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

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Line 1: Line 1:
{{Editable user page}}
{{Editable user page}}
Note: Second, sixth, and seventh names can be derived from the third names.
 
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 6: Line 8:
! rowspan="2" | Steps
! rowspan="2" | Steps
! rowspan="2" | Cents
! rowspan="2" | Cents
! rowspan="2" | Name
! rowspan="2" | Marks
! colspan="3" | Approximate Ratios
! colspan="3" | Approximate Ratios
|-
|-
Line 15: Line 17:
| 0
| 0
| 0.000
| 0.000
|Unison
| P1
|[[1/1]]
| [[1/1]]
|
|  
|
|  
|-
|-
| 1
| 1
| 3.859
| 3.859
|Keenanisma?
|  
|
| [[325/324]], [[385/384]]
|
| [[513/512]], [[715/714]]
|
|
|-
|-
| 2
| 2
| 7.717
| 7.717
|Kleisma
|  
|
| [[196/195]], [[225/224]]
|
| [[256/255]]
|
|
|-
|-
| 3
| 3
| 11.576
| 11.576
|Semicomma
|  
|
| [[144/143]], [[169/168]]
|
|
|
|
Line 43: Line 45:
| 4
| 4
| 15.434
| 15.434
|Subcomma (idk)
|  
|
| ''[[100/99]]'', [[121/120]]
|
|
|
|
Line 50: Line 52:
| 5
| 5
| 19.293
| 19.293
|Diaschisma
|  
|
| [[91/90]], [[99/98]]
|
| [[85/84]], [[92/91]], [[96/95]]
|
| ''[[82/81]]'', [[88/87]], [[93/92]]
|-
|-
| 6
| 6
| 23.151
| 23.151
|Comma
|  
|[[81/80]]
| [[78/77]], [[81/80]]
|
| [[70/69]], [[76/75]], [[77/76]]
|
| [[75/74]]
|-
|-
| 7
| 7
| 27.010
| 27.010
|Superprime?
|[[64/63]]
|
|
|
| [[64/63]], [[65/64]], [[66/65]]
| [[69/68]]
| [[63/62]]
|-
|-
| 8
| 8
| 30.868
| 30.868
|
| sd2
|
| [[55/54]], [[56/55]]
|
| [[57/56]]
|
| [[58/57]]
|-
|-
| 9
| 9
| 34.727
| 34.727
|
|
|
| [[49/48]], [[50/49]]
|
| [[51/50]], [[52/51]]
|
|
|-
|-
Line 86: Line 88:
| 38.585
| 38.585
|
|
|
| [[45/44]]
|
| [[46/45]]
|
|
|-
|-
Line 93: Line 95:
| 42.444
| 42.444
|
|
| [[40/39]]
|
|
|
| [[41/40]], [[42/41]]
|
|-
|-
| 12
| 12
| 46.302
| 46.302
|
|
| [[39/38]], [[77/75]]
|
|
|
| [[37/36]], [[38/37]]
|
|-
|-
| 13
| 13
| 50.161
| 50.161
|
|  
|[[36/35]]
| [[36/35]]
|
| [[34/33]], [[35/34]]
|
|  
|-
|-
| 14
| 14
| 54.019
| 54.019
|
|  
|[[33/32]]
| [[33/32]], [[65/63]]
|
|  
|
| [[32/31]]
|-
|-
| 15
| 15
| 57.878
| 57.878
|
| sA1
|
|  
|
|  
|
| [[30/29]], [[31/30]]
|-
|-
| 16
| 16
| 61.736
| 61.736
|Subminor 2nd
|  
|[[28/27]]
| [[28/27]]
|
|[[57/55]]
|
| [[29/28]]
|-
|-
| 17
| 17
| 65.595
| 65.595
|
|
|[[27/26]]
| [[27/26]], [[80/77]]
|
|
|
|
Line 142: Line 144:
| 69.453
| 69.453
|
|
|[[25/24]], [[26/25]]
| [[25/24]], [[26/25]]
|
| [[51/49]]
|
|
|-
|-
Line 150: Line 152:
|
|
|
|
|
| [[24/23]]
|
|
|-
|-
Line 157: Line 159:
|
|
|
|
|
| [[23/22]]
|
|
|-
|-
Line 163: Line 165:
| 81.029
| 81.029
|
|
|[[22/21]]
| [[22/21]]
|
|
|
|
Line 172: Line 174:
|[[21/20]]
|[[21/20]]
|
|
|
|[[41/39]]
|-
|-
| 23
| 23
| 88.746
| 88.746
|Pythagorean minor 2nd
| m2
|
|[[256/243]]
|
|[[20/19]]
|
|
|-
|-
Line 184: Line 186:
| 92.605
| 92.605
|
|
|
|[[135/128]]
|
|[[19/18]]
|
|[[39/37]], [[58/55]]
|-
|-
| 25
| 25
Line 193: Line 195:
|
|
|
|
|
| [[37/35]]
|-
|-
| 26
| 26
| 100.322
| 100.322
|
|
|
|[[35/33]]
|
| [[18/17]]
