77edo: Difference between revisions

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→Intervals: Removed pions column
Line 11: Line 11:
! | Degree
! | Degree
! | Cents Value
! | Cents Value
!pions
!7mus
!7mus
! | Approximate Ratios
! | Approximate Ratios
Line 17: Line 16:
in the 13-limit
in the 13-limit
|-
|-
| colspan="4" style="text-align:right;" | 0
| colspan="3" style="text-align:right;" | 0
| style="text-align:center;" | 1/1
| style="text-align:center;" | 1/1
|-
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 1
| style="text-align:right;" | 15.584
| style="text-align:right;" | 15.584
|16.5195
|19.948 (13.F2B<sub>16</sub>)
|19.948 (13.F2B<sub>16</sub>)
| style="text-align:center;" | 81/80, 99/98
| style="text-align:center;" | 81/80, 99/98
Line 28: Line 26:
| style="text-align:right;" | 2
| style="text-align:right;" | 2
| style="text-align:right;" | 31.169
| style="text-align:right;" | 31.169
|33.039
|39.896 (27.E56<sub>16</sub>)
|39.896 (27.E56<sub>16</sub>)
| style="text-align:center;" | 64/63, 49/48
| style="text-align:center;" | 64/63, 49/48
Line 34: Line 31:
| style="text-align:right;" | 3
| style="text-align:right;" | 3
| style="text-align:right;" | 46.753
| style="text-align:right;" | 46.753
|49.558
|59.844 (3B.D82<sub>16</sub>)
|59.844 (3B.D82<sub>16</sub>)
| style="text-align:center;" | 33/32, 36/35
| style="text-align:center;" | 33/32, 36/35
Line 40: Line 36:
| style="text-align:right;" | 4
| style="text-align:right;" | 4
| style="text-align:right;" | 62.338
| style="text-align:right;" | 62.338
|66.078
|79.792 (4F.CAD<sub>16</sub>)
|79.792 (4F.CAD<sub>16</sub>)
| style="text-align:center;" | 28/27, 26/25
| style="text-align:center;" | 28/27, 26/25
Line 46: Line 41:
| style="text-align:right;" | 5
| style="text-align:right;" | 5
| style="text-align:right;" | 77.922
| style="text-align:right;" | 77.922
|82.597
|99.74 (63.BD8<sub>16</sub>)
|99.74 (63.BD8<sub>16</sub>)
| style="text-align:center;" | 21/20, 25/24
| style="text-align:center;" | 21/20, 25/24
Line 52: Line 46:
| style="text-align:right;" | 6
| style="text-align:right;" | 6
| style="text-align:right;" | 93.5065
| style="text-align:right;" | 93.5065
|99.117
|119.688 (77.B03<sub>16</sub>)
|119.688 (77.B03<sub>16</sub>)
| style="text-align:center;" | 135/128
| style="text-align:center;" | 135/128
Line 58: Line 51:
| style="text-align:right;" | 7
| style="text-align:right;" | 7
| style="text-align:right;" | 109.091
| style="text-align:right;" | 109.091
|115.636
|139.636 (8B.A2F<sub>16</sub>)
|139.636 (8B.A2F<sub>16</sub>)
| style="text-align:center;" | 16/15
| style="text-align:center;" | 16/15
Line 64: Line 56:
| style="text-align:right;" | 8
| style="text-align:right;" | 8
| style="text-align:right;" | 124.675
| style="text-align:right;" | 124.675
|132.156
|159.584 (9F.95A<sub>16</sub>)
|159.584 (9F.95A<sub>16</sub>)
| style="text-align:center;" | 15/14
| style="text-align:center;" | 15/14
Line 70: Line 61:
| style="text-align:right;" | 9
| style="text-align:right;" | 9
| style="text-align:right;" | 140.26
| style="text-align:right;" | 140.26
|148.675
|179.5325 (B3.885<sub>16</sub>)
|179.5325 (B3.885<sub>16</sub>)
| style="text-align:center;" | 13/12
| style="text-align:center;" | 13/12
Line 76: Line 66:
| style="text-align:right;" | 10
| style="text-align:right;" | 10
| style="text-align:right;" | 155.844
| style="text-align:right;" | 155.844
|165.195
|199.4805 (C7.7B<sub>16</sub>)
|199.4805 (C7.7B<sub>16</sub>)
| style="text-align:center;" | 12/11, 11/10
| style="text-align:center;" | 12/11, 11/10
Line 82: Line 71:
| style="text-align:right;" | 11
