Table of 270edo intervals: Difference between revisions

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Basically finished
31-limit interpretation, favoring the most accurate ratio on similar complexity
Line 1: Line 1:
This '''table of 270edo intervals''' assumes the [[23-limit]] [[patent val]] of [[270edo]] {{val| 270 428 647 758 934 999 1104 1147 1221 }}. [[Prime harmonic]]s are in '''bold'''.  
This '''table of 270edo intervals''' assumes the [[31-limit]] [[patent val]] of [[270edo]] {{val| 270 428 647 758 934 999 1104 1147 1221 1312 1338 }}. [[Prime harmonic]]s are in '''bold'''; inconsistently mapped intervals are in ''italic''. As is analysed in the main article, besides being a strong 13-limit system, 270edo can be used in the full 23-limit with a handful of inconsistencies into the 27-odd-limit, or as a no-17 no-23 31-limit system, fully consistent to the 31-odd-limit. For this reason, intervals of 17 and 23 are given in parentheses.  


{| class="wikitable center-all right-1 right-2"
{| class="wikitable center-all right-1 right-2"
Line 10: Line 10:
! 11-limit
! 11-limit
! 13-limit
! 13-limit
! Higher Limits
! 23-limit
! 31-limit
|-
|-
| 0
| 0
Line 16: Line 17:
| P1
| P1
| '''1/1'''
| '''1/1'''
| "
| "
| "
| "
| "
Line 24: Line 26:
| 4.{{overline|4}}
| 4.{{overline|4}}
|  
|  
| 32805/32768
| ''32805/32768''
| 3136/3125
| 3136/3125
| 385/384
| 385/384
| 325/324
| "
|  
| "
| "
|-
|-
| 2
| 2
Line 36: Line 39:
| 225/224
| 225/224
| 176/175
| 176/175
| 169/168
| 196/195
|  
| "
| "
|-
|-
| 3
| 3
Line 44: Line 48:
| 78732/78125
| 78732/78125
| 126/125
| 126/125
| 121/120
| "
| "
|  
| "
| "
| "
|-
|-
| 4
| 4
Line 54: Line 59:
| "
| "
| 99/98
| 99/98
| 91/90
| "
| "
| "
| "
|-
|-
Line 64: Line 70:
| "
| "
| 78/77
| 78/77
| 76/75
| "
| "
|-
|-
| 6
| 6
Line 72: Line 79:
| 64/63
| 64/63
| "
| "
| 65/64
| "
| "
| "
| "
Line 80: Line 88:
| 3125/3072
| 3125/3072
| "
| "
| 55/54
| 56/55
| "
| "
| "
| "
| ''52/51''
|-
|-
| 8
| 8
Line 91: Line 100:
| "
| "
| "
| "
| ''46/45''
| "
| "
|-
|-
| 9
| 9
Line 99: Line 109:
| "
| "
| 45/44
| 45/44
| "
| "
| "
| "
| "
Line 110: Line 121:
| 40/39
| 40/39
| 39/38
| 39/38
| "
|-
|-
| 11
| 11
Line 118: Line 130:
| "
| "
| "
| "
| 35/34
| "
| "
|-
|-
| 12
| 12
Line 127: Line 140:
| 33/32
| 33/32
| "
| "
| 34/33
| "
| '''32/31'''
|-
|-
| 13
| 13
| 57.{{overline|7}}
| 57.{{overline|7}}
|  
|  
| 262144/253125
| ''262144/253125''
| 405/392
| 405/392
| 125/121
| 125/121
| 91/88
| 91/88
| ''88/85''
| "
| 30/29
|-
|-
| 14
| 14
Line 143: Line 158:
| 648/625
| 648/625
| 28/27
| 28/27
| "
| "
| "
| "
| "
Line 154: Line 170:
| 80/77
| 80/77
| 26/25
| 26/25
| "
| "
| "
|-
|-
Line 160: Line 177:
|  
|  
| 25/24
| 25/24
| "
| "
| "
| "
| "
Line 168: Line 186:
| 75.{{overline|5}}
| 75.{{overline|5}}
|  
|  
| 273375/262144
| ''273375/262144''
| 256/245
| 256/245
| "
| "
| 117/112
| 117/112
| 23/22
| (23/22)
| "
|-
|-
| 18
| 18
Line 180: Line 199:
| 1875/1792
| 1875/1792
| 22/21
| 22/21
| "
| "
| "
| "
| "
Line 188: Line 208:
| 6561/6250
| 6561/6250
| 21/20
| 21/20
| "
| "
| "
| "
| "
Line 200: Line 221:
| "
| "
| 20/19
| 20/19
| "
|-
|-
| 21
| 21
Line 209: Line 231:
| 96/91
| 96/91
| 19/18
| 19/18
| "
|-
|-
| 22
| 22
Line 217: Line 240:
| 128/121
| 128/121
| 55/52
| 55/52
| 18/17
| (18/17)
| "
|-
|-
| 23
| 23
Line 225: Line 249:
| 3584/3375
| 3584/3375
| 35/33
| 35/33
| "
| "
| "
| "
| "
Line 231: Line 256:
| 106.{{overline|6}}
| 106.{{overline|6}}
|  
|  
| 524288/492075
| ''524288/492075''
| 625/588
| 625/588
| "
| "
| 117/110
| 117/110
| '''17/16'''
| ('''17/16''')
| 33/31
|-
|-
| 25
| 25
Line 241: Line 267:
|  
|  
| 16/15
| 16/15
| "
| "
| "
| "
| "
Line 254: Line 281:
| "
| "
| "
| "
| 31/29
|-
|-
| 27
| 27
Line 260: Line 288:
| 3125/2916
| 3125/2916
| 15/14
| 15/14
| "
| "
| "
| "
| "
Line 267: Line 296:
| 124.{{overline|4}}
| 124.{{overline|4}}
|  
|  
| 140625/131072
| ''140625/131072''
| 672/625
| 672/625
| 189/176
| 189/176
| 130/121
| 130/121
| 102/95
| (102/95)
| 29/27
|-
|-
| 29
| 29
| 128.{{overline|8}}
| 128.{{overline|8}}
|  
|  
| 32768/30375
| ''32768/30375''
| 2205/2048
| 2205/2048
| 264/245
| 264/245
| 14/13
| 14/13
| "
| "
| "
|-
|-
Line 286: Line 317:
|  
|  
| 27/25
| 27/25
| "
| "
| "
| "
| "
Line 298: Line 330:
| 250/231
| 250/231
| 13/12
| 13/12
| "
| "
| "
|-
|-
Line 308: Line 341:
| "
| "
| 38/35
| 38/35
| "
|-
|-
| 33
| 33
Line 316: Line 350:
| "
| "
| "
| "
| ''25/23''
| (''25/23'')
| "
|-
|-
| 34
| 34
Line 324: Line 359:
| "
| "
| 12/11
| 12/11
| "
| "
| "
| "
| "
Line 334: Line 370:
| "
| "
| "
| "
| 23/21
| (23/21)
| "
|-
|-
| 36
| 36
Line 343: Line 380:
| "
| "
| 169/154
