21/20]], 360/343
| 605/576
| 605/576
Line 124: Line 124:
|  
|  
|  
|  
| 539/512
| 539/512, 625/594
| 96/91
| 96/91
|-
|-
| 16
| 16
| 96.{{overline|96}}
| 96.{{overline|96}}
| ?
| [[135/128|''135/128'']]
| 200/189, 343/324
| 200/189, 343/324
| [[128/121]]
| [[128/121]], 363/343
| ?
| ?
|-
|-
Line 152: Line 152:
|  
|  
|  
|  
| 77/72
| 77/72, 294/275
| ?
| ?
|-
|-
Line 166: Line 166:
|  
|  
|  
|  
| 320/297
| 264/245, 320/297
| [[14/13]]
| [[14/13]]
|-
|-
Line 173: Line 173:
| [[27/25]]
| [[27/25]]
| 175/162
| 175/162
| 121/112
| 121/112, 392/363
| ?
| ?
|-
|-
Line 180: Line 180:
|  
|  
|  
|  
| 693/640
| 250/231, 693/640
| [[13/12]]
| [[13/12]]
|-
|-
| 24
| 24
| 145.{{overline|45}}
| 145.{{overline|45}}
| ?
| ''625/576''
| [[49/45]], 160/147
| [[49/45]], 160/147
| ?
| ?
Line 194: Line 194:
|  
|  
|  
|  
| [[12/11]]
| [[12/11]], 275/252
| ?
| ?
|-
|-
| 26
| 26
| 157.{{overline|57}}
| 157.{{overline|57}}
| ?
| ''800/729''
| [[35/32]], 192/175
| [[35/32]], 192/175
| ?
| ?
Line 215: Line 215:
| ?
| ?
| [[54/49]], 441/400
| [[54/49]], 441/400
| ?
| 400/363
| ?
| ?
|-
|-
Line 229: Line 229:
| [[10/9]]
| [[10/9]]
| ?
| ?
| ?
| 672/605
| ?
| ?
|-
|-
Line 236: Line 236:
|  
|  
|  
|  
| 49/44
| 49/44, 600/539
| ?
| ?
|-
|-
Line 264: Line 264:
|  
|  
|  
|  
| 112/99, 275/243
| 112/99, 198/175
| ?
| ?
|-
|-
| 36
| 36
| 218.{{overline|18}}
| 218.{{overline|18}}
| ?
| ''256/225''
| 245/216, 500/441
| 245/216, 500/441
| 363/320
| 363/320, 686/605
| ?
| ?
|-
|-
Line 306: Line 306:
|  
|  
|  
|  
| ?
| 231/200, 343/297
| [[15/13]]
| [[15/13]]
|-
|-
Line 340: Line 340:
| 278.{{overline|78}}
| 278.{{overline|78}}
| ?
| ?
| 147/125, 288/245
| [[75/64|''75/64'']], 147/125
| ?
| ?
| ?
| ?
Line 353: Line 353:
| 48
| 48
| 290.{{overline|90}}
| 290.{{overline|90}}
| ?
| [[32/27|''32/27'']]
| [[189/160]]
| [[189/160]]
| 605/512
| 605/512
Line 362: Line 362:
|  
|  
|  
|  
| 385/324
| 196/165, 297/250
| ?
| ?
|-
|-
Line 383: Line 383:
| [[6/5]]
| [[6/5]]
| ?
| ?
| ?
| 605/504
| ?
| ?
|-
|-
Line 396: Line 396:
| 327.{{overline|27}}
| 327.{{overline|27}}
| ?
| ?
| [[98/81]], 756/625
| 98/81, ''135/112''
| ?
| 121/100
| ?
| ?
|-
|-
Line 404: Line 404:
|  
|  
|  
|  
| [[40/33]]
| [[40/33]], 297/245
| [[63/52]]
| [[63/52]]
|-
|-
Line 411: Line 411:
| 243/200
| 243/200
| 175/144
| 175/144
| ?
| 147/121
| ?
| ?
|-
|-
Line 418: Line 418:
|  
|  
|  
|  
| [[11/9]]
| [[11/9]], 336/275
| [[39/32]]
| [[39/32]]
|-
|-
| 58
| 58
| 351.{{overline|51}}
| 351.{{overline|51}}
| ?
| ''768/625''
| [[49/40]], [[60/49]]
| [[49/40]], [[60/49]]
| ?
| ?
Line 432: Line 432:
|  
|  
|  
|  
| [[27/22]]
| [[27/22]], 275/224
| '''[[16/13]]'''
| '''[[16/13]]'''
|-
|-
Line 439: Line 439:
| 100/81
| 100/81
| 216/175
| 216/175
| 448/363
| 121/98, 448/363
| ?
| ?
|-
|-
Line 446: Line 446:
|  
|  
|  
|  
| 99/80
| 99/80, 245/198
| [[26/21]]
| [[26/21]]
|-
|-
Line 452: Line 452:
| 375.{{overline|75}}
| 375.{{overline|75}}
| ?
| ?
| [[56/45]]
| [[56/45]], ''243/196''
| ?
| ?
| ?
| ?