| style="text-align:right;" | 11
| style="text-align:right;" | 171.429
| style="text-align:right;" | 171.429
|181.714
|219.429 (DB.6DB<sub>16</sub>)
|219.429 (DB.6DB<sub>16</sub>)
| style="text-align:center;" | 72/65
| style="text-align:center;" | 72/65
Line 88: Line 76:
| style="text-align:right;" | 12
| style="text-align:right;" | 12
| style="text-align:right;" | 187.013
| style="text-align:right;" | 187.013
|198.234
|239.377 (EF.607<sub>16</sub>)
|239.377 (EF.607<sub>16</sub>)
| style="text-align:center;" | 10/9
| style="text-align:center;" | 10/9
Line 94: Line 81:
| style="text-align:right;" | 13
| style="text-align:right;" | 13
| style="text-align:right;" | 202.597
| style="text-align:right;" | 202.597
|214.753
|259.325 (103.532<sub>16</sub>)
|259.325 (103.532<sub>16</sub>)
| style="text-align:center;" | 9/8
| style="text-align:center;" | 9/8
Line 100: Line 86:
| style="text-align:right;" | 14
| style="text-align:right;" | 14
| style="text-align:right;" | 218.182
| style="text-align:right;" | 218.182
|231.273
|279.273 (117.45D<sub>16</sub>)
|279.273 (117.45D<sub>16</sub>)
| style="text-align:center;" | 256/225
| style="text-align:center;" | 256/225
Line 106: Line 91:
| style="text-align:right;" | 15
| style="text-align:right;" | 15
| style="text-align:right;" | 233.766
| style="text-align:right;" | 233.766
|247.792
|299.221 (12B.388<sub>16</sub>)
|299.221 (12B.388<sub>16</sub>)
| style="text-align:center;" | 8/7
| style="text-align:center;" | 8/7
Line 112: Line 96:
| style="text-align:right;" | 16
| style="text-align:right;" | 16
| style="text-align:right;" | 249.351
| style="text-align:right;" | 249.351
|264.312
|319.169 (13F.2B4<sub>16</sub>)
|319.169 (13F.2B4<sub>16</sub>)
| style="text-align:center;" | 15/13
| style="text-align:center;" | 15/13
Line 118: Line 101:
| style="text-align:right;" | 17
| style="text-align:right;" | 17
| style="text-align:right;" | 264.935
| style="text-align:right;" | 264.935
|280.831
|339.117 (153.1DF<sub>16</sub>)
|339.117 (153.1DF<sub>16</sub>)
| style="text-align:center;" | 7/6
| style="text-align:center;" | 7/6
Line 124: Line 106:
| style="text-align:right;" | 18
| style="text-align:right;" | 18
| style="text-align:right;" | 280.5195
| style="text-align:right;" | 280.5195
|297.351
|359.065 (167.10A<sub>16</sub>)
|359.065 (167.10A<sub>16</sub>)
| style="text-align:center;" | 33/28
| style="text-align:center;" | 33/28
Line 130: Line 111:
| style="text-align:right;" | 19
| style="text-align:right;" | 19
| style="text-align:right;" | 296.104
| style="text-align:right;" | 296.104
|313.87
|379.013 (17B.035<sub>16</sub>)
|379.013 (17B.035<sub>16</sub>)
| style="text-align:center;" | 32/27, 13/11
| style="text-align:center;" | 32/27, 13/11
Line 136: Line 116:
| style="text-align:right;" | 20
| style="text-align:right;" | 20
| style="text-align:right;" | 311.688
| style="text-align:right;" | 311.688
|330.39
|398.961 (18E.F6<sub>16</sub>)
|398.961 (18E.F6<sub>16</sub>)
| style="text-align:center;" | 6/5
| style="text-align:center;" | 6/5
Line 142: Line 121:
| style="text-align:right;" | 21
| style="text-align:right;" | 21
| style="text-align:right;" | 327.273
| style="text-align:right;" | 327.273
|346.909
|418.909 (1A2.E8B<sub>16</sub>)
|418.909 (1A2.E8B<sub>16</sub>)
| style="text-align:center;" | 98/81
| style="text-align:center;" | 98/81
Line 148: Line 126:
| style="text-align:right;" | 22
| style="text-align:right;" | 22
| style="text-align:right;" | 342.857
| style="text-align:right;" | 342.857
|363.429
|438.857 (1B6.DB7<sub>16</sub>)
|438.857 (1B6.DB7<sub>16</sub>)
| style="text-align:center;" | 11/9, 39/32