|
|
|-
|-
Line 206: Line 208:
|
|
|
|
|
| [[17/16]]
|
|
|-
|-
Line 214: Line 216:
|
|
|
|
|
| [[33/31]]
|-
|-
| 29
| 29
| 111.897
| 111.897
|Classical minor 2nd
|
|[[16/15]]
| [[16/15]]
|
|
|
|
Line 225: Line 227:
| 30
| 30
| 115.756
| 115.756
|
|A1
|''[[2187/2048]]''
| ''[[2187/2048]]''
|
|  
|[[31/29]]
| [[31/29]]
|-
|-
| 31
| 31
| 119.614
| 119.614
|
|
|[[15/14]]
| [[15/14]]
|
|  
|
|  
|-
|-
| 32
| 32
| 123.473
| 123.473
|
|
|
|  
|
|  
|
| [[29/27]]
|-
|-
| 33
| 33
| 127.331
| 127.331
|
|
|[[14/13]]
| [[14/13]]
|
|  
|
|  
|-
|-
| 34
| 34
| 131.190
| 131.190
|
|
|
|  
|
|  
|[[41/38]]
| [[41/38]]
|-
|-
| 35
| 35
| 135.048
| 135.048
|
|
|
| [[27/25]]
|
|  
|
|[[40/37]]
|-
|-
| 36
| 36
| 138.907
| 138.907
|
|
|[[13/12]]
| [[13/12]]
|
|
|
|
Line 276: Line 278:
|
|
|
|
|
|[[25/23]]
|
|[[38/35]]
|-
|-
| 38
| 38
| 146.624
| 146.624
|Neutral 2nd
| n2
|
|[[49/45]], [[160/147]]
|
|
|
|[[37/34]]
|-
|-
| 39
| 39
| 150.482
| 150.482
|Undecimal tendoneutral 2nd
|
|[[12/11]]
| [[12/11]]
|
|
|
|
Line 296: Line 298:
| 154.341
| 154.341
|
|
|[[35/32]]
|
|
|
|[[82/75]]
|
|-
|-
| 41
| 41
Line 304: Line 306:
|
|
|
|
|
| [[23/21]]
|
| [[34/31]]
|-
|-
| 42
| 42
Line 312: Line 314:
|
|
|
|
|
|[[45/41]]
|-
|-
| 43
| 43
| 165.916
| 165.916
|
|
|[[11/10]]
| [[11/10]]
|
|
|
|
Line 326: Line 328:
|
|
|
|
|
|[[32/29]]
|-
|-
| 45
| 45
Line 332: Line 334:
|
|
|
|
|
|[[21/19]]
|
|
|-
|-
| 46
| 46
| 177.492
| 177.492
|d3
|
|
|
|
|
|[[31/28]], [[41/37]]
|
|-
|-
| 47
| 47
| 181.350
| 181.350
|Classical major 2nd
|
|[[10/9]]
|[[10/9]]
|
|
Line 352: Line 354:
| 185.209
| 185.209
|
|
|[[49/44]]
|
|
|
| [[69/62]]
|
|-
|-
| 49
| 49
Line 361: Line 363:
|
|
|
|
|[[29/26]]
| [[29/26]]
|-
|-
| 50
| 50
| 192.926
| 192.926
|Mean major 2nd
|
|
|[[19/17]]
|
| [[19/17]]
|
|
|-
|-
| 51
| 51
| 196.785
| 196.785
|
|
|
|[[28/25]]
|[[28/25]]
|
|
|
|-
|-
Line 380: Line 382:
| 200.643
| 200.643
|
|
|
| [[55/49]]
|
| [[64/57]]
|
|  
|-
|-
| 53
| 53
| 204.502
| 204.502
|Pythagorean major 2nd
| M2
|[[9/8]]
| [[9/8]]
|
|
|
|
Line 394: Line 396:
| 208.360
| 208.360
|
|
|
| [[44/39]]
|
|  
|
| [[35/31]]
|-
|-
| 55
| 55
Line 402: Line 404:
|
|
|
|
|
|[[26/23]]
|
|
|-
|-
Line 409: Line 411:
|
|
|
|
|
|[[17/15]]
|
|
|-
|-
Line 415: Line 417:
| 219.936
| 219.936
|
|
|[[25/22]]
|
|
|
|[[42/37]]
|
|-
|-
| 58
| 58
Line 423: Line 425:
|
|
|
|
|
|[[33/29]]
|
|
|-
|-
Line 430: Line 432:
|
|
|
|
|
|[[57/50]], [[65/57]]
|
|
|-
|-
| 60
| 60
| 231.511
| 231.511
|Supermajor 2nd
|
|[[8/7]]
|[[8/7]]
|
|
Line 442: Line 444:
| 61
| 61
| 235.370
| 235.370
|
|sd3
|
|[[55/48]], [[63/55]]
|
|
|
|
Line 450: Line 452:
| 239.228
| 239.228
|
|
|[[147/128]]
|
|
|
|[[31/27]]
|
|-
|-
| 63
| 63
Line 458: Line 460:
|
|
|
|
|
|[[23/20]], [[38/33]]
|
|
|-
|-
Line 465: Line 467:
|
|
|[[15/13]]
|[[15/13]]
|
|[[98/85]]
|
|
|-
|-
Line 471: Line 473:
| 250.804
| 250.804
|
|
|[[52/45]]
|
|
|
|[[37/32]]
|
|-
|-
| 66
| 66
Line 479: Line 481:
|
|
|
|
|
|[[22/19]], [[80/69]]
|
|
|-
|-
Line 487: Line 489:
|
|
|
|
|
|[[29/25]], [[36/31]]
|-
|-
| 68
| 68
| 262.379
| 262.379
|
|sA2
|
|[[64/55]]
|
|[[57/49]]
|
|
|-
|-
| 69
| 69
| 266.238
| 266.238
|Subminor 3rd
|
|[[7/6]]
|[[7/6]]
|
|
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 521: Line 523:
|
|
|
|
|
|[[27/23]]
|
|
|-
|-
| 73
| 73
| 281.672
| 281.672
|Diatismic minor 3rd
|
|
|
|
|[[20/17]]
|
|
|-
|-
| 74
| 74
| 285.531
| 285.531
|Pentacircle minor 3rd
|
|[[33/28]]
|[[33/28]]
|
|
Line 540: Line 542:
| 75
| 75
| 289.389
| 289.389
|Major minthmic minor 3rd
|
|[[13/11]]
|[[13/11]]
|
|
Line 547: Line 549:
| 76
| 76
| 293.248
| 293.248
|Pythagorean minor 3rd
|m3
|[[32/27]]
|[[32/27]], [[77/65]]
|
|[[45/38]]
|
|
|-
|-
| 77
| 77
| 297.106
| 297.106
|Boethius minor 3rd
|
|
|
|
|[[19/16]]
|
|
|-
|-
| 78
| 78
| 300.965
| 300.965
|Quasi-tempered minor 3rd?
|
|[[25/21]]
|[[25/21]]
|
|
|
|[[44/37]]
|-
|-
| 79
| 79
Line 571: Line 573:
|
|
|
|
|
|[[31/26]], [[37/31]]
|-
|-
| 80
| 80
Line 578: Line 580:
|
|
|
|
|
|[[49/41]]
|-
|-
| 81
| 81
Line 584: Line 586:
|
|
|
|
|
|[[91/76]]
|
|
|-
|-
| 82
| 82
| 316.399
| 316.399
|Classical minor 3rd
|
|[[6/5]]
|[[6/5]]
|
|
Line 596: Line 598:
| 83
| 83
| 320.257
| 320.257
|Keenanismic minor 3rd
|A2
|[[77/64]]
|[[77/64]]
|
|
Line 603: Line 605:
| 84
| 84
| 324.116
| 324.116
|Marvelous minor 3rd
|
|[[135/112]]
|[[135/112]]
|
|
|
|[[35/29]]
|-
|-
| 85
| 85
| 327.974
| 327.974
|Undetricesimal supraminor 3rd
|
|
|
|
|29/24
|
|[[29/24]]
|-
|-
| 86
| 86
| 331.833
| 331.833
|
|
|[[40/33]]
|[[40/33]], [[63/52]]
|
|[[23/19]]
|
|
|-
|-
Line 631: Line 633:
| 88
| 88
| 339.550
| 339.550
|Amity supraminor 3rd
|
|
|
|[[243/200]]
|[[28/23]]
|
|
|-
|-
| 89
| 89
| 343.408
| 343.408
|Tridecimal subneutral 3rd
|[[39/32]]
|
|
|[[39/32]], [[128/105]]
|
|
|[[50/41]]
|-
|-
| 90
| 90
| 347.267
| 347.267
|Undecimal artoneutral 3rd
|
|[[11/9]]
|[[11/9]]
|
|
Line 652: Line 654:
| 91
| 91
| 351.125
| 351.125
|Neutral 3rd
|n3
|
|[[49/40]], [[60/49]]
|
|
|
|
Line 659: Line 661:
| 92
| 92
| 354.984
| 354.984
|Undecimal tendoneutral 3rd
|
|[[27/22]]
|[[27/22]]
|
|
Line 666: Line 668:
| 93
| 93
| 358.842
| 358.842
|Tridecimal supraneutral 3rd
|
|[[16/13]]
|[[16/13]]
|
|
Line 673: Line 675:
| 94
| 94
| 362.701
| 362.701
|Amity submajor 3rd
|
|
|
|
|[[100/81]]
|[[69/56]]
|[[37/30]]
|-
|-
| 95
| 95
Line 682: Line 684:
|
|
|
|
|
|[[21/17]], [[68/55]]
|
|
|-
|-
Line 688: Line 690:
| 370.418
| 370.418
|
|
|[[26/21]], [[99/80]]
|
|
|
|[[31/25]]
|
|-
|-
| 97
| 97
| 374.277
| 374.277
|Undetricesimal submajor 3rd
|
|
|
|
|36/29
|
|[[36/29]], [[41/33]]
|-
|-
| 98
| 98
| 378.135
| 378.135
|Marvelous major 3rd
|
|
|
|[[56/45]]
|
|
|[[46/37]], [[51/41]]
|-
|-
| 99
| 99
| 381.994
| 381.994
|Keenanismic major 3rd
|d4
|
|[[81/65]], [[96/77]]
|
|
|
|
Line 715: Line 717:
| 100
| 100
| 385.852
| 385.852
|Classical major 3rd
|
|[[5/4]]
|[[5/4]]
|
|
Line 724: Line 726:
|
|
|
|
|
|[[114/91]]
|
|
|-
|-
Line 730: Line 732:
| 393.569
| 393.569
|
|
|
|[[49/39]]
|
|[[64/51]], [[69/55]]
|