Line 460: Line 460:
|  
|  
|  
|  
| 96/77, 539/432
| 96/77, 343/275
| ?
| ?
|-
|-
Line 467: Line 467:
| '''[[5/4]]'''
| '''[[5/4]]'''
| ?
| ?
| ?
| 756/605
| ?
| ?
|-
|-
Line 479: Line 479:
| 66
| 66
| 400.00
| 400.00
| ?
| ''512/405''
| [[63/50]], 432/343
| [[63/50]], 432/343
| [[121/96]]
| [[121/96]]
Line 488: Line 488:
|  
|  
|  
|  
| 486/385
| 125/99, 486/385
| ?
| ?
|-
|-
| 68
| 68
| 412.{{overline|12}}
| 412.{{overline|12}}
| ?
| [[81/64|''81/64'']]
| [[80/63]], 343/270
| [[80/63]], 343/270
| 768/605
| 768/605
Line 516: Line 516:
|  
|  
|  
|  
| 77/60
| 77/60, 440/343
| ?
| ?
|-
|-
Line 537: Line 537:
| 162/125
| 162/125
| [[35/27]]
| [[35/27]]
| ?
| 363/280, 784/605
| ?
| ?
|-
|-
Line 544: Line 544:
|  
|  
|  
|  
| ?
| 100/77, 343/264
| [[13/10]]
| [[13/10]]
|-
|-
| 76
| 76
| 460.{{overline|60}}
| 460.{{overline|60}}
| ?
| ''125/96''
| [[64/49]], 98/75
| [[64/49]], 98/75
| ?
| ?
Line 586: Line 586:
|  
|  
|  
|  
| 297/224, 512/385
| 175/132, 297/224
| ?
| ?
|-
|-
Line 600: Line 600:
|  
|  
|  
|  
| 385/288
| 147/110, 385/288
| ?
| ?
|-
|-
Line 606: Line 606:
| 509.{{overline|09}}
| 509.{{overline|09}}
| ?
| ?
| 343/256
| [[75/56|''75/56'']], 168/125
| ?
| ?
| ?
| ?
Line 621: Line 621:
| [[27/20]]
| [[27/20]]
| ?
| ?
| ?
| 490/343, 605/448
| ?
| ?
|-
|-
Line 633: Line 633:
| 88
| 88
| 533.{{overline|33}}
| 533.{{overline|33}}
| ?
| ''512/375''
| [[49/36]], 200/147
| [[49/36]], 200/147
| ?
| ?
Line 656: Line 656:
|  
|  
|  
|  
| '''[[11/8]]'''
| '''[[11/8]]''', 378/275
| ?
| ?
|-
|-
| 92
| 92
| 557.{{overline|57}}
| 557.{{overline|57}}
| ?
| ''864/625''
| 441/320
| [[112/81|''112/81'']], 441/320
| ?
| ?
| ?
| ?
Line 670: Line 670:
|  
|  
|  
|  
| 320/231
| 320/231, 686/495
| [[18/13]]
| [[18/13]]
|-
|-
Line 698: Line 698:
|  
|  
|  
|  
| 108/77, 539/384
| 108/77, 275/196
| ?
| ?
|-
|-
| 98
| 98
| 593.{{overline|93}}
| 593.{{overline|93}}
| ?
| [[45/32|''45/32'']]
| 343/243, 800/567
| 343/243, 800/567
| 512/363
| 484/343, 512/363
| ?
| ?
|-
|-
Line 717: Line 717:
| 100
| 100
| 606.{{overline|06}}
| 606.{{overline|06}}
| ?
| [[64/45|''64/45'']]
| 486/343, 567/400
| 486/343, 567/400
| 363/256
| 343/242, 363/256
| ?
| ?
|-
|-
Line 726: Line 726:
|  
|  
|  
|  
| 77/54, 768/539
| 77/54, 392/275
| ?
| ?
|-
|-
Line 754: Line 754:
|  
|  
|  
|  
| 231/160
| 231/160, 495/343
| [[13/9]]
| [[13/9]]
|-
|-
| 106
| 106
| 642.{{overline|42}}
| 642.{{overline|42}}
| ?
| ''625/432''
| 640/441
| [[81/56|''81/56'']], 640/441
| ?
| ?
| ?
| ?
Line 768: Line 768:
|  
|  
|  
|  
| '''[[16/11]]'''
| '''[[16/11]]''', 275/189
| ?
| ?
|-
|-
Line 787: Line 787:
| 110
| 110
| 666.{{overline|66}}
| 666.{{overline|66}}
| ?
| ''375/256''
| [[72/49]], 147/100
| [[72/49]], 147/100
| ?
| ?