| style="text-align:center;" | 11/9, 39/32
Line 154: Line 131:
| style="text-align:right;" | 23
| style="text-align:right;" | 23
| style="text-align:right;" | 358.442
| style="text-align:right;" | 358.442
|379.948
|458.805 (1CA.CE2<sub>16</sub>)
|458.805 (1CA.CE2<sub>16</sub>)
| style="text-align:center;" | 16/13
| style="text-align:center;" | 16/13
Line 160: Line 136:
| style="text-align:right;" | 24
| style="text-align:right;" | 24
| style="text-align:right;" | 374.026
| style="text-align:right;" | 374.026
|396.4675
|478.753 (1DE.C0D<sub>16</sub>)
|478.753 (1DE.C0D<sub>16</sub>)
| style="text-align:center;" | 56/45, 26/21
| style="text-align:center;" | 56/45, 26/21
Line 166: Line 141:
| style="text-align:right;" | 25
| style="text-align:right;" | 25
| style="text-align:right;" | 389.61
| style="text-align:right;" | 389.61
|412.987
|498.701 (1F2.B388<sub>16</sub>)
|498.701 (1F2.B388<sub>16</sub>)
| style="text-align:center;" | 5/4
| style="text-align:center;" | 5/4
Line 172: Line 146:
| style="text-align:right;" | 26
| style="text-align:right;" | 26
| style="text-align:right;" | 405.195
| style="text-align:right;" | 405.195
|429.5065
|518.649 (206.A64<sub>16</sub>)
|518.649 (206.A64<sub>16</sub>)
| style="text-align:center;" | 33/26, 81/64
| style="text-align:center;" | 33/26, 81/64
Line 178: Line 151:
| style="text-align:right;" | 27
| style="text-align:right;" | 27
| style="text-align:right;" | 420.779
| style="text-align:right;" | 420.779
|446.026
|538.597 (21A.98F<sub>16</sub>)
|538.597 (21A.98F<sub>16</sub>)
| style="text-align:center;" | 14/11, 32/25
| style="text-align:center;" | 14/11, 32/25
Line 184: Line 156:
| style="text-align:right;" | 28
| style="text-align:right;" | 28
| style="text-align:right;" | 436.364
| style="text-align:right;" | 436.364
|462.5455
|558.5455 (22E.8BA<sub>16</sub>)
|558.5455 (22E.8BA<sub>16</sub>)
| style="text-align:center;" | 9/7
| style="text-align:center;" | 9/7
Line 190: Line 161:
| style="text-align:right;" | 29
| style="text-align:right;" | 29
| style="text-align:right;" | 451.948
| style="text-align:right;" | 451.948
|479.065
|578.4935 (242.7E5<sub>16</sub>)
|578.4935 (242.7E5<sub>16</sub>)
| style="text-align:center;" | 13/10
| style="text-align:center;" | 13/10
Line 196: Line 166:
| style="text-align:right;" | 30
| style="text-align:right;" | 30
| style="text-align:right;" | 467.5325
| style="text-align:right;" | 467.5325
|495.584
|598.442 (256.711<sub>16</sub>)
|598.442 (256.711<sub>16</sub>)
| style="text-align:center;" | 21/16
| style="text-align:center;" | 21/16
Line 202: Line 171:
| style="text-align:right;" | 31
| style="text-align:right;" | 31
| style="text-align:right;" | 483.117
| style="text-align:right;" | 483.117
|512.104
|618.39 (26A.63C<sub>16</sub>)
|618.39 (26A.63C<sub>16</sub>)
| style="text-align:center;" | 120/91
| style="text-align:center;" | 120/91
Line 208: Line 176:
| style="text-align:right;" | 32
| style="text-align:right;" | 32
| style="text-align:right;" | 498.701
| style="text-align:right;" | 498.701
|528.623
|638.338 (27E.567<sub>16</sub>)
|638.338 (27E.567<sub>16</sub>)
| style="text-align:center;" | 4/3
| style="text-align:center;" | 4/3
Line 214: Line 181:
| style="text-align:right;" | 33
| style="text-align:right;" | 33
| style="text-align:right;" | 514.286
| style="text-align:right;" | 514.286
|545.143
|658.286 (292.492<sub>16</sub>)
|658.286 (292.492<sub>16</sub>)
| style="text-align:center;" | 27/20
| style="text-align:center;" | 27/20
Line 220: Line 186:
| style="text-align:right;" | 34
| style="text-align:right;" | 34
| style="text-align:right;" | 529.87