|
|-
|-
Line 737: Line 739:
| 397.428
| 397.428
|
|
|
|[[44/35]]
|
|[[34/27]]
|
|[[39/31]]
|-
|-
| 104
| 104
Line 746: Line 748:
|
|
|
|
|
|[[29/23]]
|-
|-
| 105
| 105
| 405.145
| 405.145
|Boethius major 3rd
|
|
|
|[[91/72]]
|[[24/19]]
|
|
|-
|-
| 106
| 106
| 409.003
| 409.003
|Pythagorean major 3rd
|M3
|
|[[81/64]]
|
|[[19/15]]
|
|
|-
|-
| 107
| 107
| 412.862
| 412.862
|Major minthmic major 3rd
|
|
|[[33/26]]
|
|
|
|
Line 771: Line 773:
| 108
| 108
| 416.720
| 416.720
|Pentacircle major 3rd
|
|[[14/11]]
|[[14/11]]
|
|
Line 778: Line 780:
| 109
| 109
| 420.579
| 420.579
|Diatismic major 3rd
|
|
|
|
|[[51/40]]
|
|
|-
|-
| 110
| 110
| 424.437
| 424.437
|Shrubmajor 3rd?
|
|
|
|[[23/18]]
|[[23/18]]
Line 793: Line 795:
| 428.296
| 428.296
|
|
|[[32/25]], [[50/39]]
|
|
|
|[[41/32]]
|
|-
|-
| 112
| 112
| 432.154
| 432.154
|Swetismic supermajor 3rd
|
|
|[[77/60]]
|
|
|
|
Line 806: Line 808:
| 113
| 113
| 436.013
| 436.013
|Septimal major 3rd
|
|[[9/7]]
|[[9/7]]
|
|
Line 813: Line 815:
| 114
| 114
| 439.871
| 439.871
|sd4
|
|
|
|[[49/38]]
|
|[[40/31]]
|
|-
|-
| 115
| 115
| 443.730
| 443.730
|
|
|[[128/99]]
|
|
|
|[[31/24]]
|
|-
|-
| 116
| 116
| 447.588
| 447.588
|
|
|
|[[35/27]]
|
|[[22/17]], [[57/44]]
|
|
|-
|-
Line 835: Line 837:
| 451.447
| 451.447
|
|
|
|[[135/104]]
|
|
|
|
Line 842: Line 844:
| 455.305
| 455.305
|
|
|
|[[13/10]]
|
|
|
|
Line 850: Line 852:
|
|
|
|
|
|[[30/23]]
|
|
|-
|-
Line 856: Line 858:
| 463.023
| 463.023
|
|
|
|[[64/49]], [[98/75]]
|
|[[17/13]]
|
|[[81/62]]
|-
|-
| 121
| 121
| 466.881
| 466.881
|sA3
|[[55/42]], [[72/55]]
|
|
|
|[[38/29]]
|
|
|-
|-
| 122
| 122
| 470.740
| 470.740
|
|
|
|[[21/16]]
|
|
|
|
Line 878: Line 880:
|
|
|
|
|
|[[25/19]]
|
|
|-
|-
Line 886: Line 888:
|
|
|
|
|
|[[29/22]]
|-
|-
| 125
| 125
| 482.315
| 482.315
|
|
|[[33/25]]
|
|
|
|[[37/28]]
|
|-
|-
| 126
| 126
Line 899: Line 901:
|
|
|
|
|
|[[45/34]]
|
|[[49/37]]
|-
|-
| 127
| 127
| 490.032
| 490.032
|
|
|
|[[65/49]]
|
|[[69/52]], [[85/64]]
|
|
|-
|-
Line 918: Line 920:
| 129
| 129
| 497.749
| 497.749
|Perfect fourth
|P4
|[[4/3]]
|[[4/3]]
|
|
Line 947: Line 949:
| 513.183
| 513.183
|
|
|[[35/26]]
|
|
|
|[[39/29]]
|
|-
|-
| 134
| 134
Line 956: Line 958:
|
|
|
|
|
|[[31/23]]
|-
|-
| 135
| 135
| 520.900
| 520.900
|
|
|[[27/20]]
|
|
|
|[[50/37]]
|
|-
|-
| 136
| 136
| 524.759
| 524.759
|A3
|
|
|
|[[23/17]]
|
|
|
|-
|-
Line 976: Line 978:
|
|
|
|
|
|[[19/14]]
|
|
|-
|-
Line 983: Line 985:
|
|
|
|
|
|[[34/25]]
|
|
|-
|-
Line 989: Line 991:
| 536.334
| 536.334
|
|
|
|[[15/11]]
|
|
|
|
Line 998: Line 1,000:
|
|
|
|
|
|[[41/30]]
|-
|-
| 141
| 141
Line 1,004: Line 1,006:
|
|
|
|
|
|[[26/19]]
|
|
|-
|-
Line 1,010: Line 1,012:
| 547.910
| 547.910
|
|
|
|[[48/35]]
|
|
|
|
Line 1,017: Line 1,019:
| 551.768
| 551.768
|
|
|
|[[11/8]]
|
|
|
|
Line 1,023: Line 1,025:
| 144
| 144
| 555.627
| 555.627
|
|sA4
|
|
|
|
Line 1,038: Line 1,040:
| 563.344
| 563.344
|
|
|
|[[18/13]]
|
|
|
|
Line 1,045: Line 1,047:
| 567.203
| 567.203
|
|
|
|[[25/18]]
