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User:Overthink/Table of 311edo intervals: Difference between revisions

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Overthink (talk | contribs)
autopatrolled
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finish replacing names with diatonic interval categories; + some more ratios
Overthink (talk | contribs)
autopatrolled
2,790 edits
add more ratios
 
(12 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Editable user page}}
{{Editable user page}}
This table assumes 41-limit patent val of 311edo.
 
This table assumes the [[41-limit]] [[patent val]] {{Val|311 493 722 873 1076 1151 1271 1321 1407 1511 1541 1620 1666}} of [[311edo]]. Intervals that differ by their assigned steps by more than 50%, but less than 100%, are marked with ''italics''. Intervals that differ by more than 100% are not shown. Since 311edo supports true hemififths, a hemipyth marking is provided.
 
{| class="wikitable mw-collapsible right-1 right-2"
{| class="wikitable mw-collapsible right-1 right-2"
|+ Intervals of 311edo
|+ Intervals of 311edo
Line 23: Line 25:
| 3.859
| 3.859
|  
|  
| [[385/384]]
| [[325/324]], [[385/384]]
|  
| [[513/512]], [[715/714]]
|  
|
|-
|-
| 2
| 2
| 7.717
| 7.717
|  
|  
| [[225/224]]
| [[196/195]], [[225/224]]
|  
| [[256/255]]
|  
|
|-
|-
| 3
| 3
| 11.576
| 11.576
|  
|  
|
| [[144/143]], [[169/168]]
|
|
|
|
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| 15.434
| 15.434
|  
|  
|
| ''[[100/99]]'', [[121/120]]
|
|
|
|
Line 51: Line 53:
| 19.293
| 19.293
|  
|  
|
| [[91/90]], [[99/98]]
|
| [[85/84]], [[92/91]], [[96/95]]
|
| ''[[82/81]]'', [[88/87]], [[93/92]]
|-
|-
| 6
| 6
| 23.151
| 23.151
|  
|  
| [[81/80]]
| [[78/77]], [[81/80]]
|
| [[70/69]], [[76/75]], [[77/76]]
|
| [[75/74]]
|-
|-
| 7
| 7
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|
|
| [[40/39]]
| [[40/39]]
|  
|
| [[41/40]], [[42/41]]
| [[41/40]], [[42/41]]
|-
|-
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| 46.302
| 46.302
|
|
| [[39/38]]
| [[39/38]], [[77/75]]
|  
|
| [[37/36]], [[38/37]]
| [[37/36]], [[38/37]]
|-
|-
| 13
| 13
| 50.161
| 50.161
|
|  
| [[36/35]]
| [[36/35]]
| [[34/33]], [[35/34]]
| [[34/33]], [[35/34]]
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| 14
| 14
| 54.019
| 54.019
|
|  
| [[33/32]]
| [[33/32]], [[65/63]]
|
|  
| [[32/31]]
| [[32/31]]
|-
|-
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| 57.878
| 57.878
| sA1
| sA1
|
|  
|
|  
| [[30/29]], [[31/30]]
| [[30/29]], [[31/30]]
|-
|-
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|  
|  
| [[28/27]]
| [[28/27]]
|
|[[57/55]]
| [[29/28]]
| [[29/28]]
|-
|-
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| 65.595
| 65.595
|
|
| [[27/26]]
| [[27/26]], [[80/77]]
|
|
|
|
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|
|
| [[25/24]], [[26/25]]
| [[25/24]], [[26/25]]
|
| [[51/49]]
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|
|-
|-
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|
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|
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|[[24/23]]
| [[24/23]]
|
|
|-
|-
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|
|
|
|
|[[23/22]]
| [[23/22]]
|
|
|-
|-
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| 81.029
| 81.029
|
|
|[[22/21]]
| [[22/21]]
|
|
|
|
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|[[21/20]]
|[[21/20]]
|
|
|
|[[41/39]]
|-
|-
| 23
| 23
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| 92.605
| 92.605
|
|
|
|[[135/128]]
|[[19/18]]
|[[19/18]]
|
|[[39/37]], [[58/55]]
|-
|-
| 25
| 25
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|
|
|
|
|
| [[37/35]]
|-
|-
| 26
| 26
| 100.322
| 100.322
|
|
|
|[[35/33]]
|[[18/17]]
| [[18/17]]
|
|
|-
|-
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|