| style="text-align:right;" | 529.87
|561.662
|678.234 (2A6.3BD8<sub>16</sub>)
|678.234 (2A6.3BD8<sub>16</sub>)
| style="text-align:center;" | 49/36
| style="text-align:center;" | 49/36
Line 226: Line 191:
| style="text-align:right;" | 35
| style="text-align:right;" | 35
| style="text-align:right;" | 545.4545
| style="text-align:right;" | 545.4545
|578.182
|698.182 (2BA.2E9<sub>16</sub>)
|698.182 (2BA.2E9<sub>16</sub>)
| style="text-align:center;" | 11/8, 15/11
| style="text-align:center;" | 11/8, 15/11
Line 232: Line 196:
| style="text-align:right;" | 36
| style="text-align:right;" | 36
| style="text-align:right;" | 561.039
| style="text-align:right;" | 561.039
|594.701
|718.13 (2CE.214<sub>16</sub>)
|718.13 (2CE.214<sub>16</sub>)
| style="text-align:center;" | 18/13
| style="text-align:center;" | 18/13
Line 238: Line 201:
| style="text-align:right;" | 37
| style="text-align:right;" | 37
| style="text-align:right;" | 576.623
| style="text-align:right;" | 576.623
|611.221
|738.078 (2E2.13F<sub>16</sub>)
|738.078 (2E2.13F<sub>16</sub>)
| style="text-align:center;" | 7/5
| style="text-align:center;" | 7/5
Line 244: Line 206:
| style="text-align:right;" | 38
| style="text-align:right;" | 38
| style="text-align:right;" | 592.208
| style="text-align:right;" | 592.208
|627.74
|758.026 (2F6.06A<sub>16</sub>)
|758.026 (2F6.06A<sub>16</sub>)
| style="text-align:center;" | 45/32
| style="text-align:center;" | 45/32
Line 250: Line 211:
| style="text-align:right;" | 39
| style="text-align:right;" | 39
| style="text-align:right;" | 607.792
| style="text-align:right;" | 607.792
|644.26
|777.974 (309.F96<sub>16</sub>)
|777.974 (309.F96<sub>16</sub>)
| style="text-align:center;" | 64/45
| style="text-align:center;" | 64/45
Line 256: Line 216:
| style="text-align:right;" | 40
| style="text-align:right;" | 40
| style="text-align:right;" | 623.377
| style="text-align:right;" | 623.377
|660.779
|797.922 (31D.EC1<sub>16</sub>)
|797.922 (31D.EC1<sub>16</sub>)
| style="text-align:center;" | 10/7
| style="text-align:center;" | 10/7
Line 262: Line 221:
| style="text-align:right;" | 41
| style="text-align:right;" | 41
| style="text-align:right;" | 638.961
| style="text-align:right;" | 638.961
|677.299
|817.87 (331.DEC<sub>16</sub>)
|817.87 (331.DEC<sub>16</sub>)
| style="text-align:center;" | 13/9
| style="text-align:center;" | 13/9
Line 268: Line 226:
| style="text-align:right;" | 42
| style="text-align:right;" | 42
| style="text-align:right;" | 654.5455
| style="text-align:right;" | 654.5455
|693.818
|837.818 (345.D17<sub>16</sub>)
|837.818 (345.D17<sub>16</sub>)
| style="text-align:center;" | 16/11, 22/15
| style="text-align:center;" | 16/11, 22/15
Line 274: Line 231:
| style="text-align:right;" | 43
| style="text-align:right;" | 43
| style="text-align:right;" | 670.13
| style="text-align:right;" | 670.13
|710.338
|857.766 (359.C428<sub>16</sub>)
|857.766 (359.C428<sub>16</sub>)
| style="text-align:center;" | 72/49
| style="text-align:center;" | 72/49
Line 280: Line 236:
| style="text-align:right;" | 44
| style="text-align:right;" | 44
| style="text-align:right;" | 685.714
| style="text-align:right;" | 685.714
|726.857
|877.714 (36D.B6E<sub>16</sub>)
|877.714 (36D.B6E<sub>16</sub>)
| style="text-align:center;" | 40/27
| style="text-align:center;" | 40/27
Line 286: Line 241:
| style="text-align:right;" | 45
| style="text-align:right;" | 45
| style="text-align:right;" | 701.299
| style="text-align:right;" | 701.299
|743.377
|897.662 (381.A99<sub>16</sub>)
|897.662 (381.A99<sub>16</sub>)
| style="text-align:center;" | 3/2
| style="text-align:center;" | 3/2