| 169/154
| 56/51
| (56/51)
| (34/31)
|-
|-
| 37
| 37
Line 351: Line 389:
| "
| "
| 11/10
| 11/10
| "
| "
| "
| "
| "
Line 362: Line 401:
| "
| "
| "
| "
| '''32/29'''
|-
|-
| 39
| 39
Line 371: Line 411:
| "
| "
| 21/19
| 21/19
| "
|-
|-
| 40
| 40
| 177.{{overline|7}}
| 177.{{overline|7}}
|  
|  
| 65536/59049
| ''65536/59049''
| 567/512
| 567/512
| 256/231
| 256/231
| 72/65
| 72/65
| "
| "
| 31/28
|-
|-
| 41
| 41
Line 385: Line 427:
|  
|  
| 10/9
| 10/9
| "
| "
| "
| "
| "
Line 393: Line 436:
| 186.{{overline|6}}
| 186.{{overline|6}}
|  
|  
| 18225/16384
| ''18225/16384''
| 4096/3675
| 4096/3675
| 49/44
| 49/44
| 39/35
| 39/35
| "
| "
| "
|-
|-
Line 406: Line 450:
| "
| "
| "
| "
| 19/17
| (19/17)
| 29/26
|-
|-
| 44
| 44
Line 413: Line 458:
| 17496/15625
| 17496/15625
| 28/25
| 28/25
| "
| "
| "
| "
| "
Line 423: Line 469:
| "
| "
| 55/49
| 55/49
| "
| "
| "
| "
| "
Line 430: Line 477:
| M2
| M2
| 9/8
| 9/8
| "
| "
| "
| "
| "
Line 443: Line 491:
| 44/39
| 44/39
| "
| "
| 35/31
|-
|-
| 48
| 48
Line 451: Line 500:
| 112/99
| 112/99
| "
| "
| 26/23
| (26/23)
| "
|-
|-
| 49
| 49
Line 460: Line 510:
| "
| "
| 143/126
| 143/126
| 17/15
| (17/15)
| "
|-
|-
| 50
| 50
Line 468: Line 519:
| "
| "
| 25/22
| 25/22
| "
| "
| "
| "
| "
Line 479: Line 531:
| "
| "
| 57/50
| 57/50
| "
|-
|-
| 52
| 52
Line 485: Line 538:
| 2500/2187
| 2500/2187
| '''8/7'''
| '''8/7'''
| "
| "
| "
| "
| "
Line 496: Line 550:
| 55/48
| 55/48
| "
| "
| 39/34
| (39/34)
| "
|-
|-
| 54
| 54
| 240.0
| 240.0
|  
|  
| 524288/455625
| ''524288/455625''
| 147/128
| 147/128
| "
| "
| "
| "
| 23/20
| (23/20)
| 31/27
|-
|-
| 55
| 55
Line 515: Line 571:
| "
| "
| 38/33
| 38/33
| "
|-
|-
| 56
| 56
Line 523: Line 580:
| 231/200
| 231/200
| 15/13
| 15/13
| "
| "
| "
|-
|-
Line 533: Line 591:
| "
| "
| 22/19
| 22/19
| "
|-
|-
| 58
| 58
| 257.{{overline|7}}
| 257.{{overline|7}}
|  
|  
| 151875/131072
| ''151875/131072''
| 512/441
| 512/441
| 297/256
| 297/256
| 65/56
| 65/56
| "
| "
| 29/25
|-
|-
| 59
| 59
| 262.{{overline|2}}
| 262.{{overline|2}}
|  
|  
| 32768/28125
| ''32768/28125''
| 3125/2688
| 3125/2688
| 64/55
| 64/55
| "
| "
| 57/49
| 57/49
| "
|-
|-
| 60
| 60
Line 557: Line 618:
| 729/625
| 729/625
| 7/6
| 7/6
| "
| "
| "
| "
| "
Line 569: Line 631:
| "
| "
| 76/65
| 76/65
| "
|-
|-
| 62
| 62
Line 578: Line 641:
| "
| "
| "
| "
| (34/29)
|-
|-
| 63
| 63
Line 586: Line 650:
| "
| "
| "
| "
| 20/17
| (20/17)
| "
|-
|-
| 64
| 64
Line 594: Line 659:
| 7168/6075
| 7168/6075
| 33/28
| 33/28
| "
| "
| "
| "
| "
Line 604: Line 670:
| "
| "
| 13/11
| 13/11
| "
| "
| "
|-
|-
Line 610: Line 677:
| m3
| m3
| 32/27
| 32/27
| "
| "
| "
| "
| "
Line 623: Line 691:
| 108/91
| 108/91
| '''19/16'''
| '''19/16'''
| "
|-
|-
| 68
| 68
Line 629: Line 698:
| 15625/13122
| 15625/13122
| 25/21
| 25/21
| "
| "
| "
| "
| "
Line 636: Line 706:
| 306.{{overline|6}}
| 306.{{overline|6}}
|  
|  
| 78125/65536
| ''78125/65536''
| 448/375
| 448/375
| 105/88
| 105/88
| 68/57
| "
| "
| (68/57)
| 31/26
|-
|-
| 70
| 70
| 311.{{overline|1}}
| 311.{{overline|1}}
|  
|  
| 65536/54675
| ''65536/54675''
| 1225/1024
| 1225/1024
| 176/147
| 176/147
| 140/117
| 140/117
| 91/76
| 91/76
| "
|-
|-
| 71
| 71
Line 655: Line 727:
|  
|  
| 6/5
| 6/5
| "
| "
| "
| "
| "
Line 663: Line 736:
| 320.0
| 320.0
|  
|  
| 19683/16384
| ''19683/16384''
| 2048/1701
| 2048/1701
| 77/64
| 77/64
| 65/54
| 65/54
| "
| "
| "
|-
|-
Line 677: Line 751:
| "
| "
| 76/63
| 76/63
| 35/29
|-
|-
| 74
| 74
Line 685: Line 760:
| "
| "
| "
| "
| 23/19
| (23/19)
| 29/24
|-
|-
| 75
| 75
Line 693: Line 769:
| "
| "
| 40/33
| 40/33
| "
| "
| "
| "
| "
Line 703: Line 780:
| 147/121
| 147/121
| "
| "
| 17/14
| (17/14)
| "
|-
|-
| 77
| 77
Line 712: Line 790:
| "
| "
| 39/32
| 39/32
| 28/23
| (28/23)
| "
|-
|-
| 78
| 78
Line 720: Line 799:
| "
| "
| 11/9
| 11/9
| "
| "
| "
| "
| "
Line 731: Line 811:
| "
| "
| "
| "
| 38/31
|-
|-
| 80
| 80
Line 738: Line 819:
| "
| "
| 27/22
| 27/22
| "
| "
| "
| "
| "
Line 748: Line 830:
| 154/125
| 154/125
| '''16/13'''
| '''16/13'''
| "
| "
| "
|-
|-
Line 757: Line 840:
| "
| "
| "
| "
| 21/17
| (21/17)
| "
|-
|-
| 83
| 83
Line 766: Line 850:
| 99/80
| 99/80
| 26/21
| 26/21
| "
| "
| "
|-
|-
Line 775: Line 860:
| 150/121
| 150/121
| "
| "
| 57/46
| (57/46)
| 31/25
|-
|-
| 85
| 85
Line 782: Line 868:
| 3888/3125
| 3888/3125
| 56/45
| 56/45
| "
| "
| "
| "
| "
Line 793: Line 880:
| 96/77
| 96/77
| 81/65
| 81/65
| "
| "
| "
|-
|-
Line 799: Line 887:
|  
|  
| '''5/4'''
| '''5/4'''
| "
| "
| "
| "
| "
Line 807: Line 896:
| 391.{{overline|1}}
| 391.{{overline|1}}
|  
|  
| 164025/131072
| ''164025/131072''
| 784/625