Line 803: Line 803:
| [[40/27]]
| [[40/27]]
| ?
| ?
| ?
| 363/245, 896/605
| ?
| ?
|-
|-
Line 816: Line 816:
| 690.{{overline|90}}
| 690.{{overline|90}}
| ?
| ?
| 125/84, 512/343
| [[112/75|''112/75'']], 125/84
| ?
| ?
| ?
| ?
Line 824: Line 824:
|  
|  
|  
|  
| 576/385
| 220/147, 539/360
| ?
| ?
|-
|-
Line 838: Line 838:
|  
|  
|  
|  
| 385/256, 448/297
| 264/175, 385/256
| ?
| ?
|-
|-
Line 871: Line 871:
| 122
| 122
| 739.{{overline|39}}
| 739.{{overline|39}}
| ?
| ''192/125''
| [[49/32]], 75/49
| [[49/32]], 75/49
| ?
| ?
Line 880: Line 880:
|  
|  
|  
|  
| ?
| 77/50, 528/343
| [[20/13]]
| [[20/13]]
|-
|-
Line 887: Line 887:
| 125/81
| 125/81
| [[54/35]]
| [[54/35]]
| ?
| 560/363, 605/392
| ?
| ?
|-
|-
Line 908: Line 908:
|  
|  
|  
|  
| 120/77
| 120/77, 343/220
| ?
| ?
|-
|-
Line 927: Line 927:
| 130
| 130
| 787.{{overline|87}}
| 787.{{overline|87}}
| ?
| [[128/81|''128/81'']]
| [[63/40]], 540/343
| [[63/40]], 540/343
| 605/384
| 605/384
Line 936: Line 936:
|  
|  
|  
|  
| 385/243
| 198/125, 385/243
| ?
| ?
|-
|-
| 132
| 132
| 800.00
| 800.00
| ?
| ''405/256''
| [[100/63]], 343/216
| [[100/63]], 343/216
| [[192/121]]
| [[192/121]]
Line 957: Line 957:
| '''[[8/5]]'''
| '''[[8/5]]'''
| ?
| ?
| ?
| 605/378
| ?
| ?
|-
|-
Line 964: Line 964:
|  
|  
|  
|  
| 77/48, 864/539
| 77/48, 441/275
| ?
| ?
|-
|-
Line 970: Line 970:
| 824.{{overline|24}}
| 824.{{overline|24}}
| ?
| ?
| [[45/28]]
| [[45/28]], ''392/243''
| ?
| ?
| ?
| ?
Line 978: Line 978:
|  
|  
|  
|  
| 160/99
| 160/99, 396/245
| [[21/13]]
| [[21/13]]
|-
|-
Line 985: Line 985:
| 81/50
| 81/50
| 175/108
| 175/108
| 363/224
| 196/121, 363/224
| ?
| ?
|-
|-
Line 992: Line 992:
|  
|  
|  
|  
| [[44/27]]
| [[44/27]], 448/275
| '''[[13/8]]'''
| '''[[13/8]]'''
|-
|-
| 140
| 140
| 848.{{overline|48}}
| 848.{{overline|48}}
| ?
| ''625/384''
| [[49/30]], [[80/49]]
| [[49/30]], [[80/49]]
| ?
| ?
Line 1,006: Line 1,006:
|  
|  
|  
|  
| [[18/11]]
| [[18/11]], 275/168
| [[64/39]]
| [[64/39]]
|-
|-
Line 1,013: Line 1,013:
| 400/243
| 400/243
| 288/175
| 288/175
| ?
| 242/147
| ?
| ?
|-
|-
Line 1,020: Line 1,020:
|  
|  
|  
|  
| [[33/20]]
| [[33/20]], 490/297
| [[104/63]]
| [[104/63]]
|-
|-
Line 1,026: Line 1,026:
| 872.{{overline|72}}
| 872.{{overline|72}}
| ?
| ?
| [[81/49]], 625/378
| [[81/49]], ''224/135''
| ?
| 200/121
| ?
| ?
|-
|-
Line 1,041: Line 1,041:
| [[5/3]]
| [[5/3]]
| ?
| ?
| ?
| 1008/605
| ?
| ?
|-
|-
Line 1,062: Line 1,062:
|  
|  
|  
|  
| 648/385
| 165/98, 500/297
| ?
| ?
|-
|-
| 150
| 150
| 909.{{overline|09}}
| 909.{{overline|09}}
| ?
| [[27/16|''27/16'']]
| [[320/189]]
| [[320/189]]
| 1024/605
| 1024/605
Line 1,082: Line 1,082:
| 921.{{overline|21}}
| 921.{{overline|21}}
| ?
| ?
| 245/144, 250/147
| [[128/75|''128/75'']], 245/144
| ?
| ?
| ?
| ?