Line 292: Line 246:
| style="text-align:right;" | 46
| style="text-align:right;" | 46
| style="text-align:right;" | 716.883
| style="text-align:right;" | 716.883
|759.896
|917.61 (395.9C4<sub>16</sub>)
|917.61 (395.9C4<sub>16</sub>)
| style="text-align:center;" | 91/60
| style="text-align:center;" | 91/60
Line 298: Line 251:
| style="text-align:right;" | 47
| style="text-align:right;" | 47
| style="text-align:right;" | 732.4675
| style="text-align:right;" | 732.4675
|776.416
|937.558 (3A9.8EF<sub>16</sub>)
|937.558 (3A9.8EF<sub>16</sub>)
| style="text-align:center;" | 32/21
| style="text-align:center;" | 32/21
Line 304: Line 256:
| style="text-align:right;" | 48
| style="text-align:right;" | 48
| style="text-align:right;" | 748.052
| style="text-align:right;" | 748.052
|792.935
|957.5065 (3BD.81B<sub>16</sub>)
|957.5065 (3BD.81B<sub>16</sub>)
| style="text-align:center;" | 20/13
| style="text-align:center;" | 20/13
Line 310: Line 261:
| style="text-align:right;" | 49
| style="text-align:right;" | 49
| style="text-align:right;" | 763.636
| style="text-align:right;" | 763.636
|809.4545
|977.4545 (3D1.746<sub>16</sub>)
|977.4545 (3D1.746<sub>16</sub>)
| style="text-align:center;" | 14/9
| style="text-align:center;" | 14/9
Line 316: Line 266:
| style="text-align:right;" | 50
| style="text-align:right;" | 50
| style="text-align:right;" | 779.221
| style="text-align:right;" | 779.221
|825.974
|997.403 (3E5.671<sub>16</sub>)
|997.403 (3E5.671<sub>16</sub>)
| style="text-align:center;" | 11/7, 25/16
| style="text-align:center;" | 11/7, 25/16
Line 322: Line 271:
| style="text-align:right;" | 51
| style="text-align:right;" | 51
| style="text-align:right;" | 794.805
| style="text-align:right;" | 794.805
|842.4935
|1017.351 (3F9.59C<sub>16</sub>)
|1017.351 (3F9.59C<sub>16</sub>)
| style="text-align:center;" | 52/33, 128/81
| style="text-align:center;" | 52/33, 128/81
Line 328: Line 276:
| style="text-align:right;" | 52
| style="text-align:right;" | 52
| style="text-align:right;" | 810.39
| style="text-align:right;" | 810.39
|859.013
|1037.299 (40D.4C78<sub>16</sub>)
|1037.299 (40D.4C78<sub>16</sub>)
| style="text-align:center;" | 8/5
| style="text-align:center;" | 8/5
Line 334: Line 281:
| style="text-align:right;" | 53
| style="text-align:right;" | 53
| style="text-align:right;" | 825.974
| style="text-align:right;" | 825.974
|875.5325
|1057.247 (421.3F3<sub>16</sub>)
|1057.247 (421.3F3<sub>16</sub>)
| style="text-align:center;" | 45/28, 21/13
| style="text-align:center;" | 45/28, 21/13
Line 340: Line 286:
| style="text-align:right;" | 54
| style="text-align:right;" | 54
| style="text-align:right;" | 841.558
| style="text-align:right;" | 841.558
|892.052
|1077.195 (435.31E<sub>16</sub>)
|1077.195 (435.31E<sub>16</sub>)
| style="text-align:center;" | 13/8
| style="text-align:center;" | 13/8
Line 346: Line 291:
| style="text-align:right;" | 55
| style="text-align:right;" | 55
| style="text-align:right;" | 857.143
| style="text-align:right;" | 857.143
|908.571
|1097.143 (449.249<sub>16</sub>)
|1097.143 (449.249<sub>16</sub>)
| style="text-align:center;" | 18/11, 64/39
| style="text-align:center;" | 18/11, 64/39
Line 352: Line 296:
| style="text-align:right;" | 56
| style="text-align:right;" | 56
| style="text-align:right;" | 872.727
| style="text-align:right;" | 872.727
|925.091
|1117.091 (45D.174<sub>16</sub>)
|1117.091 (45D.174<sub>16</sub>)
| style="text-align:center;" | 81/49
| style="text-align:center;" | 81/49
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| style="text-align:right;" | 57
| style="text-align:right;" | 57