| 784/625
| 441/352
| 441/352
| 351/280
| 351/280
| 64/51
| (64/51)
| "
|-
|-
| 89
| 89
Line 819: Line 909:
| 1125/896
| 1125/896
| 44/35
| 44/35
| "
| "
| "
| "
| "
Line 829: Line 920:
| "
| "
| "
| "
| 34/27
| (34/27)
| 39/31
|-
|-
| 91
| 91
Line 839: Line 931:
| 91/72
| 91/72
| 24/19
| 24/19
| "
|-
|-
| 92
| 92
Line 848: Line 941:
| "
| "
| 19/15
| 19/15
| "
|-
|-
| 93
| 93
Line 856: Line 950:
| "
| "
| 33/26
| 33/26
| "
| "
| "
|-
|-
Line 864: Line 959:
| 7168/5625
| 7168/5625
| 14/11
| 14/11
| "
| "
| "
| "
| "
Line 870: Line 966:
| 422.{{overline|2}}
| 422.{{overline|2}}
|  
|  
| 1048576/820125
| ''1048576/820125''
| 125/98
| 125/98
| "
| "
| "
| "
| 23/18
| (23/18)
| "
|-
|-
| 96
| 96
Line 880: Line 977:
|  
|  
| 32/25
| 32/25
| "
| "
| "
| "
| "
Line 892: Line 990:
| 77/60
| 77/60
| 50/39
| 50/39
| "
| "
| "
|-
|-
Line 899: Line 998:
| 625/486
| 625/486
| 9/7
| 9/7
| "
| "
| "
| "
| "
Line 906: Line 1,006:
| 440.0
| 440.0
|  
|  
| 84375/65536
| ''84375/65536''
| 1568/1215
| 1568/1215
| 165/128
| 165/128
| 156/121
| 156/121
| 49/38
| 49/38
| 40/31
|-
|-
| 100
| 100
| 444.{{overline|4}}
| 444.{{overline|4}}
|  
|  
| 65536/50625
| ''65536/50625''
| 1323/1024
| 1323/1024
| 128/99
| 128/99
| 84/65
| 84/65
| 22/17
| (22/17)
| 31/24
|-
|-
| 101
| 101
Line 926: Line 1,028:
| 162/125
| 162/125
| 35/27
| 35/27
| "
| "
| "
| "
| "
Line 937: Line 1,040:
| 100/77
| 100/77
| 13/10
| 13/10
| "
| "
| "
|-
|-
Line 947: Line 1,051:
| "
| "
| 99/76
| 99/76
| "
|-
|-
| 104
| 104
| 462.{{overline|2}}
| 462.{{overline|2}}
|  
|  
| 1366875/1048576
| ''1366875/1048576''
| 64/49
| 64/49
| "
| "
| "
| "
| ''30/23''
| (''30/23'')
| "
|-
|-
| 105
| 105
Line 964: Line 1,070:
| 55/42
| 55/42
| "
| "
| ''17/13''
| (''17/13'')
| 38/29
|-
|-
| 106
| 106
Line 971: Line 1,078:
| 6561/5000
| 6561/5000
| 21/16
| 21/16
| "
| "
| "
| "
| "
Line 983: Line 1,091:
| 154/117
| 154/117
| 25/19
| 25/19
| "
|-
|-
| 108
| 108
Line 992: Line 1,101:
| "
| "
| "
| "
| 29/22
|-
|-
| 109
| 109
Line 1,000: Line 1,110:
| 160/121
| 160/121
| 143/108
| 143/108
| 45/34
| (45/34)
| "
|-
|-
| 110
| 110
Line 1,009: Line 1,120:
| 175/132
| 175/132
| 65/49
| 65/49
| "
| "
| "
|-
|-
Line 1,014: Line 1,126:
| 493.{{overline|3}}
| 493.{{overline|3}}
|  
|  
| 131072/98415
| ''131072/98415''
| 1701/1280
| 1701/1280
| 512/385
| 512/385
| 117/88
| 117/88
| 85/64
| (85/64)
| "
|-
|-
| 112
| 112
Line 1,024: Line 1,137:
| P4
| P4
| 4/3
| 4/3
| "
| "
| "
| "
| "
Line 1,032: Line 1,146:
| 502.{{overline|2}}
| 502.{{overline|2}}
|  
|  
| 10935/8192
| ''10935/8192''
| 8192/6125
| 8192/6125
| 147/110
| 147/110
| "
| "
| 91/68
| (91/68)
| "
|-
|-
| 114
| 114
Line 1,043: Line 1,158:
| 15625/11664
| 15625/11664
| 75/56
| 75/56
| "
| "
| "
| "
| "
Line 1,054: Line 1,170:
| 121/90
| 121/90
| "
| "
| 51/38
| (51/38)
| 39/29
|-
|-
| 116
| 116
Line 1,063: Line 1,180:
| 66/49
| 66/49
| 35/26
| 35/26
| "
| "
| "
|-
|-
Line 1,072: Line 1,190:
| "
| "
| "
| "
| ''23/17''
| (''23/17'')
| "
|-
|-
| 118
| 118
Line 1,082: Line 1,201:
| 65/48
| 65/48
| "
| "
| 42/31
|-
|-
| 119
| 119
Line 1,091: Line 1,211:
| "
| "
| 19/14
| 19/14
| "
|-
|-
| 120
| 120
Line 1,099: Line 1,220:
| "
| "
| "
| "
| 34/25
| (34/25)
| "
|-
|-
| 121
| 121
Line 1,107: Line 1,229:
| "
| "
| 15/11
| 15/11
| "
| "
| "
| "
| "
Line 1,118: Line 1,241:
| 160/117
| 160/117
| 26/19
| 26/19
| "
|-
|-
| 123
| 123
Line 1,124: Line 1,248:
| 1000/729
| 1000/729
| 48/35
| 48/35
| "
| "
| "
| "
| "
Line 1,134: Line 1,259:
| "
| "
| '''11/8'''
| '''11/8'''
| "
| "
| "
| "
| "
Line 1,140: Line 1,266:
| 555.{{overline|5}}
| 555.{{overline|5}}
|  
|  
| 1048576/759375
| ''1048576/759375''
| 135/98
| 135/98
| "
| "
| 91/66
| 91/66
| 69/50
| (69/50)
| 40/29
|-
|-
| 126
| 126
Line 1,154: Line 1,281:
| "
| "
| 105/76
| 105/76
| 29/21
|-
|-
| 127
| 127
| 564.{{overline|4}}
| 564.{{overline|4}}
|  
|  
| 81920/59049
| ''81920/59049''
| 2835/2048
| 2835/2048
| 320/231
| 320/231
| 18/13
| 18/13
| "
| "
| "
|-
|-
Line 1,168: Line 1,297:
|  
|  
| 25/18
| 25/18
| "
| "
| "
| "
| "
Line 1,176: Line 1,306:
| 573.{{overline|3}}
| 573.{{overline|3}}
|  
|  
| 91125/65536
| ''91125/65536''
| 1024/735
| 1024/735
| 245/176
| 245/176
| 39/28
| 39/28
| '''32/23'''
| ('''32/23''')
| "
|-
|-
| 130
| 130
| 577.{{overline|7}}
| 577.{{overline|7}}
|  
|  
| 65536/46875
| ''65536/46875''
| 625/448
| 625/448
| 88/63
| 88/63
| "
| "
| "
| "
| "
Line 1,196: Line 1,328:
| 4374/3125
| 4374/3125
| 7/5
| 7/5
| "
| "
| "
| "
| "
Line 1,208: Line 1,341:
| "
| "
| 80/57
| 80/57
| "
|-
|-
| 133
| 133
Line 1,217: Line 1,351:
| "
| "
| 38/27
| 38/27
| "
|-
|-
| 134
| 134