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|
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|[[17/16]]
| [[17/16]]
|
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|-
|-
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|
|
|
|
|
| [[33/31]]
|-
|-
| 29
| 29
Line 227: Line 229:
|A1
|A1
| ''[[2187/2048]]''
| ''[[2187/2048]]''
|
|  
| [[31/29]]
| [[31/29]]
|-
|-
Line 234: Line 236:
|
|
| [[15/14]]
| [[15/14]]
|
|  
|
|  
|-
|-
| 32
| 32
| 123.473
| 123.473
|
|
|
|  
|
|  
|
| [[29/27]]
|-
|-
| 33
| 33
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|
|
| [[14/13]]
| [[14/13]]
|
|  
|
|  
|-
|-
| 34
| 34
| 131.190
| 131.190
|
|
|
|  
|
|  
| [[41/38]]
| [[41/38]]
|-
|-
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| 135.048
| 135.048
|
|
|
| [[27/25]]
|
|  
|
|[[40/37]]
|-
|-
| 36
| 36
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|
|
|
|
|
|[[25/23]]
|
|[[38/35]]
|-
|-
| 38
| 38
| 146.624
| 146.624
| n2
| n2
|[[49/45]], [[160/147]]
|
|
|
|[[37/34]]
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|-
|-
| 39
| 39
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| 154.341
| 154.341
|
|
|[[35/32]]
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|[[82/75]]
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|-
|-
| 41
| 41
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| [[23/21]]
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| [[34/31]]
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| 42
| 42
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|-
| 43
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| 45
| 45
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|-
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|[[31/28]], [[41/37]]
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|-
| 47
| 47
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| 185.209
| 185.209
|
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|[[49/44]]
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| [[69/62]]
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|-
|-
| 49
| 49
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|[[29/26]]
| [[29/26]]
|-
|-
| 50
| 50
Line 367: Line 369:
|
|
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|[[19/17]]
| [[19/17]]
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|-
|-
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| 196.785
| 196.785
|
|
|[[28/25]]
|
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|[[28/25]]
|
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|-
|-
Line 380: Line 382:
| 200.643
| 200.643
|
|
| [[55/49]]
| [[64/57]]
|
|-
| 53
| 204.502
| M2
| [[9/8]]
|
|
|
|
|-
| 54
| 208.360
|
|
|-
| [[44/39]]
| 53
|  
| 204.502
| [[35/31]]
|M2
|[[9/8]]
|
|
|-
| 54
| 208.360
|
|
|
|
|-
|-
| 55
| 55
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|[[26/23]]
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|-
|-
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|[[17/15]]
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|-
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| 219.936
| 219.936
|
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|[[25/22]]
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|[[42/37]]
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|-
|-
| 58
| 58
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|[[33/29]]
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|-
|-
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|
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|[[57/50]], [[65/57]]
|
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|-
|-
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| 235.370
| 235.370
|sd3
|sd3
|
|[[55/48]], [[63/55]]
|
|
|
|
Line 450: Line 452:
| 239.228
| 239.228
|
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|[[147/128]]