| style="text-align:right;" | 888.312
| style="text-align:right;" | 888.312
|941.61
|1137.039 (471.0A<sub>16</sub>)
|1137.039 (471.0A<sub>16</sub>)
| style="text-align:center;" | 5/3
| style="text-align:center;" | 5/3
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| style="text-align:right;" | 58
| style="text-align:right;" | 58
| style="text-align:right;" | 903.896
| style="text-align:right;" | 903.896
|958.13
|1156.987 (484.FCB<sub>16</sub>)
|1156.987 (484.FCB<sub>16</sub>)
| style="text-align:center;" | 27/16, 22/13
| style="text-align:center;" | 27/16, 22/13
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| style="text-align:right;" | 59
| style="text-align:right;" | 59
| style="text-align:right;" | 919.4805
| style="text-align:right;" | 919.4805
|974.649
|1176.935 (498.EF6<sub>16</sub>)
|1176.935 (498.EF6<sub>16</sub>)
| style="text-align:center;" | 56/33
| style="text-align:center;" | 56/33
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| style="text-align:right;" | 60
| style="text-align:right;" | 60
| style="text-align:right;" | 935.065
| style="text-align:right;" | 935.065
|991.169
|1196.883 (4AC.E21<sub>16</sub>)
|1196.883 (4AC.E21<sub>16</sub>)
| style="text-align:center;" | 12/7
| style="text-align:center;" | 12/7
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| style="text-align:right;" | 61
| style="text-align:right;" | 61
| style="text-align:right;" | 950.649
| style="text-align:right;" | 950.649
|1007.688
|1216.831 (4C0.D4C<sub>16</sub>)
|1216.831 (4C0.D4C<sub>16</sub>)
| style="text-align:center;" | 26/15
| style="text-align:center;" | 26/15
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| style="text-align:right;" | 62
| style="text-align:right;" | 62
| style="text-align:right;" | 966.234
| style="text-align:right;" | 966.234
|1024.208
|1236.77 (4D4.C78<sub>16</sub>)
|1236.77 (4D4.C78<sub>16</sub>)
| style="text-align:center;" | 7/4
| style="text-align:center;" | 7/4
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| style="text-align:right;" | 63
| style="text-align:right;" | 63
| style="text-align:right;" | 981.818
| style="text-align:right;" | 981.818
|1040.727
|1256.727 (4E8.BA3<sub>16</sub>)
|1256.727 (4E8.BA3<sub>16</sub>)
| style="text-align:center;" | 225/128
| style="text-align:center;" | 225/128
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| style="text-align:right;" | 64
| style="text-align:right;" | 64
| style="text-align:right;" | 997.403
| style="text-align:right;" | 997.403
|1057.247
|1276.675 (4FC.ACE<sub>16</sub>)
|1276.675 (4FC.ACE<sub>16</sub>)
| style="text-align:center;" | 16/9
| style="text-align:center;" | 16/9
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| style="text-align:right;" | 65
| style="text-align:right;" | 65
| style="text-align:right;" | 1012.987
| style="text-align:right;" | 1012.987
|1073.766
|1296.623 (510.9F9<sub>16</sub>)
|1296.623 (510.9F9<sub>16</sub>)
| style="text-align:center;" | 9/5
| style="text-align:center;" | 9/5
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| style="text-align:right;" | 66
| style="text-align:right;" | 66
| style="text-align:right;" | 1028.571
| style="text-align:right;" | 1028.571
|1090.285
|1316.571 (524.924<sub>16</sub>)
|1316.571 (524.924<sub>16</sub>)
| style="text-align:center;" | 65/36
| style="text-align:center;" | 65/36
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| style="text-align:right;" | 67
| style="text-align:right;" | 67
| style="text-align:right;" | 1044.156
| style="text-align:right;" | 1044.156
|1106.805
|1336.5195 (538.85<sub>16</sub>)
|1336.5195 (538.85<sub>16</sub>)