|
|
|
|
Line 1,059: Line 1,061:
| 574.920
| 574.920
|
|
|
|[[39/28]]
|
|
|
|
Line 1,073: Line 1,075:
| 582.637
| 582.637
|
|
|
|[[7/5]]
|
|
|
|
Line 1,079: Line 1,081:
| 152
| 152
| 586.495
| 586.495
|
|d5
|
|[[1024/729]]
|
|
|
|
Line 1,087: Line 1,089:
| 590.354
| 590.354
|
|
|
|[[45/32]]
|
|[[38/27]]
|
|
|-
|-
Line 1,094: Line 1,096:
| 594.212
| 594.212
|
|
|[[55/39]]
|
|
|
|[[31/22]]
|
|-
|-
| 155
| 155
Line 1,102: Line 1,104:
|
|
|
|
|
|[[24/17]]
|
|[[41/29]]
|-
|-
| 156
| 156
Line 1,109: Line 1,111:
|
|
|
|
|
|[[17/12]]
|
|[[58/41]]
|-
|-
| 157
| 157
| 605.788
| 605.788
|
|
|[[78/55]]
|
|
|
|[[44/31]]
|
|-
|-
| 158
| 158
| 609.646
| 609.646
|
|
|
|[[64/45]]
|
|[[27/19]]
|
|
|-
|-
| 159
| 159
| 613.505
| 613.505
|
|A4
|
|[[729/512]]
|
|
|
|
Line 1,136: Line 1,138:
| 617.363
| 617.363
|
|
|
|[[10/7]]
|
|
|
|
Line 1,158: Line 1,160:
|
|
|
|
|
|[[23/16]]
|
|
|-
|-
Line 1,164: Line 1,166:
| 632.797
| 632.797
|
|
|
|[[36/25]]
|
|
|
|
Line 1,171: Line 1,173:
| 636.656
| 636.656
|
|
|
|[[13/9]]
|
|
|
|
Line 1,184: Line 1,186:
| 167
| 167
| 644.373
| 644.373
|
|sd5
|
|
|
|
Line 1,192: Line 1,194:
| 648.232
| 648.232
|
|
|
|[[16/11]]
|
|
|
|
Line 1,199: Line 1,201:
| 652.090
| 652.090
|
|
|
|[[35/24]]
|
|
|
|
Line 1,220: Line 1,222:
| 663.666
| 663.666
|
|
|
|[[22/15]]
|
|
|
|
Line 1,228: Line 1,230:
|
|
|
|
|
|[[25/17]]
|
|
|-
|-
Line 1,235: Line 1,237:
|
|
|
|
|
|[[28/19]]
|
|
|-
|-
| 175
| 175
| 675.241
| 675.241
|d6
|
|
|
|[[34/23]]
|
|
|
|-
|-
| 176
| 176
| 679.100
| 679.100
|Grave fifth
|
|
|[[40/27]]
|
|
|
|
Line 1,262: Line 1,264:
| 686.817
| 686.817
|
|
|
|[[52/35]]
|
|
|
|
Line 1,276: Line 1,278:
| 694.534
| 694.534
|
|
|
|[[112/75]]
|
|
|
|
Line 1,289: Line 1,291:
| 182
| 182
| 702.251
| 702.251
|Perfect fifth
|P5
|[[3/2]]
|[[3/2]]
|
|
Line 1,297: Line 1,299:
| 706.109
| 706.109
|
|
|
|[[176/117]], [[182/121]]
|
|
|
|
Line 1,305: Line 1,307:
|
|
|
|
|
|[[128/85]]
|
|
|-
|-
Line 1,318: Line 1,320:
| 717.685
| 717.685
|
|
|
|[[50/33]]
|
|
|
|
Line 1,333: Line 1,335:
|
|
|
|
|
|[[38/25]]
|
|
|-
|-
Line 1,339: Line 1,341:
| 729.260
| 729.260
|
|
|
|[[32/21]]
|
|
|
|
Line 1,345: Line 1,347:
| 190
| 190
| 733.119
| 733.119
|sd6
|[[55/36]], [[84/55]]
|
|
|
|[[29/19]]
|
|
|-
|-
| 191
| 191
| 736.977
| 736.977
|
|
|
|[[49/32]]
|
|[[26/17]]
|
|
|-
|-
Line 1,361: Line 1,363:
|
|
|
|
|
|[[23/15]]
|
|
|-
|-
Line 1,367: Line 1,369:
| 744.695
| 744.695
|
|
|
|[[20/13]]
|
|
|
|
Line 1,381: Line 1,383:
| 752.412
| 752.412
|
|
|
|[[54/35]]
|
|[[17/11]]
|
|
|-
|-
Line 1,388: Line 1,390:
| 756.270
| 756.270
|
|
|
|[[99/64]]
|
|
|
|
Line 1,394: Line 1,396:
| 197
| 197
| 760.129
| 760.129
|
|sA5
|
|
|
|
Line 1,402: Line 1,404:
| 763.987
| 763.987
|
|
|
|[[14/9]]
|
|
|
|
Line 1,409: Line 1,411:
| 767.846
| 767.846
|
|
|
|[[120/77]]
|
|
|
|
Line 1,416: Line 1,418:
| 771.704
| 771.704
|
|
|
|[[25/16]], [[39/25]]
|
|
|
|
Line 1,424: Line 1,426:
|
|
|
|
|
|[[36/23]]
|
|
|-
|-
Line 1,431: Line 1,433:
|
|
|
|
|
|[[80/51]]
|