|
|
|
|[[31/27]]
|
|-
|-
| 63
| 63
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|[[23/20]], [[38/33]]
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|-
|-
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|
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|[[15/13]]
|[[15/13]]
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|[[98/85]]
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|-
|-
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| 250.804
| 250.804
|
|
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|[[52/45]]
|
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|[[37/32]]
|[[37/32]]
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|[[22/19]], [[80/69]]
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|-
|-
Line 487: Line 489:
|
|
|
|
|
|[[29/25]], [[36/31]]
|-
|-
| 68
| 68
| 262.379
| 262.379
|sA2
|sA2
|
|[[64/55]]
|
|[[57/49]]
|
|
|-
|-
Line 506: Line 508:
| 270.096
| 270.096
|
|
|
|[[90/77]]
|
|[[76/65]]
|
|
|-
|-
Line 513: Line 515:
| 273.955
| 273.955
|
|
|[[75/64]]
|
|
|
|[[34/29]], [[41/35]]
|
|-
|-
| 72
| 72
Line 548: Line 550:
| 293.248
| 293.248
|m3
|m3
|[[32/27]]
|[[32/27]], [[77/65]]
|
|[[45/38]]
|
|
|-
|-
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|
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|[[19/16]]
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|-
|-
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|[[25/21]]
|[[25/21]]
|
|
|
|[[44/37]]
|-
|-
| 79
| 79
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|
|
|
|
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|[[31/26]], [[37/31]]
|-
|-
| 80
| 80
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|
|
|
|
|
|[[49/41]]
|-
|-
| 81
| 81
Line 584: Line 586:
|
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|
|
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|[[91/76]]
|
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|-
|-
Line 606: Line 608:
|[[135/112]]
|[[135/112]]
|
|
|
|[[35/29]]
|-
|-
| 85
| 85
Line 618: Line 620:
| 331.833
| 331.833
|
|
|[[40/33]]
|[[40/33]], [[63/52]]
|
|[[23/19]]
|
|
|-
|-
Line 632: Line 634:
| 339.550
| 339.550
|
|
|
|[[243/200]]
|
|[[28/23]]
|
|
|-
|-
Line 639: Line 641:
| 343.408
| 343.408
|
|
|[[39/32]]
|[[39/32]], [[128/105]]
|
|
|
|[[50/41]]
|-
|-
| 90
| 90
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| 362.701
| 362.701
|
|
|
|[[100/81]]
|
|[[69/56]]
|
|[[37/30]]
|-
|-
| 95
| 95
Line 682: Line 684:
|
|
|
|
|[[21/17]]
|[[21/17]], [[68/55]]
|
|
|-
|-
Line 688: Line 690:
| 370.418
| 370.418
|
|
|[[26/21]]
|[[26/21]], [[99/80]]
|
|
|
|[[31/25]]
|-
|-
| 97
| 97
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|
|
|
|
|[[36/29]]
|[[36/29]], [[41/33]]
|-
|-
| 98
| 98
| 378.135
| 378.135
|
|
|[[56/45]]
|
|
|
|[[46/37]], [[51/41]]
|
|-
|-
| 99
| 99
| 381.994
| 381.994
|d4
|d4
|
|[[81/65]], [[96/77]]
|
|
|
|
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|
|
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|[[114/91]]
|
|
|-
|-
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| 393.569
| 393.569
|
|
|
|[[49/39]]
|
|[[64/51]], [[69/55]]
|
|
|-
|-
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| 397.428
| 397.428
|
|
|
|[[44/35]]
|
|[[34/27]]
|
|[[39/31]]
|-
|-
| 104
| 104
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|[[29/23]]
|-
|-
| 105
| 105
| 405.145
| 405.145
|
|
|
|[[91/72]]
|
|[[24/19]]
|
|
|-
|-
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|M3
|M3
|[[81/64]]
|[[81/64]]
|
|[[19/15]]
|
|
|-
|-
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| 432.154
| 432.154
|
|
|
|[[77/60]]
|
|
|
|
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| 114
| 114
| 439.871
| 439.871
|sD4
|sd4
|
|
|
|
|[[49/38]]
|[[40/31]]
|-
|-
| 115
| 115
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|[[128/99]]