Line 1,118: Line 1,118:
|  
|  
|  
|  
| ?
| 343/198, 400/231
| [[26/15]]
| [[26/15]]
|-
|-
Line 1,151: Line 1,151:
| 162
| 162
| 981.{{overline|81}}
| 981.{{overline|81}}
| ?
| ''225/128''
| 432/245, 441/250
| 432/245, 441/250
| 640/363
| 605/343, 640/363
| ?
| ?
|-
|-
Line 1,160: Line 1,160:
|  
|  
|  
|  
| 99/56, 486/275
| 99/56, 175/99
| ?
| ?
|-
|-
Line 1,188: Line 1,188:
|  
|  
|  
|  
| 88/49
| 88/49, 539/300
| ?
| ?
|-
|-
Line 1,195: Line 1,195:
| [[9/5]]
| [[9/5]]
| ?
| ?
| ?
| 605/336
| ?
| ?
|-
|-
Line 1,209: Line 1,209:
| ?
| ?
| [[49/27]], 800/441
| [[49/27]], 800/441
| ?
| 363/200
| ?
| ?
|-
|-
Line 1,221: Line 1,221:
| 172
| 172
| 1042.{{overline|42}}
| 1042.{{overline|42}}
| ?
| ''729/400''
| [[64/35]], 175/96
| [[64/35]], 175/96
| ?
| ?
Line 1,230: Line 1,230:
|  
|  
|  
|  
| [[11/6]]
| [[11/6]], 504/275
| ?
| ?
|-
|-
| 174
| 174
| 1054.{{overline|54}}
| 1054.{{overline|54}}
| ?
| ''1152/625''
| [[90/49]], 147/80
| [[90/49]], 147/80
| ?
| ?
Line 1,244: Line 1,244:
|  
|  
|  
|  
| 1280/693
| 231/125, 1280/693
| [[24/13]]
| [[24/13]]
|-
|-
Line 1,251: Line 1,251:
| [[50/27]]
| [[50/27]]
| 324/175
| 324/175
| 224/121
| 224/121, 363/196
| ?
| ?
|-
|-
Line 1,258: Line 1,258:
|  
|  
|  
|  
| 297/160
| 245/132, 297/160
| [[13/7]]
| [[13/7]]
|-
|-
Line 1,272: Line 1,272:
|  
|  
|  
|  
| 144/77, 539/288
| 144/77, 275/147
| ?
| ?
|-
|-
Line 1,291: Line 1,291:
| 182
| 182
| 1103.{{overline|03}}
| 1103.{{overline|03}}
| ?
| ''256/135''
| 189/100, 648/343
| 189/100, 648/343
| [[121/64]]
| [[121/64]], 686/363
| ?
| ?
|-
|-
Line 1,300: Line 1,300:
|  
|  
|  
|  
| 1024/539
| 1024/539, 1188/625
| 91/48
| 91/48
|-
|-
| 184
| 184
| 1115.{{overline|15}}
| 1115.{{overline|15}}
| ?
| [[243/128|''243/128'']]
| [[40/21]], 343/180
| [[40/21]], 343/180
| 1152/605
| 1152/605
Line 1,328: Line 1,328:
|  
|  
|  
|  
| 77/40
| 77/40, 660/343
| [[25/13]], [[52/27]]
| [[25/13]], [[52/27]]
|-
|-
Line 1,335: Line 1,335:
| 625/324
| 625/324
| [[27/14]]
| [[27/14]]
| ?
| 700/363
| ?
| ?
|-
|-
Line 1,342: Line 1,342:
|  
|  
|  
|  
| [[64/33]]
| [[64/33]], 1100/567
| [[126/65]]
| [[126/65]]
|-
|-
Line 1,356: Line 1,356:
|  
|  
|  
|  
| ?
| 343/176
| [[39/20]]
| [[39/20]]
|-
|-
| 192
| 192
| 1163.{{overline|63}}
| 1163.{{overline|63}}
| ?
| ''125/64''
| 96/49, 49/25
| 49/25, 96/49
| ?
| ?
| ?
| ?
Line 1,390: Line 1,390:
| 1187.{{overline|87}}
| 1187.{{overline|87}}
| ?
| ?
| 125/63, 486/245
| 125/63, ''448/225''
| 240/121
| 240/121
| 143/72, 336/169
| 143/72, 336/169
Line 1,398: Line 1,398:
|  
|  
|  
|  
| 768/385, 880/441, 539/270
| 539/270, 768/385
| 195/98, 648/325, 700/351, 363/182
| 195/98, 363/182
|-
|-
| 198
| 198
Retrieved from "https://en.xen.wiki/w/Table_of_198edo_intervals"