|
|-
|-
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 1,450: Line 1,452:
| 205
| 205
| 790.997
| 790.997
|
|m6
|
|[[128/81]]
|
|[[30/19]]
|
|
|-
|-
Line 1,459: Line 1,461:
|
|
|
|
|
|[[19/12]]
|
|
|-
|-
Line 1,493: Line 1,495:
| 814.148
| 814.148
|
|
|
|[[8/5]]
|
|
|
|
Line 1,499: Line 1,501:
| 212
| 212
| 818.006
| 818.006
|
|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 1,542: Line 1,544:
| 841.158
| 841.158
|
|
|
|[[13/8]]
|
|
|
|
Line 1,549: Line 1,551:
| 845.016
| 845.016
|
|
|
|[[44/27]]
|
|
|
|
Line 1,555: Line 1,557:
| 220
| 220
| 848.875
| 848.875
|
|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 1,611: Line 1,613:
| 228
| 228
| 879.743
| 879.743
|
|d7
|
|
|
|
Line 1,619: Line 1,621:
| 883.601
| 883.601
|
|
|
|[[5/3]]
|
|
|
|
Line 1,647: Line 1,649:
| 899.035
| 899.035
|
|
|
|[[42/25]]
|
|
|
|
Line 1,655: Line 1,657:
|
|
|
|
|
|[[32/19]]
|
|
|-
|-
| 235
| 235
| 906.752
| 906.752
|
|M6
|
|[[27/16]]
|
|
|
|
Line 1,710: Line 1,712:
| 933.762
| 933.762
|
|
|
|[[12/7]]
|
|
|
|
Line 1,716: Line 1,718:
| 243
| 243
| 937.621
| 937.621
|
|sd7
|
|
|
|
Line 1,740: Line 1,742:
|
|
|
|
|
|[[64/37]]
|-
|-
| 247
| 247
| 953.055
| 953.055
|
|
|
|[[26/15]]
|
|
|
|
Line 1,765: Line 1,767:
| 250
| 250
| 964.630
| 964.630
|
|sA6
|
|
|
|
Line 1,773: Line 1,775:
| 968.489
| 968.489
|
|
|
|[[7/4]]
|
|
|
|
Line 1,821: Line 1,823:
| 258
| 258
| 995.498
| 995.498
|
|m7
|
|[[16/9]]
|
|
|
|
Line 1,844: Line 1,846:
|
|
|
|
|
|[[34/19]]
|
|
|-
|-
Line 1,864: Line 1,866:
| 1018.650
| 1018.650
|
|
|
|[[9/5]]
|
|
|
|
Line 1,870: Line 1,872:
| 265
| 265
| 1022.508
| 1022.508
|
|A6
|
|
|
|
Line 1,887: Line 1,889:
|
|
|
|
|
|[[29/16]]
|-
|-
| 268
| 268
| 1034.084
| 1034.084
|
|
|
|[[20/11]]
|
|
|
|
Line 1,920: Line 1,922:
| 1049.518
| 1049.518
|
|
|
|[[11/6]]
|
|
|
|
Line 1,926: Line 1,928:
| 273
| 273
| 1053.376
| 1053.376
|
|n7
|
|[[90/49]]
|
|
|
|
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 1,976: Line 1,978:
| 1080.386
| 1080.386
|
|
|
|[[28/15]]
|
|
|
|
Line 1,982: Line 1,984:
| 281
| 281
| 1084.244
| 1084.244
|
|d8
|
|
|
|
Line 1,990: Line 1,992:
| 1088.103
| 1088.103
|
|
|
|[[15/8]]
|
|
|
|
Line 2,005: Line 2,007:
|
|
|
|
|
|[[32/17]]
|
|
|-
|-
Line 2,012: Line 2,014:
|
|
|
|
|
|[[17/9]]
|
|
|-
|-
Line 2,026: Line 2,028:
|
|
|
|
|
|[[36/19]]
|
|
|-
|-
| 288
| 288
| 1111.254
| 1111.254
|
|M7
|
|[[243/128]]
|
|[[19/10]]
|
|
|-
|-
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
| 1142.122
| 1142.122
|sd8
|
|
|
|
|
|[[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]]
|
|
|-
|-
| 303
| 303
| 1169.132
| 1169.132
|
|sA7
|
|[[55/28]], [[108/55]]
|
|[[112/57]]
|
|[[57/29]]
|-
|-
| 304
| 304
| 1172.990
| 1172.990
|
|
|
|[[63/32]]
|
|
|
|
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]]
|
|
|
|
|}
|}

Latest revision as of 01:21, 6 May 2026

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This table assumes the 41-limit patent 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.