Line 1,225: Line 1,360:
| "
| "
| 55/39
| 55/39
| 24/17
| (24/17)
| 31/22
|-
|-
| 135
| 135
Line 1,233: Line 1,369:
| 10125/7168
| 10125/7168
| 99/70
| 99/70
| "
| "
| "
| "
| "
Line 1,243: Line 1,380:
| 343/242
| 343/242
| 78/55
| 78/55
| 17/12
| (17/12)
| 44/31
|-
|-
| 137
| 137
Line 1,253: Line 1,391:
| "
| "
| 27/19
| 27/19
| "
|-
|-
| 138
| 138
Line 1,262: Line 1,401:
| "
| "
| 57/40
| 57/40
| "
|-
|-
| 139
| 139
Line 1,268: Line 1,408:
| 3125/2187
| 3125/2187
| 10/7
| 10/7
| "
| "
| "
| "
| "
Line 1,275: Line 1,416:
| 622.{{overline|2}}
| 622.{{overline|2}}
|  
|  
| 46875/32768
| ''46875/32768''
| 896/625
| 896/625
| 63/44
| 63/44
| "
| "
| "
| "
| "
Line 1,284: Line 1,426:
| 626.{{overline|6}}
| 626.{{overline|6}}
|  
|  
| 131072/91125
| ''131072/91125''
| 735/512
| 735/512
| 352/245
| 352/245
| 56/39
| 56/39
| '''23/16'''
| ('''23/16''')
| "
|-
|-
| 142
| 142
Line 1,294: Line 1,437:
|  
|  
| 36/25
| 36/25
| "
| "
| "
| "
| "
Line 1,302: Line 1,446:
| 635.{{overline|5}}
| 635.{{overline|5}}
|  
|  
| 59049/40960
| ''59049/40960''
| 4096/2835
| 4096/2835
| 231/160
| 231/160
| 13/9
| 13/9
| "
| "
| "
|-
|-
Line 1,316: Line 1,461:
| "
| "
| "
| "
| 42/29
|-
|-
| 145
| 145
| 644.{{overline|4}}
| 644.{{overline|4}}
|  
|  
| 759375/524288
| ''759375/524288''
| 196/135
| 196/135
| "
| "
| 132/91
| 132/91
| 100/69
| (100/69)
| 29/20
|-
|-
| 146
| 146
Line 1,332: Line 1,479:
| "
| "
| '''16/11'''
| '''16/11'''
| "
| "
| "
| "
| "
Line 1,340: Line 1,488:
| 729/500
| 729/500
| 35/24
| 35/24
| "
| "
| "
| "
| "
Line 1,352: Line 1,501:
| 117/80
| 117/80
| 19/13
| 19/13
| "
|-
|-
| 149
| 149
Line 1,359: Line 1,509:
| "
| "
| 22/15
| 22/15
| "
| "
| "
| "
| "
Line 1,369: Line 1,520:
| "
| "
| "
| "
| 25/17
| (25/17)
| "
|-
|-
| 151
| 151
Line 1,379: Line 1,531:
| "
| "
| 28/19
| 28/19
| "
|-
|-
| 152
| 152
Line 1,388: Line 1,541:
| 65/44
| 65/44
| "
| "
| 31/21
|-
|-
| 153
| 153
Line 1,396: Line 1,550:
| "
| "
| "
| "
| ''34/23''
| (''34/23'')
| "
|-
|-
| 154
| 154
Line 1,404: Line 1,559:
| "
| "
| 49/33
| 49/33
| "
| "
| "
| "
| "
Line 1,414: Line 1,570:
| "
| "
| "
| "
| 76/51
| (76/51)
| 58/39
|-
|-
| 156
| 156
Line 1,423: Line 1,580:
| "
| "
| "
| "
| 85/57
| (85/57)
| "
|-
|-
| 157
| 157
| 697.{{overline|7}}
| 697.{{overline|7}}
|  
|  
| 16384/10935
| ''16384/10935''
| 6125/4096
| 6125/4096
| 220/147
| 220/147
| 175/117
| 175/117
| 136/91
| (136/91)
| "
|-
|-
| 158
| 158
Line 1,438: Line 1,597:
| P5
| P5
| 3/2
| 3/2
| "
| "
| "
| "
| "
Line 1,446: Line 1,606:
| 706.{{overline|6}}
| 706.{{overline|6}}
|  
|  
| 98415/65536
| ''98415/65536''
| 2560/1701
| 2560/1701
| 385/256
| 385/256
| 176/117
| 176/117
| 128/85
| (128/85)
| "
|-
|-
| 160
| 160
Line 1,460: Line 1,621:
| 98/65
| 98/65
| 95/63
| 95/63
| "
|-
|-
| 161
| 161
Line 1,468: Line 1,630:
| 121/80
| 121/80
| "
| "
| 68/45
| (68/45)
| "
|-
|-
| 162
| 162
Line 1,478: Line 1,641:
| "
| "
| "
| "
| 44/29
|-
|-
| 163
| 163
Line 1,487: Line 1,651:
| 117/77
| 117/77
| 38/25
| 38/25
| "
|-
|-
| 164
| 164
Line 1,493: Line 1,658:
| 10000/6561
| 10000/6561
| 32/21
| 32/21
| "
| "
| "
| "
| "
Line 1,504: Line 1,670:
| 55/36
| 55/36
| "
| "
| ''26/17''
| (''26/17'')
| 29/19
|-
|-
| 166
| 166
| 737.{{overline|7}}
| 737.{{overline|7}}
|  
|  
| 2097152/1366875
| ''2097152/1366875''
| 49/32
| 49/32
| "
| "
| "
| "
| ''23/15''
| (''23/15'')
| "
|-
|-
| 167
| 167
Line 1,521: Line 1,689:
| "
| "
| 135/88
| 135/88
| "
| "
| "
| "
| "
Line 1,531: Line 1,700:
| 77/50
| 77/50
| 20/13
| 20/13
| "
| "
| "
|-
|-
Line 1,538: Line 1,708:
| 125/81
| 125/81
| 54/35
| 54/35
| "
| "
| "
| "
| "
Line 1,545: Line 1,716:
| 755.{{overline|5}}
| 755.{{overline|5}}
|  
|  
| 50625/32768
| ''50625/32768''
| 2048/1323
| 2048/1323
| 99/64
| 99/64
| 65/42
| 65/42
| 17/11
| (17/11)
| 48/31
|-
|-
| 171
| 171
| 760.0
| 760.0
|  
|  
| 131072/84375
| ''131072/84375''
| 1215/784
| 1215/784
| 256/165
| 256/165
| 121/78
| 121/78
| 76/49
| 76/49
| 31/20
|-
|-
| 172
| 172
Line 1,565: Line 1,738:
| 972/625
| 972/625
| 14/9
| 14/9
| "
| "
| "
| "
| "
Line 1,576: Line 1,750:
| 120/77
| 120/77
| 39/25
| 39/25
| "
| "
| "
|-
|-
Line 1,582: Line 1,757:
|  
|  
| 25/16
| 25/16
| "
| "
| "
| "
| "
Line 1,590: Line 1,766:
| 777.{{overline|7}}
| 777.{{overline|7}}
|  
|  
| 820125/524288
| ''820125/524288''
| 196/125
| 196/125
| "
| "
| "
| "
| 36/23
| (36/23)
| "
|-
|-
| 176
| 176
Line 1,602: Line 1,779:
| 5625/3584
| 5625/3584
| 11/7
| 11/7
| "
| "
| "
| "
| "
Line 1,612: Line 1,790:
| "
| "
| 52/33
| 52/33
| "
| "
| "
|-
|-
Line 1,622: Line 1,801:
| "
| "
| 30/19
| 30/19
| "
|-
|-
| 179
| 179
Line 1,631: Line 1,811:
| 144/91
| 144/91
| 19/12