|[[128/99]]
|
|
|
|[[31/24]]
|-
|-
| 116
| 116
| 447.588
| 447.588
|
|
|
|[[35/27]]
|
|[[22/17]], [[57/44]]
|
|
|-
|-
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| 451.447
| 451.447
|
|
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|[[135/104]]
|
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|
|
Line 850: Line 852:
|
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|
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|[[30/23]]
|
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|-
|-
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| 463.023
| 463.023
|
|
|
|[[64/49]], [[98/75]]
|
|[[17/13]]
|
|[[81/62]]
|-
|-
| 121
| 121
| 466.881
| 466.881
|sA3
|sA3
|[[55/42]], [[72/55]]
|
|
|
|[[38/29]]
|
|-
|-
| 122
| 122
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|[[25/19]]
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|-
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|[[29/22]]
|-
|-
| 125
| 125
| 482.315
| 482.315
|
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|[[33/25]]
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|[[37/28]]
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|-
|-
| 126
| 126
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|[[45/34]]
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|[[49/37]]
|-
|-
| 127
| 127
| 490.032
| 490.032
|
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|[[65/49]]
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|[[69/52]], [[85/64]]
|
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|-
|-
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| 513.183
| 513.183
|
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|[[35/26]]
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|[[39/29]]
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|-
|-
| 134
| 134
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|[[31/23]]
|-
|-
| 135
| 135
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|[[27/20]]
|[[27/20]]
|
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|[[50/37]]
|-
|-
| 136
| 136
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|A3
|A3
|
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|[[23/17]]
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|-
|-
Line 976: Line 978:
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|[[19/14]]
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|[[34/25]]
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| 536.334
| 536.334
|
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|[[15/11]]
|
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Line 998: Line 1,000:
|
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|[[41/30]]
|-
|-
| 141
| 141
Line 1,004: Line 1,006:
|
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|[[26/19]]
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|-
|-
Line 1,010: Line 1,012:
| 547.910
| 547.910
|
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|[[48/35]]
|
|
|
|
Line 1,038: Line 1,040:
| 563.344
| 563.344
|
|
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|[[18/13]]
|
|
|
|
Line 1,045: Line 1,047:
| 567.203
| 567.203
|
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|[[25/18]]
|
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|
|
Line 1,059: Line 1,061:
| 574.920
| 574.920
|
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|[[39/28]]
|
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|
Line 1,088: Line 1,090:
|
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|[[45/32]]
|[[45/32]]
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|[[38/27]]
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|-
|-
Line 1,094: Line 1,096:
| 594.212
| 594.212
|
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|[[55/39]]
|