Intervals of 311edo
Steps Cents Marks Approximate Ratios
13-limit 23-limit 41-limit
0 0.000 P1 1/1
1 3.859 325/324, 385/384 513/512, 715/714
2 7.717 196/195, 225/224 256/255
3 11.576 144/143, 169/168
4 15.434 100/99, 121/120
5 19.293 91/90, 99/98 85/84, 92/91, 96/95 82/81, 88/87, 93/92
6 23.151 78/77, 81/80 70/69, 76/75, 77/76 75/74
7 27.010 64/63, 65/64, 66/65 69/68 63/62
8 30.868 sd2 55/54, 56/55 57/56 58/57
9 34.727 49/48, 50/49 51/50, 52/51
10 38.585 45/44 46/45
11 42.444 40/39 41/40, 42/41
12 46.302 39/38, 77/75 37/36, 38/37
13 50.161 36/35 34/33, 35/34
14 54.019 33/32, 65/63 32/31
15 57.878 sA1 30/29, 31/30
16 61.736 28/27 57/55 29/28
17 65.595 27/26, 80/77
18 69.453 25/24, 26/25 51/49
19 73.312 24/23
20 77.170 23/22
21 81.029 22/21
22 84.887 21/20 41/39
23 88.746 m2 256/243 20/19
24 92.605 135/128 19/18 39/37, 58/55
25 96.463 37/35
26 100.322 35/33 18/17
27 104.180 17/16
28 108.039 33/31
29 111.897 16/15
30 115.756 A1 2187/2048 31/29
31 119.614 15/14
32 123.473 29/27
33 127.331 14/13
34 131.190 41/38
35 135.048 27/25 40/37
36 138.907 13/12
37 142.765 25/23 38/35
38 146.624 n2 49/45, 160/147 37/34
39 150.482 12/11
40 154.341 35/32 82/75
41 158.199 23/21 34/31
42 162.058 45/41
43 165.916 11/10
44 169.775 32/29
45 173.633 21/19
46 177.492 d3 31/28, 41/37
47 181.350 10/9
48 185.209 49/44 69/62
49 189.068 29/26
50 192.926 19/17
51 196.785 28/25
52 200.643 55/49 64/57
53 204.502 M2 9/8
54 208.360 44/39 35/31
55 212.219 26/23
56 216.077 17/15
57 219.936 25/22 42/37
58 223.794 33/29
59 227.653 57/50, 65/57
60 231.511 8/7
61 235.370 sd3 55/48, 63/55
62 239.228 147/128 31/27
63 243.087 23/20, 38/33
64 246.945 15/13 98/85
65 250.804 52/45 37/32
66 254.662 22/19, 80/69
67 258.521 29/25, 36/31
68 262.379 sA2 64/55 57/49
69 266.238 7/6
70 270.096 90/77 76/65
71 273.955 75/64 34/29, 41/35
72 277.814 27/23
73 281.672 20/17
74 285.531 33/28
75 289.389 13/11
76 293.248 m3 32/27, 77/65 45/38
77 297.106 19/16
78 300.965 25/21 44/37
79 304.823 31/26, 37/31
80 308.682 49/41
81 312.540 91/76
82 316.399 6/5
83 320.257 A2 77/64
84 324.116 135/112 35/29
85 327.974 29/24
86 331.833 40/33, 63/52 23/19
87 335.691 17/14
88 339.550 243/200 28/23
89 343.408 39/32, 128/105 50/41
90 347.267 11/9
91 351.125 n3 49/40, 60/49
92 354.984 27/22
93 358.842 16/13
94 362.701 100/81 69/56 37/30
95 366.559 21/17, 68/55
96 370.418 26/21, 99/80 31/25
97 374.277 36/29, 41/33
98 378.135 56/45 46/37, 51/41
99 381.994 d4 81/65, 96/77
100 385.852 5/4
101 389.711 114/91
102 393.569 49/39 64/51, 69/55
103 397.428 44/35 34/27 39/31
104 401.286 29/23
105 405.145 91/72 24/19
106 409.003 M3 81/64 19/15
107 412.862 33/26
108 416.720 14/11
109 420.579 51/40
110 424.437 23/18
111 428.296 32/25, 50/39 41/32
112 432.154 77/60
113 436.013 9/7
114 439.871 sd4 49/38 40/31
115 443.730 128/99 31/24
116 447.588 35/27 22/17, 57/44
117 451.447 135/104
118 455.305 13/10
119 459.164 30/23
120 463.023 64/49, 98/75 17/13 81/62
121 466.881 sA3 55/42, 72/55 38/29
122 470.740 21/16
123 474.598 25/19
124 478.457 29/22
125 482.315 33/25 37/28
126 486.174 45/34 49/37
127 490.032 65/49 69/52, 85/64
128 493.891
129 497.749 P4 4/3
130 501.608
131 505.466
132 509.325
133 513.183 35/26 39/29
134 517.042 31/23
135 520.900 27/20 50/37
136 524.759 A3 23/17