| 19/12
| "
|-
|-
| 180
| 180
Line 1,639: Line 1,820:
| "
| "
| "
| "
| 27/17
| (27/17)
| 62/39
|-
|-
| 181
| 181
Line 1,647: Line 1,829:
| 1792/1125
| 1792/1125
| 35/22
| 35/22
| "
| "
| "
| "
| "
Line 1,653: Line 1,836:
| 808.{{overline|8}}
| 808.{{overline|8}}
|  
|  
| 262144/164025
| ''262144/164025''
| 625/392
| 625/392
| "
| "
| 351/220
| 351/220
| 51/32
| (51/32)
| "
|-
|-
| 183
| 183
Line 1,663: Line 1,847:
|  
|  
| '''8/5'''
| '''8/5'''
| "
| "
| "
| "
| "
Line 1,674: Line 1,859:
| "
| "
| 77/48
| 77/48
| "
| "
| "
| "
| "
Line 1,682: Line 1,868:
| 3125/1944
| 3125/1944
| 45/28
| 45/28
| "
| "
| "
| "
| "
Line 1,693: Line 1,880:
| 121/75
| 121/75
| "
| "
| 92/57
| (92/57)
| 29/18
|-
|-
| 187
| 187
Line 1,702: Line 1,890:
| 160/99
| 160/99
| 21/13
| 21/13
| "
| "
| "
|-
|-
Line 1,711: Line 1,900:
| "
| "
| "
| "
| 34/21
| (34/21)
| "
|-
|-
| 189
| 189
Line 1,720: Line 1,910:
| 125/77
| 125/77
| '''13/8'''
| '''13/8'''
| "
| "
| "
|-
|-
Line 1,728: Line 1,919:
| "
| "
| 44/27
| 44/27
| "
| "
| "
| "
| "
Line 1,739: Line 1,931:
| "
| "
| "
| "
| 31/19
|-
|-
| 192
| 192
Line 1,746: Line 1,939:
| "
| "
| 18/11
| 18/11
| "
| "
| "
| "
| "
Line 1,756: Line 1,950:
| "
| "
| 64/39
| 64/39
| 23/14
| (23/14)
| "
|-
|-
| 194
| 194
Line 1,765: Line 1,960:
| 242/147
| 242/147
| "
| "
| 28/17
| (28/17)
| "
|-
|-
| 195
| 195
Line 1,773: Line 1,969:
| "
| "
| 33/20
| 33/20
| "
| "
| "
| "
| "
Line 1,783: Line 1,980:
| "
| "
| "
| "
| 38/23
| (38/23)
| 48/29
|-
|-
| 197
| 197
Line 1,793: Line 1,991:
| "
| "
| 63/38
| 63/38
| 58/35
|-
|-
| 198
| 198
| 880.0
| 880.0
|  
|  
| 32768/19683
| ''32768/19683''
| 1701/1024
| 1701/1024
| 128/77
| 128/77
| 108/65
| 108/65
| "
| "
| "
|-
|-
Line 1,807: Line 2,007:
|  
|  
| 5/3
| 5/3
| "
| "
| "
| "
| "
Line 1,815: Line 2,016:
| 888.{{overline|8}}
| 888.{{overline|8}}
|  
|  
| 54675/32768
| ''54675/32768''
| 2048/1225
| 2048/1225
| 147/88
| 147/88
| 117/70
| 117/70
| "
| "
| "
|-
|-
Line 1,829: Line 2,031:
| 57/34
| 57/34
| "
| "
| 52/31
|-
|-
| 202
| 202
Line 1,835: Line 2,038:
| 26244/15625
| 26244/15625
| 42/25
| 42/25
| "
| "
| "
| "
| "
Line 1,847: Line 2,051:
| 91/54
| 91/54
| '''32/19'''
| '''32/19'''
| "
|-
|-
| 204
| 204
Line 1,852: Line 2,057:
| M6
| M6
| 27/16
| 27/16
| "
| "
| "
| "
| "
Line 1,864: Line 2,070:
| "
| "
| 22/13
| 22/13
| "
| "
| "
|-
|-
Line 1,873: Line 2,080:
| 56/33
| 56/33
| "
| "
| 39/23
| (39/23)
| "
|-
|-
| 207
| 207
Line 1,882: Line 2,090:
| "
| "
| 143/84
| 143/84
| 17/10
| (17/10)
| "
|-
|-
| 208
| 208
Line 1,892: Line 2,101:
| "
| "
| "
| "
| (29/17)
|-
|-
| 209
| 209
Line 1,901: Line 2,111:
| "
| "
| 65/38
| 65/38
| "
|-
|-
| 210
| 210
Line 1,907: Line 2,118:
| 1250/729
| 1250/729
| 12/7
| 12/7
| "
| "
| "
| "
| "
Line 1,914: Line 2,126:
| 937.{{overline|7}}
| 937.{{overline|7}}
|  
|  
| 28125/16384
| ''28125/16384''
| 5376/3125
| 5376/3125
| 55/32
| 55/32
| "
| "
| "
| "
| "
Line 1,923: Line 2,136:
| 942.{{overline|2}}
| 942.{{overline|2}}
|  
|  
| 262144/151875
| ''262144/151875''
| 441/256
| 441/256
| "
| "
| 112/65
| 112/65
| 69/40
| (69/40)
| 31/18
|-
|-
| 213
| 213
Line 1,937: Line 2,151:
| "
| "
| 19/11
| 19/11
| "
|-
|-
| 214
| 214
Line 1,945: Line 2,160:
| 343/198
| 343/198
| 26/15
| 26/15
| "
| "
| "
|-
|-
Line 1,955: Line 2,171:
| "
| "
| 33/19
| 33/19
| "
|-
|-
| 216
| 216
| 960.0
| 960.0
|  
|  
| 455625/262144
| ''455625/262144''
| 256/147
| 256/147
| "
| "
| 195/112
| 195/112
| 40/23
| (40/23)
| 54/31
|-
|-
| 217
| 217
Line 1,972: Line 2,190:
| 96/55
| 96/55
| "
| "
| 68/39
| (68/39)
| "
|-
|-
| 218
| 218
Line 1,979: Line 2,198:
| 2187/1250
| 2187/1250
| '''7/4'''
| '''7/4'''
| "
| "
| "
| "
| "
Line 1,991: Line 2,211:
| "
| "
| 100/57
| 100/57
| "
|-
|-
| 220
| 220
Line 1,998: Line 2,219:
| "
| "
| 44/25
| 44/25
| "
| "
| "
| "
| "
Line 2,008: Line 2,230:
| "
| "
| 143/81
| 143/81
| 30/17
| (30/17)
| "
|-
|-
| 222
| 222
Line 2,017: Line 2,240:
| 99/56
| 99/56
| "
| "
| 23/13
| (23/13)
| "
|-
|-
| 223
| 223
Line 2,026: Line 2,250:
| "
| "
| 39/22
| 39/22
| "
| "
| "
|-
|-
Line 2,032: Line 2,257:
| m7
| m7
| 16/9
| 16/9
| "
| "
| "
| "
| "
Line 2,045: Line 2,271:
| "
| "
| 57/32
| 57/32
| "
|-
|-
| 226
| 226
Line 2,051: Line 2,278:
| 15625/8748
| 15625/8748
| 25/14
| 25/14
| "
| "
| "
| "
| "
Line 2,062: Line 2,290:
| "
| "
| "
| "
| 34/19
| (34/19)
| 52/29
|-
|-
| 228
| 228
| 1013.{{overline|3}}
| 1013.{{overline|3}}
|  
|  
| 32768/18225
| ''32768/18225''
| 3675/2048
| 3675/2048
| 88/49
| 88/49
| 70/39
| 70/39
| "
| "
| "
|-
|-
Line 2,077: Line 2,307:
|  
|  
| 9/5
| 9/5
| "
| "
| "
| "
| "
Line 2,085: Line 2,316:
| 1022.{{overline|2}}