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|[[31/22]]
|
|-
|-
| 155
| 155
Line 1,102: Line 1,104:
|
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|[[24/17]]
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|[[41/29]]
|-
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| 156
| 156
Line 1,109: Line 1,111:
|
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|[[17/12]]
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|[[58/41]]
|-
|-
| 157
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| 605.788
| 605.788
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|[[78/55]]
|
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|[[44/31]]
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|-
|-
| 158
| 158
Line 1,123: Line 1,125:
|
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|[[64/45]]
|[[64/45]]
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|[[27/19]]
|
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|-
|-
Line 1,158: Line 1,160:
|
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|[[23/16]]
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|-
|-
Line 1,164: Line 1,166:
| 632.797
| 632.797
|
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|[[36/25]]
|
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|
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Line 1,171: Line 1,173:
| 636.656
| 636.656
|
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|[[13/9]]
|
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|
Line 1,199: Line 1,201:
| 652.090
| 652.090
|
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|[[35/24]]
|
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Line 1,220: Line 1,222:
| 663.666
| 663.666
|
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|[[22/15]]
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Line 1,228: Line 1,230:
|
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|[[25/17]]
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Line 1,235: Line 1,237:
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|[[28/19]]
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Line 1,242: Line 1,244:
|d6
|d6
|
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|[[34/23]]
|
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|-
|-
Line 1,262: Line 1,264:
| 686.817
| 686.817
|
|
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|[[52/35]]
|
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|
|
Line 1,276: Line 1,278:
| 694.534
| 694.534
|
|
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|[[112/75]]
|
|
|
|
Line 1,297: Line 1,299:
| 706.109
| 706.109
|
|
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|[[176/117]], [[182/121]]
|
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Line 1,305: Line 1,307:
|
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|[[128/85]]
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|-
|-
Line 1,318: Line 1,320:
| 717.685
| 717.685
|
|
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|[[50/33]]
|
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|
|
Line 1,333: Line 1,335:
|
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|[[38/25]]
|
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|-
|-
Line 1,346: Line 1,348:
| 733.119
| 733.119
|sd6
|sd6
|[[55/36]], [[84/55]]
|
|
|
|[[29/19]]
|
|-
|-
| 191
| 191
| 736.977
| 736.977
|
|
|
|[[49/32]]
|
|[[26/17]]
|
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|-
|-
Line 1,361: Line 1,363:
|
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|[[23/15]]
|
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|-
|-
Line 1,381: Line 1,383:
| 752.412
| 752.412
|
|
|
|[[54/35]]
|
|[[17/11]]
|
|
|-
|-
Line 1,409: Line 1,411:
| 767.846
| 767.846
|
|
|
|[[120/77]]
|
|
|
|
Line 1,424: Line 1,426:
|
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|[[36/23]]