| style="text-align:center;" | 11/6, 20/11
| style="text-align:center;" | 11/6, 20/11
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| style="text-align:right;" | 68
| style="text-align:right;" | 68
| style="text-align:right;" | 1059.74
| style="text-align:right;" | 1059.74
|1123.325
|1356.4675 (54C.77B<sub>16</sub>)
|1356.4675 (54C.77B<sub>16</sub>)
| style="text-align:center;" | 24/13
| style="text-align:center;" | 24/13
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| style="text-align:right;" | 69
| style="text-align:right;" | 69
| style="text-align:right;" | 1075.325
| style="text-align:right;" | 1075.325
|1139.844
|1376.416 (560.6A6<sub>16</sub>)
|1376.416 (560.6A6<sub>16</sub>)
| style="text-align:center;" | 28/15
| style="text-align:center;" | 28/15
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| style="text-align:right;" | 70
| style="text-align:right;" | 70
| style="text-align:right;" | 1090.909
| style="text-align:right;" | 1090.909
|1156.364
|1396.364 (574.5D1<sub>16</sub>)
|1396.364 (574.5D1<sub>16</sub>)
| style="text-align:center;" | 15/8
| style="text-align:center;" | 15/8
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| style="text-align:right;" | 71
| style="text-align:right;" | 71
| style="text-align:right;" | 1106.4935
| style="text-align:right;" | 1106.4935
|1172.883
|1416.312 (588.4FD<sub>16</sub>)
|1416.312 (588.4FD<sub>16</sub>)
| style="text-align:center;" | 256/135
| style="text-align:center;" | 256/135
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| style="text-align:right;" | 72
| style="text-align:right;" | 72
| style="text-align:right;" | 1122.078
| style="text-align:right;" | 1122.078
|1189.403
|1436.26 (59C.426<sub>16</sub>)
|1436.26 (59C.426<sub>16</sub>)
| style="text-align:center;" | 40/21, 48/25
| style="text-align:center;" | 40/21, 48/25
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| style="text-align:right;" | 73
| style="text-align:right;" | 73
| style="text-align:right;" | 1137.662
| style="text-align:right;" | 1137.662
|1205.922
|1456.208 (5B0.353<sub>16</sub>)
|1456.208 (5B0.353<sub>16</sub>)
| style="text-align:center;" | 27/14, 25/13
| style="text-align:center;" | 27/14, 25/13
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| style="text-align:right;" | 74
| style="text-align:right;" | 74
| style="text-align:right;" | 1153.247
| style="text-align:right;" | 1153.247
|1222.442
|1476.156 (5C4.27E<sub>16</sub>)
|1476.156 (5C4.27E<sub>16</sub>)
| style="text-align:center;" | 64/33, 35/18
| style="text-align:center;" | 64/33, 35/18
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| style="text-align:right;" | 75
| style="text-align:right;" | 75
| style="text-align:right;" | 1168.831
| style="text-align:right;" | 1168.831
|1238.961
|1496.104 (5D8.1AA<sub>16</sub>)
|1496.104 (5D8.1AA<sub>16</sub>)
| style="text-align:center;" | 63/32, 96/49
| style="text-align:center;" | 63/32, 96/49
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| style="text-align:right;" | 76
| style="text-align:right;" | 76
| style="text-align:right;" | 1184.416
| style="text-align:right;" | 1184.416
|1255.4805
|1516.052 (5EC.0D5<sub>16</sub>)
|1516.052 (5EC.0D5<sub>16</sub>)
| style="text-align:center;" | 160/81, 196/99
| style="text-align:center;" | 160/81, 196/99
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| style="text-align:right;" | 77
| style="text-align:right;" | 77
| style="text-align:right;" | 1200
| style="text-align:right;" | 1200
|1272
|1536 (600<sub>16</sub>)
|1536 (600<sub>16</sub>)
| style="text-align:center;" | 2/1
| style="text-align:center;" | 2/1