| 1022.{{overline|2}}
|  
|  
| 59049/32768
| ''59049/32768''
| 1024/567
| 1024/567
| 231/128
| 231/128
| 65/36
| 65/36
| "
| "
| 56/31
|-
|-
| 231
| 231
Line 2,099: Line 2,331:
| "
| "
| 38/21
| 38/21
| "
|-
|-
| 232
| 232
Line 2,108: Line 2,341:
| "
| "
| "
| "
| '''29/16'''
|-
|-
| 233
| 233
Line 2,115: Line 2,349:
| "
| "
| 20/11
| 20/11
| "
| "
| "
| "
| "
Line 2,125: Line 2,360:
| "
| "
| "
| "
| 51/28
| (51/28)
| (31/17)
|-
|-
| 235
| 235
Line 2,134: Line 2,370:
| "
| "
| "
| "
| 42/23
| (42/23)
| "
|-
|-
| 236
| 236
Line 2,142: Line 2,379:
| "
| "
| 11/6
| 11/6
| "
| "
| "
| "
| "
Line 2,152: Line 2,390:
| "
| "
| "
| "
| ''46/25''
| (''46/25'')
| "
|-
|-
| 238
| 238
Line 2,162: Line 2,401:
| "
| "
| 35/19
| 35/19
| "
|-
|-
| 239
| 239
Line 2,170: Line 2,410:
| 231/125
| 231/125
| 24/13
| 24/13
| "
| "
| "
|-
|-
Line 2,176: Line 2,417:
|  
|  
| 50/27
| 50/27
| "
| "
| "
| "
| "
Line 2,184: Line 2,426:
| 1071.{{overline|1}}
| 1071.{{overline|1}}
|  
|  
| 30375/16384
| ''30375/16384''
| 4096/2205
| 4096/2205
| 245/132
| 245/132
| 13/7
| 13/7
| "
| "
| "
|-
|-
Line 2,193: Line 2,436:
| 1075.{{overline|5}}
| 1075.{{overline|5}}
|  
|  
| 262144/140625
| ''262144/140625''
| 625/336
| 625/336
| 225/121
| 225/121
| 121/65
| 121/65
| 95/51
| (95/51)
| 54/29
|-
|-
| 243
| 243
Line 2,204: Line 2,448:
| 5832/3125
| 5832/3125
| 28/15
| 28/15
| "
| "
| "
| "
| "
Line 2,216: Line 2,461:
| "
| "
| "
| "
| 58/31
|-
|-
| 245
| 245
Line 2,221: Line 2,467:
|  
|  
| 15/8
| 15/8
| "
| "
| "
| "
| "
Line 2,229: Line 2,476:
| 1093.{{overline|3}}
| 1093.{{overline|3}}
|  
|  
| 492075/262144
| ''492075/262144''
| 1176/625
| 1176/625
| 847/450
| 847/450
| 220/117
| 220/117
| '''32/17'''
| ('''32/17''')
| 62/33
|-
|-
| 247
| 247
Line 2,242: Line 2,490:
| 66/35
| 66/35
| 49/26
| 49/26
| "
| "
| "
|-
|-
Line 2,251: Line 2,500:
| 121/64
| 121/64
| 104/55
| 104/55
| 17/9
| (17/9)
| "
|-
|-
| 249
| 249
Line 2,261: Line 2,511:
| 91/48
| 91/48
| 36/19
| 36/19
| "
|-
|-
| 250
| 250
Line 2,270: Line 2,521:
| "
| "
| 19/10
| 19/10
| "
|-
|-
| 251
| 251
Line 2,276: Line 2,528:
| 12500/6561
| 12500/6561
| 40/21
| 40/21
| "
| "
| "
| "
| "
Line 2,286: Line 2,539:
| 3584/1875
| 3584/1875
| 21/11
| 21/11
| "
| "
| "
| "
| "
Line 2,292: Line 2,546:
| 1124.{{overline|4}}
| 1124.{{overline|4}}
|  
|  
| 524288/273375
| ''524288/273375''
| 245/128
| 245/128
| "
| "
| 224/117
| 224/117
| 23/12
| (23/12)
| "
|-
|-
| 254
| 254
Line 2,302: Line 2,557:
|  
|  
| 48/25
| 48/25
| "
| "
| "
| "
| "
Line 2,314: Line 2,570:
| 77/40
| 77/40
| 25/13
| 25/13
| "
| "
| "
|-
|-
Line 2,321: Line 2,578:
| 625/324
| 625/324
| 27/14
| 27/14
| "
| "
| "
| "
| "
Line 2,328: Line 2,586:
| 1142.{{overline|2}}
| 1142.{{overline|2}}
|  
|  
| 253125/131072
| ''253125/131072''
| 784/405
| 784/405
| 242/125
| 242/125
| 176/91
| 176/91
| ''85/44''
| (''85/44'')
| 29/15
|-
|-
| 258
| 258
Line 2,341: Line 2,600:
| 64/33
| 64/33
| "
| "
| 33/17
| (33/17)
| '''31/16'''
|-
|-
| 259
| 259
Line 2,348: Line 2,608:
| 243/125
| 243/125
| 35/18
| 35/18
| "
| "
| "
| "
| "
Line 2,359: Line 2,620:
| 150/77
| 150/77
| 39/20
| 39/20
| "
| "
| "
|-
|-
Line 2,367: Line 2,629:
| "
| "
| 88/45
| 88/45
| "
| "
| "
| "
| "
Line 2,377: Line 2,640:
| "
| "
| "
| "
| ''45/23''
| (''45/23'')
| "
|-
|-
| 263
| 263
Line 2,386: Line 2,650:
| 55/28
| 55/28
| "
| "
| ''51/26''
| (''51/26'')
| "
|-
|-
| 264
| 264
Line 2,393: Line 2,658:
| 19683/10000
| 19683/10000
| 63/32
| 63/32
| "
| "
| "
| "
| "
Line 2,405: Line 2,671:
| 77/39
| 77/39
| 75/38
| 75/38
| "
|-
|-
| 266
| 266
Line 2,413: Line 2,680:
| 99/50
| 99/50
| "
| "
| 91/46
| (91/46)
| 87/44
|-
|-
| 267
| 267
Line 2,422: Line 2,690:
| "
| "
| "
| "
|  
| "
| "
|-
|-
| 268
| 268
Line 2,431: Line 2,700:
| 175/88
| 175/88
| "
| "
|  
| "
| "
|-
|-
| 269
| 269
| 1195.{{overline|5}}
| 1195.{{overline|5}}
|  
|  
| 65536/32805
| ''65536/32805''
| 3125/1568
| 3125/1568
| 768/385
| 768/385
| 648/325
| 648/325
|  
| (''255/128'')
| "
|-
|-
| 270
| 270
Line 2,446: Line 2,717:
| P8
| P8
| '''2/1'''
| '''2/1'''
| "
| "
| "
| "
| "

Revision as of 14:38, 26 July 2024

This table of 270edo intervals assumes the 31-limit patent val of 270edo ⟨270 428 647 758 934 999 1104 1147 1221 1312 1338]. Prime harmonics are in bold; inconsistently mapped intervals are in italic. As is analysed in the main article, besides being a strong 13-limit system, 270edo can be used in the full 23-limit with a handful of inconsistencies into the 27-odd-limit, or as a no-17 no-23 31-limit system, fully consistent to the 31-odd-limit. For this reason, intervals of 17 and 23 are given in parentheses.