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|-
|-
Line 1,431: Line 1,433:
|
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|[[80/51]]
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|-
|-
Line 1,437: Line 1,439:
| 783.280
| 783.280
|
|
|
|[[11/7]]
|
|
|
|
Line 1,444: Line 1,446:
| 787.138
| 787.138
|
|
|
|[[52/33]]
|
|
|
|
Line 1,452: Line 1,454:
|m6
|m6
|[[128/81]]
|[[128/81]]
|
|[[30/19]]
|
|
|-
|-
Line 1,459: Line 1,461:
|
|
|
|
|
|[[19/12]]
|
|
|-
|-
Line 1,500: Line 1,502:
| 818.006
| 818.006
|A5
|A5
|
|[[77/48]], [[130/81]]
|
|
|
|
Line 1,507: Line 1,509:
| 821.865
| 821.865
|
|
|
|[[45/28]]
|
|
|
|
Line 1,521: Line 1,523:
| 829.582
| 829.582
|
|
|
|[[21/13]], [[160/99]]
|
|
|
|
Line 1,529: Line 1,531:
|
|
|
|
|
|[[34/21]], [[55/34]]
|
|
|-
|-
Line 1,535: Line 1,537:
| 837.299
| 837.299
|
|
|
|[[81/50]]
|
|
|
|
Line 1,549: Line 1,551:
| 845.016
| 845.016
|
|
|
|[[44/27]]
|
|
|
|
Line 1,556: Line 1,558:
| 848.875
| 848.875
|n6
|n6
|
|[[49/30]], [[80/49]]
|
|
|
|
Line 1,563: Line 1,565:
| 852.733
| 852.733
|
|
|
|[[18/11]]
|
|
|
|
Line 1,570: Line 1,572:
| 856.592
| 856.592
|
|
|
|[[64/39]], [[105/64]]
|
|
|
|
Line 1,578: Line 1,580:
|
|
|
|
|
|[[23/12|23/14]]
|
|
|-
|-
Line 1,585: Line 1,587:
|
|
|
|
|
|[[28/17]]
|
|
|-
|-
Line 1,591: Line 1,593:
| 868.167
| 868.167
|
|
|
|[[33/20]], [[104/63]]
|
|[[38/23]]
|
|
|-
|-
Line 1,647: Line 1,649:
| 899.035
| 899.035
|
|
|
|[[42/25]]
|
|
|
|
Line 1,655: Line 1,657:
|
|
|
|
|
|[[32/19]]
|
|
|-
|-
Line 1,844: Line 1,846:
|
|
|
|
|
|[[34/19]]
|
|
|-
|-
Line 1,887: Line 1,889:
|
|
|
|
|
|[[29/16]]
|-
|-
| 268
| 268
| 1034.084
| 1034.084
|
|
|
|[[20/11]]
|
|
|
|
Line 1,941: Line 1,943:
| 1061.093
| 1061.093
|
|
|
|[[24/13]]
|
|
|
|
Line 1,962: Line 1,964:
| 1072.669
| 1072.669
|
|
|
|[[13/7]]
|
|
|
|
Line 2,005: Line 2,007:
|
|
|
|
|
|[[32/17]]
|
|
|-
|-
Line 2,012: Line 2,014:
|
|
|
|
|
|[[17/9]]
|
|
|-
|-
Line 2,026: Line 2,028:
|
|
|
|
|
|[[36/19]]
|
|
|-
|-
Line 2,039: Line 2,041:
| 1115.113
| 1115.113
|
|
|
|[[40/21]]
|
|
|
|
Line 2,046: Line 2,048:
| 1118.971
| 1118.971
|
|
|
|[[21/11]]
|
|
|
|
Line 2,054: Line 2,056:
|
|
|
|
|
|[[44/23]]
|
|
|-
|-
Line 2,061: Line 2,063:
|
|
|
|
|
|[[23/12]]
|
|
|-
|-
Line 2,067: Line 2,069:
| 1130.547
| 1130.547
|
|
|
|[[25/13]], [[48/25]]
|
|
|
|
Line 2,074: Line 2,076:
| 1134.405
| 1134.405
|
|
|
|[[27/13]], [[77/40]]
|
|
|
|
Line 2,081: Line 2,083:
| 1138.264
| 1138.264
|
|
|[[27/14]]
|
|
|
|[[56/29]]
|
|-
|-
| 296
| 296
Line 2,090: Line 2,092:
|
|
|
|
|
|[[29/15]], [[60/31]]
|-
|-
| 297
| 297
| 1145.981
| 1145.981
|
|
|[[64/33]]
|
|
|
|[[31/16]]
|
|-
|-
| 298
| 298
| 1149.839
| 1149.839
|
|
|
|[[35/18]]
|
|[[33/17]], [[68/35]]
|
|
|-
|-
Line 2,110: Line 2,112:
|
|
|
|
|
|[[76/39]]
|
|[[37/19]], [[72/37]]
|-
|-
| 300
| 300
| 1157.556
| 1157.556
|
|
|[[39/20]]
|
|
|
|[[41/21]], [[80/41]]
|
|-
|-
| 301
| 301
| 1161.415
| 1161.415
|
|
|
|[[88/45]]
|
|[[45/23]]
|
|
|-
|-
Line 2,130: Line 2,132:
| 1165.273
| 1165.273
|
|
|
|[[49/25]], [[96/49]]
|
|[[51/26]], [[100/51]]
|
|
|-
|-
Line 2,137: Line 2,139:
| 1169.132
| 1169.132
|sA7
|sA7
|
|[[55/28]], [[108/55]]
|
|[[112/57]]
|
|[[57/29]]
|-
|-
| 304
| 304
Line 2,151: Line 2,153:
| 1176.849
| 1176.849
|
|
|
|[[160/81]]
|
|
|
|
Line 2,158: Line 2,160:
| 1180.707
| 1180.707
|
|
|
|[[196/99]]
|
|
|
|
Line 2,165: Line 2,167:
| 1184.566
| 1184.566
|
|
|
|''[[99/50]],'' [[208/105]]
|
|
|
|
Line 2,172: Line 2,174:
| 1188.424
| 1188.424
|
|
|
|[[143/72]]
|
|
|
|
Line 2,179: Line 2,181:
| 1192.283
| 1192.283
|
|
|
|[[448/225]]
|
|[[255/128]]
|
|
|-
|-
Line 2,186: Line 2,188:
| 1196.141
| 1196.141
|
|
|
|[[768/385]]
|
|
|
|
Line 2,192: Line 2,194:
| 311
| 311
| 1200.000
| 1200.000
|Octave
| P8
|[[2/1]]
| [[2/1]]
|
|
|
|
|}
|}
Retrieved from "https://en.xen.wiki/w/User:Overthink/Table_of_311edo_intervals"