137 528.617 19/14
138 532.476 34/25
139 536.334 15/11
140 540.193 41/30
141 544.051 26/19
142 547.910 48/35
143 551.768 11/8
144 555.627 sA4
145 559.486
146 563.344 18/13
147 567.203 25/18
148 571.061
149 574.920 39/28
150 578.778
151 582.637 7/5
152 586.495 d5 1024/729
153 590.354 45/32 38/27
154 594.212 55/39 31/22
155 598.071 24/17 41/29
156 601.929 17/12 58/41
157 605.788 78/55 44/31
158 609.646 64/45 27/19
159 613.505 A4 729/512
160 617.363 10/7
161 621.222
162 625.080
163 628.939 23/16
164 632.797 36/25
165 636.656 13/9
166 640.514
167 644.373 sd5
168 648.232 16/11
169 652.090 35/24
170 655.949
171 659.807
172 663.666 22/15
173 667.524 25/17
174 671.383 28/19
175 675.241 d6 34/23
176 679.100 40/27
177 682.958
178 686.817 52/35
179 690.675
180 694.534 112/75
181 698.392
182 702.251 P5 3/2
183 706.109 176/117, 182/121
184 709.968 128/85
185 713.826
186 717.685 50/33
187 721.543
188 725.402 38/25
189 729.260 32/21
190 733.119 sd6 55/36, 84/55 29/19
191 736.977 49/32 26/17
192 740.836 23/15
193 744.695 20/13
194 748.553
195 752.412 54/35 17/11
196 756.270 99/64
197 760.129 sA5
198 763.987 14/9
199 767.846 120/77
200 771.704 25/16, 39/25
201 775.563 36/23
202 779.421 80/51
203 783.280 11/7
204 787.138 52/33
205 790.997 m6 128/81 30/19
206 794.855 19/12
207 798.714
208 802.572
209 806.431
210 810.289
211 814.148 8/5
212 818.006 A5 77/48, 130/81
213 821.865 45/28
214 825.723
215 829.582 21/13, 160/99
216 833.441 34/21, 55/34
217 837.299 81/50
218 841.158 13/8
219 845.016 44/27
220 848.875 n6 49/30, 80/49
221 852.733 18/11
222 856.592 64/39, 105/64
223 860.450 23/14
224 864.309 28/17
225 868.167 33/20, 104/63 38/23
226 872.026
227 875.884
228 879.743 d7
229 883.601 5/3
230 887.460
231 891.318
232 895.177
233 899.035 42/25
234 902.894 32/19
235 906.752 M6 27/16
236 910.611
237 914.469
238 918.328
239 922.186
240 926.045
241 929.904
242 933.762 12/7
243 937.621 sd7
244 941.479
245 945.338
246 949.196 64/37
247 953.055 26/15
248 956.913
249 960.772
250 964.630 sA6
251 968.489 7/4
252 972.347
253 976.206
254 980.064
255 983.923
256 987.781
257 991.640
258 995.498 m7 16/9
259 999.357
260 1003.215
261 1007.074 34/19
262 1010.932
263 1014.791
264 1018.650 9/5
265 1022.508 A6
266 1026.367
267 1030.225 29/16
268 1034.084 20/11
269 1037.942
270 1041.801
271 1045.659
272 1049.518 11/6
273 1053.376 n7 90/49
274 1057.235
275 1061.093 24/13
276 1064.952
277 1068.810
278 1072.669 13/7
279 1076.527
280 1080.386 28/15
281 1084.244 d8
282 1088.103 15/8
283 1091.961
284 1095.820 32/17
285 1099.678 17/9
286 1103.537
287 1107.395 36/19
288 1111.254 M7 243/128 19/10
289 1115.113 40/21
290 1118.971 21/11
291 1122.830 44/23
292 1126.688 23/12
293 1130.547 25/13, 48/25
294 1134.405 27/13, 77/40
295 1138.264 27/14 56/29
296 1142.122 sd8 29/15, 60/31
297 1145.981 64/33 31/16
298 1149.839 35/18 33/17, 68/35
299 1153.698 76/39 37/19, 72/37
300 1157.556 39/20 41/21, 80/41
301 1161.415 88/45 45/23
302 1165.273 49/25, 96/49 51/26, 100/51
303 1169.132 sA7 55/28, 108/55 112/57 57/29
304 1172.990 63/32
305 1176.849 160/81
306 1180.707 196/99
307 1184.566 99/50, 208/105
308 1188.424 143/72
309 1192.283 448/225 255/128
310 1196.141 768/385
311 1200.000 P8 2/1
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