# Cents Marks 5-limit 7-limit 11-limit 13-limit 23-limit 31-limit
0 0.0 P1 1/1 " " " " "
1 4.4 32805/32768 3136/3125 385/384 " " "
2 8.8 15625/15552 225/224 176/175 196/195 " "
3 13.3 78732/78125 126/125 " " " "
4 17.7 2048/2025 " 99/98 " " "
5 22.2 81/80 " " 78/77 " "
6 26.6 20000/19683 64/63 " 65/64 " "
7 31.1 3125/3072 " 56/55 " " "
8 35.5 1594323/1562500 49/48 " " " "
9 40.0 128/125 " 45/44 " " "
10 44.4 6561/6400 525/512 77/75 40/39 39/38 "
11 48.8 250/243 36/35 " " " "
12 53.3 16875/16384 4096/3969 33/32 " " 32/31
13 57.7 262144/253125 405/392 125/121 91/88 " 30/29
14 62.2 648/625 28/27 " " " "
15 66.6 20480/19683 8192/7875 80/77 26/25 " "
16 71.1 25/24 " " " " "
17 75.5 273375/262144 256/245 " 117/112 (23/22) "
18 80.0 16384/15625 1875/1792 22/21 " " "
19 84.4 6561/6250 21/20 " " " "
20 88.8 m2 256/243 " 81/77 " 20/19 "
21 93.3 135/128 " 132/125 96/91 19/18 "
22 97.7 62500/59049 200/189 128/121 55/52 (18/17) "
23 102.2 78125/73728 3584/3375 35/33 " " "
24 106.6 524288/492075 625/588 " 117/110 (17/16) 33/31
25 111.1 16/15 " " " " "
26 115.5 2187/2048 " 77/72 " " 31/29
27 120.0 3125/2916 15/14 " " " "
28 124.4 140625/131072 672/625 189/176 130/121 (102/95) 29/27
29 128.8 32768/30375 2205/2048 264/245 14/13 " "
30 133.3 27/25 " " " " "
31 137.7 64000/59049 1024/945 250/231 13/12 " "
32 142.2 625/576 243/224 88/81 " 38/35 "
33 146.6 2125764/1953125 49/45 " " (25/23) "
34 151.1 2048/1875 " 12/11 " " "
35 155.5 2187/2000 35/32 " " (23/21) "
36 160.0 800/729 192/175 " 169/154 (56/51) (34/31)
37 164.4 1125/1024 " 11/10 " " "
38 168.8 390625/354294 54/49 " " " 32/29
39 173.3 3456/3125 448/405 243/220 " 21/19 "
40 177.7 65536/59049 567/512 256/231 72/65 " 31/28
41 182.2 10/9 " " " " "
42 186.6 18225/16384 4096/3675 49/44 39/35 " "
43 191.1 78125/69984 125/112 " " (19/17) 29/26
44 195.5 17496/15625 28/25 " " " "
45 200.0 4096/3645 " 55/49 " " "
46 204.4 M2 9/8 " " " " "
47 208.8 200000/177147 640/567 " 44/39 " 35/31
48 213.3 15625/13824 2025/1792 112/99 " (26/23) "
49 217.7 177147/156250 245/216 " 143/126 (17/15) "
50 222.2 256/225 " 25/22 " " "
51 226.6 729/640 " 154/135 " 57/50 "
52 231.1 2500/2187 8/7 " " " "
53 235.5 9375/8192 3584/3125 55/48 " (39/34) "
54 240.0 524288/455625 147/128 " " (23/20) 31/27
55 244.4 144/125 " 121/105 " 38/33 "
56 248.8 59049/51200 4725/4096 231/200 15/13 " "
57 253.3 125/108 81/70 " " 22/19 "
58 257.7 151875/131072 512/441 297/256 65/56 " 29/25
59 262.2 32768/28125 3125/2688 64/55 " 57/49 "
60 266.6 729/625 7/6 " " " "
61 271.1 2560/2187 1024/875 90/77 " 76/65 "
62 275.5 75/64 " " " " (34/29)
63 280.0 625000/531441 147/125 " " (20/17) "
64 284.4 18432/15625 7168/6075 33/28 " " "
65 288.8 59049/50000 189/160 " 13/11 " "
66 293.3 m3 32/27 " " " " "
67 297.7 1215/1024 " 196/165 108/91 19/16 "
68 302.2 15625/13122 25/21 " " " "
69 306.6 78125/65536 448/375 105/88 " (68/57) 31/26
70 311.1 65536/54675 1225/1024 176/147 140/117 91/76 "
71 315.5 6/5 " " " " "
72 320.0 19683/16384 2048/1701 77/64 65/54 " "
73 324.4 3125/2592 135/112 " " 76/63 35/29
74 328.8 472392/390625 98/81 " " (23/19) 29/24
75 333.3 4096/3375 " 40/33 " " "
76 337.7 243/200 175/144 147/121 " (17/14) "
77 342.2 8000/6561 128/105 " 39/32 (28/23) "
78 346.6 625/512 " 11/9 " " "
79 351.1 1953125/1594323 49/40 " " " 38/31
80 355.5 768/625 " 27/22 " " "
81 360.0 19683/16000 315/256 154/125 16/13 " "
82 364.4 100/81 " " " (21/17) "
83 368.8 10125/8192 8192/6615 99/80 26/21 " "
84 373.3 390625/314928 243/196 150/121 " (57/46) 31/25
85 377.7 3888/3125 56/45 " " " "
86 382.2 8192/6561 5103/4096 96/77 81/65 " "
87 386.6 5/4 " " " " "
88 391.1 164025/131072 784/625 441/352 351/280 (64/51) "
89 395.5 78125/62208 1125/896 44/35 " " "
90 400.0 19683/15625 63/50 " " (34/27) 39/31
91 404.4 512/405 " 125/99 91/72 24/19 "
92 408.8 M3 81/64 " " " 19/15 "
93 412.2 25000/19683 80/63 " 33/26 " "
94 417.7 15625/12288 7168/5625 14/11 " " "
95 422.2 1048576/820125 125/98 " " (23/18) "
96 426.6 32/25 " " " " "
97 431.1 6561/5120 2625/2048 77/60 50/39 " "
98 435.5 625/486 9/7 " " " "
99 440.0 84375/65536 1568/1215 165/128 156/121 49/38 40/31
100 444.4 65536/50625 1323/1024 128/99 84/65 (22/17) 31/24
101 448.8 162/125 35/27 " " " "
102 453.3 25600/19683 2048/1575 100/77 13/10 " "
103 457.7 125/96 " " " 99/76 "
104 462.2 1366875/1048576 64/49 " " (30/23) "
105 466.6 4096/3125 " 55/42 " (17/13) 38/29
106 471.1 6561/5000 21/16 " " " "
107 475.5 320/243 " " 154/117 25/19 "
108 480.0 675/512 " 33/25 " " 29/22
109 484.4 78125/59049 250/189 160/121 143/108 (45/34) "
110 488.8 20736/15625 896/675 175/132 65/49 " "
111 493.3 131072/98415 1701/1280 512/385 117/88 (85/64) "
112 497.7 P4 4/3 " " " " "
113 502.2 10935/8192 8192/6125 147/110 " (91/68) "
114 506.6 15625/11664 75/56 " " " "
115 511.1 104976/78125 168/125 121/90 " (51/38) 39/29
116 515.5 8192/6075 " 66/49 35/26 " "
117 520.0 27/20 " " " (23/17) "
118 524.4 80000/59049 256/189 " 65/48 " 42/31
119 528.8 3125/2304 1215/896 110/81 " 19/14 "
120 533.3 531441/390625 49/36 " " (34/25) "
121 537.7 512/375 " 15/11 " " "
122 542.2 2187/1600 175/128 " 160/117 26/19 "
123 546.6 1000/729 48/35 " " " "
124 551.1 5625/4096 " 11/8 " " "
125 555.5 1048576/759375 135/98 " 91/66 (69/50) 40/29
126 560.0 864/625 112/81 " " 105/76 29/21
127 564.4 81920/59049 2835/2048 320/231 18/13 " "
128 568.8 25/18 " " " " "
129 573.3 91125/65536 1024/735 245/176 39/28 (32/23) "
130 577.7 65536/46875 625/448 88/63 " " "
131 582.2 4374/3125 7/5 " " " "
132 586.6 d5 1024/729 " 108/77 " 80/57 "
133 591.1 45/32 " " " 38/27 "
134 595.5 250000/177147 343/243 " 55/39 (24/17) 31/22
135 600.0 78125/55296 10125/7168 99/70 " " "
136 604.4 177147/125000 486/343 343/242 78/55 (17/12) 44/31
137 608.8 64/45 " " " 27/19 "