Revision as of 12:36, 12 December 2019

77 tone Equal Temperament

77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 cents each. With fifths less than a cent flat, major thirds a bit over three cents sharp and 7/4s less flat than that, it represents an excellent tuning choice for both valentine, the 31&46 temperament, and starling, the 126/125 planar temperament, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as 11-limit starling and oxpecker temperaments. It also gives the optimal patent val for various members of the unicorn family, with a generator of 4\77 instead of the 5\77 which gives valentine. These are 7-limit alicorn and 11- and 13-limit camahueto.

77et tempers out 32805/32768 in the 5-limit, 126/125, 1029/1024 and 6144/6125 in the 7-limit, 121/120, 176/175, 385/384 and 441/440 in the 11-limit, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the 13-limit.

Intervals

Degree Cents Value 7mus Approximate Ratios

in the 13-limit

0 1/1
1 15.584 19.948 (13.F2B16) 81/80, 99/98
2 31.169 39.896 (27.E5616) 64/63, 49/48
3 46.753 59.844 (3B.D8216) 33/32, 36/35
4 62.338 79.792 (4F.CAD16) 28/27, 26/25
5 77.922 99.74 (63.BD816) 21/20, 25/24
6 93.5065 119.688 (77.B0316) 135/128
7 109.091 139.636 (8B.A2F16) 16/15
8 124.675 159.584 (9F.95A16) 15/14
9 140.26 179.5325 (B3.88516) 13/12
10 155.844 199.4805 (C7.7B16) 12/11, 11/10
11 171.429 219.429 (DB.6DB16) 72/65
12 187.013 239.377 (EF.60716) 10/9
13 202.597 259.325 (103.53216) 9/8
14 218.182 279.273 (117.45D16) 256/225
15 233.766 299.221 (12B.38816) 8/7
16 249.351 319.169 (13F.2B416) 15/13
17 264.935 339.117 (153.1DF16) 7/6
18 280.5195 359.065 (167.10A16) 33/28
19 296.104 379.013 (17B.03516) 32/27, 13/11
20 311.688 398.961 (18E.F616) 6/5
21 327.273 418.909 (1A2.E8B16) 98/81
22 342.857 438.857 (1B6.DB716) 11/9, 39/32
23 358.442 458.805 (1CA.CE216) 16/13
24 374.026 478.753 (1DE.C0D16) 56/45, 26/21
25 389.61 498.701 (1F2.B38816) 5/4
26 405.195 518.649 (206.A6416) 33/26, 81/64
27 420.779 538.597 (21A.98F16) 14/11, 32/25
28 436.364 558.5455 (22E.8BA16) 9/7
29 451.948 578.4935 (242.7E516) 13/10
30 467.5325 598.442 (256.71116) 21/16
31 483.117 618.39 (26A.63C16) 120/91
32 498.701 638.338 (27E.56716) 4/3
33 514.286 658.286 (292.49216) 27/20
34 529.87 678.234 (2A6.3BD816) 49/36
35 545.4545 698.182 (2BA.2E916) 11/8, 15/11
36 561.039 718.13 (2CE.21416) 18/13
37 576.623 738.078 (2E2.13F16) 7/5
38 592.208 758.026 (2F6.06A16) 45/32
39 607.792 777.974 (309.F9616) 64/45
40 623.377 797.922 (31D.EC116) 10/7
41 638.961 817.87 (331.DEC16) 13/9
42 654.5455 837.818 (345.D1716) 16/11, 22/15
43 670.13 857.766 (359.C42816) 72/49
44 685.714 877.714 (36D.B6E16) 40/27
45 701.299 897.662 (381.A9916) 3/2
46 716.883 917.61 (395.9C416) 91/60
47 732.4675 937.558 (3A9.8EF16) 32/21
48 748.052 957.5065 (3BD.81B16) 20/13
49 763.636 977.4545 (3D1.74616) 14/9
50 779.221 997.403 (3E5.67116) 11/7, 25/16
51 794.805 1017.351 (3F9.59C16) 52/33, 128/81
52 810.39 1037.299 (40D.4C7816) 8/5
53 825.974 1057.247 (421.3F316) 45/28, 21/13
54 841.558 1077.195 (435.31E16) 13/8
55 857.143 1097.143 (449.24916) 18/11, 64/39
56 872.727 1117.091 (45D.17416) 81/49
57 888.312 1137.039 (471.0A16) 5/3
58 903.896 1156.987 (484.FCB16) 27/16, 22/13
59 919.4805 1176.935 (498.EF616) 56/33
60 935.065 1196.883 (4AC.E2116) 12/7
61 950.649 1216.831 (4C0.D4C16) 26/15
62 966.234 1236.77 (4D4.C7816) 7/4
63 981.818 1256.727 (4E8.BA316) 225/128
64 997.403 1276.675 (4FC.ACE16) 16/9
65 1012.987 1296.623 (510.9F916) 9/5
66 1028.571 1316.571 (524.92416) 65/36
67 1044.156 1336.5195 (538.8516) 11/6, 20/11
68 1059.74 1356.4675 (54C.77B16) 24/13
69 1075.325 1376.416 (560.6A616) 28/15
70 1090.909 1396.364 (574.5D116) 15/8
71 1106.4935 1416.312 (588.4FD16) 256/135
72 1122.078 1436.26 (59C.42616) 40/21, 48/25
73 1137.662 1456.208 (5B0.35316) 27/14, 25/13
74 1153.247 1476.156 (5C4.27E16) 64/33, 35/18
75 1168.831 1496.104 (5D8.1AA16) 63/32, 96/49
76 1184.416 1516.052 (5EC.0D516) 160/81, 196/99
77 1200 1536 (60016) 2/1

Linear temperaments

Periods

per Octave

Generator Temperaments
1 1\77
1 2\77
1 3\77
1 4\77 Unicorn/alicorn/camahueto/qilin
1 5\77 Valentine
1 6\77
1 8\77
1 9\77 Tsaharuk
1 10\77
1 12\77
1 13\77
1 15\77 Guiron
1 16\77 Hemischis
1 17\77
1 18\77
1 19\77
1 20\77
1 23\77 Restles (77&87)
1 24\77
1 25\77
1 26\77
1 27\77
1 29\77
1 30\77
1 31\77 Hemiseven
1 32\77 Hendecatonic, grackle
1 34\77 Mabila (34&43)
1 36\77
1 37\77
1 38\77
7 1\77 "Absurdity" (7&84)
7 2\77
7 3\77
7 4\77
7 5\77
11 1\77
11 2\77
11 3\77

Music

Star 1-GrimaldiA+Bmod by Joel Grant Taylor

77et Star by Chris Vaisvil

A Seed Planted A Seed Planted by Jake Freivald, in an organ version of Claudi Meneghin.

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