138 613.3 A4 729/512 " 77/54 " 57/40 "
139 617.7 3125/2187 10/7 " " " "
140 622.2 46875/32768 896/625 63/44 " " "
141 626.6 131072/91125 735/512 352/245 56/39 (23/16) "
142 631.1 36/25 " " " " "
143 635.5 59049/40960 4096/2835 231/160 13/9 " "
144 640.0 625/432 81/56 " " " 42/29
145 644.4 759375/524288 196/135 " 132/91 (100/69) 29/20
146 648.8 8192/5625 " 16/11 " " "
147 653.3 729/500 35/24 " " " "
148 657.7 3200/2187 256/175 225/154 117/80 19/13 "
149 662.2 375/256 " 22/15 " " "
150 666.6 781250/531441 72/49 " " (25/17) "
151 671.1 4608/3125 1792/1215 81/55 " 28/19 "
152 675.5 59049/40000 189/128 " 65/44 " 31/21
153 680.0 40/27 " " " (34/23) "
154 684.4 6075/4096 " 49/33 " " "
155 688.8 78125/52488 125/84 " " (76/51) 58/39
156 693.3 23328/15625 112/75 " " (85/57) "
157 697.7 16384/10935 6125/4096 220/147 175/117 (136/91) "
158 702.2 P5 3/2 " " " " "
159 706.6 98415/65536 2560/1701 385/256 176/117 (128/85) "
160 711.1 15625/10368 675/448 264/175 98/65 95/63 "
161 715.5 118098/78125 189/125 121/80 " (68/45) "
162 720.0 1024/675 " 50/33 " " 44/29
163 724.4 243/160 " " 117/77 38/25 "
164 728.8 10000/6561 32/21 " " " "
165 733.3 3125/2048 " 55/36 " (26/17) 29/19
166 737.7 2097152/1366875 49/32 " " (23/15) "
167 742.2 192/125 " 135/88 " " "
168 746.6 19683/12800 1575/1024 77/50 20/13 " "
169 751.1 125/81 54/35 " " " "
170 755.5 50625/32768 2048/1323 99/64 65/42 (17/11) 48/31
171 760.0 131072/84375 1215/784 256/165 121/78 76/49 31/20
172 764.4 972/625 14/9 " " " "
173 768.8 10240/6561 4096/2625 120/77 39/25 " "
174 773.3 25/16 " " " " "
175 777.7 820125/524288 196/125 " " (36/23) "
176 782.2 24576/15625 5625/3584 11/7 " " "
177 786.6 19683/12500 63/40 " 52/33 " "
178 791.1 m6 128/81 " " " 30/19 "
179 795.5 405/256 " 198/125 144/91 19/12 "
180 800.0 31250/19683 100/63 " " (27/17) 62/39
181 804.4 78125/49152 1792/1125 35/22 " " "
182 808.8 262144/164025 625/392 " 351/220 (51/32) "
183 813.3 8/5 " " " " "
184 817.7 6561/4096 " 77/48 " " "
185 822.2 3125/1944 45/28 " " " "
186 826.6 421875/262144 392/243 121/75 " (92/57) 29/18
187 831.1 16384/10125 6615/4096 160/99 21/13 " "
188 835.5 81/50 " " " (34/21) "
189 840.0 32000/19683 512/315 125/77 13/8 " "
190 844.4 625/384 " 44/27 " " "
191 848.8 3188646/1953125 49/30 " " " 31/19
192 853.3 1024/625 " 18/11 " " "
193 857.7 6561/4000 105/64 " 64/39 (23/14) "
194 862.2 400/243 288/175 242/147 " (28/17) "
195 866.6 3375/2048 " 33/20 " " "
196 871.1 390625/236196 81/49 " " (38/23) 48/29
197 875.5 5184/3125 224/135 " " 63/38 58/35
198 880.0 32768/19683 1701/1024 128/77 108/65 " "
199 884.4 5/3 " " " " "
200 888.8 54675/32768 2048/1225 147/88 117/70 " "
201 893.3 78125/46656 375/224 176/105 57/34 " 52/31
202 897.7 26244/15625 42/25 " " " "
203 902.2 2048/1215 " 165/98 91/54 32/19 "
204 906.6 M6 27/16 " " " " "
205 911.1 100000/59049 320/189 " 22/13 " "
206 915.5 15625/9216 6075/3584 56/33 " (39/23) "
207 920.0 531441/312500 245/144 " 143/84 (17/10) "
208 924.4 128/75 " 75/44 " " (29/17)
209 928.8 2187/1280 875/512 77/45 " 65/38 "
210 933.3 1250/729 12/7 " " " "
211 937.7 28125/16384 5376/3125 55/32 " " "
212 942.2 262144/151875 441/256 " 112/65 (69/40) 31/18
213 946.6 216/125 140/81 121/70 " 19/11 "
214 951.1 102400/59049 8192/4725 343/198 26/15 " "
215 955.5 125/72 " " " 33/19 "
216 960.0 455625/262144 256/147 " 195/112 (40/23) 54/31
217 964.4 16384/9375 3125/1792 96/55 " (68/39) "
218 968.8 2187/1250 7/4 " " " "
219 973.3 1280/729 " 135/77 " 100/57 "
220 977.7 225/128 " 44/25 " " "
221 982.2 312500/177147 432/245 " 143/81 (30/17) "
222 986.6 27648/15625 3584/2025 99/56 " (23/13) "
223 991.1 177147/100000 567/320 " 39/22 " "
224 995.5 m7 16/9 " " " " "
225 1000.0 3645/2048 " 98/55 " 57/32 "
226 1004.4 15625/8748 25/14 " " " "
227 1008.8 139968/78125 224/125 " " (34/19) 52/29
228 1013.3 32768/18225 3675/2048 88/49 70/39 " "
229 1017.7 9/5 " " " " "
230 1022.2 59049/32768 1024/567 231/128 65/36 " 56/31
231 1026.6 3125/1728 405/224 " " 38/21 "
232 1031.1 708588/390625 49/27 " " " 29/16
233 1035.5 2048/1125 " 20/11 " " "
234 1040.0 729/400 175/96 " " (51/28) (31/17)
235 1044.4 4000/2187 64/35 " " (42/23) "
236 1048.8 1875/1024 " 11/6 " " "
237 1053.3 1953125/1062882 90/49 " " (46/25) "
238 1057.7 1152/625 448/243 81/44 " 35/19 "
239 1062.2 59049/32000 945/512 231/125 24/13 " "
240 1066.6 50/27 " " " " "
241 1071.1 30375/16384 4096/2205 245/132 13/7 " "
242 1075.5 262144/140625 625/336 225/121 121/65 (95/51) 54/29
243 1080.0 5832/3125 28/15 " " " "
244 1084.4 4096/2187 " 144/77 " " 58/31
245 1088.8 15/8 " " " " "
246 1093.3 492075/262144 1176/625 847/450 220/117 (32/17) 62/33
247 1097.7 78125/41472 3375/1792 66/35 49/26 " "
248 1102.2 59049/31250 189/100 121/64 104/55 (17/9) "
249 1106.6 256/135 " 125/66 91/48 36/19 "
250 1111.1 M7 243/128 " 154/81 " 19/10 "
251 1115.5 12500/6561 40/21 " " " "
252 1120.0 15625/8192 3584/1875 21/11 " " "
253 1124.4 524288/273375 245/128 " 224/117 (23/12) "
254 1128.8 48/25 " " " " "
255 1133.3 19683/10240 7875/4096 77/40 25/13 " "
256 1137.7 625/324 27/14 " " " "
257 1142.2 253125/131072 784/405 242/125 176/91 (85/44) 29/15
258 1147.7 32768/16875 3969/2048 64/33 " (33/17) 31/16
259 1151.1 243/125 35/18 " " " "
260 1155.5 12800/6561 1024/525 150/77 39/20 " "
261 1160.0 125/64 " 88/45 " " "
262 1164.4 3125000/1594323 49/25 " " (45/23) "
263 1168.8 6144/3125 " 55/28 " (51/26) "
264 1173.3 19683/10000 63/32 " " " "
265 1177.7 160/81 " " 77/39 75/38 "
266 1182.2 2025/1024 " 99/50 " (91/46) 87/44
267 1186.6 78125/39366 125/63 " " " "
268 1191.1 31104/15625 448/225 175/88 " " "
269 1195.5 65536/32805 3125/1568 768/385 648/325 (255/128) "
270 1200.0 P8 2/1 " " " " "
Retrieved from "https://en.xen.wiki/index.php?title=Table_of_270edo_intervals&oldid=148871"