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=<span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span>=


77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent|cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7/4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Valentine|valentine]], the 31&amp;46 temperament, and [[Starling_temperaments|starling]], the 126/125 [[Planar_Temperament|planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling_family#x7-limit starling-11-limit|11-limit starling]] and [[Starling_family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[Unicorn_family|unicorn family]], with a [[generator|generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn_family#Alicorn|alicorn]] and 11- and 13-limit camahueto.
== Theory ==
77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent|cents]] each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7/4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[valentine]], the 31&amp;46 temperament, and [[Starling_family|starling]], the [[126/125]] [[Planar_Temperament|planar temperament]], giving the [[optimal patent val]] for [[11-limit]] valentine and its [[13-limit]] extensions dwynwen and valentino, as well as [[Starling_family #11-limit|11-limit starling]] and [[Starling_family #Oxpecker|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 [[Unicorn_family #Alicorn|alicorn]] and 11- and 13-limit [[Starling temperaments #camahueto|camahueto]].


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


{| class="wikitable"
{| class="wikitable center-all right-2 left-3"
|-
|-
! | Degree
! Degree
! | Cents Value
! Cents
! | Approximate Ratios
! Approximate Ratios<br>in the 13-limit
 
in the 13-limit
|-
|-
| style="text-align:right;" | 0
| 0
| style="text-align:right;" | 0.000
| 0.000
| style="text-align:center;" | 1/1
| 1/1
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 15.584
| 15.584
| style="text-align:center;" | 81/80, 99/98
| 81/80, 99/98
|-
|-
| style="text-align:right;" | 2
| 2
| style="text-align:right;" | 31.169
| 31.169
| style="text-align:center;" | 64/63, 49/48
| 64/63, 49/48
|-
|-
| style="text-align:right;" | 3
| 3
| style="text-align:right;" | 46.753
| 46.753
| style="text-align:center;" | 33/32, 36/35
| 33/32, 36/35
|-
|-
| style="text-align:right;" | 4
| 4
| style="text-align:right;" | 62.338
| 62.338
| style="text-align:center;" | 28/27, 26/25
| 28/27, 26/25
|-
|-
| style="text-align:right;" | 5
| 5
| style="text-align:right;" | 77.922
| 77.922
| style="text-align:center;" | 21/20, 25/24
| 21/20, 25/24
|-
|-
| style="text-align:right;" | 6
| 6
| style="text-align:right;" | 93.5065
| 93.506
| style="text-align:center;" | 135/128
| 135/128
|-
|-
| style="text-align:right;" | 7
| 7
| style="text-align:right;" | 109.091
| 109.091
| style="text-align:center;" | 16/15
| 16/15
|-
|-
| style="text-align:right;" | 8
| 8
| style="text-align:right;" | 124.675
| 124.675
| style="text-align:center;" | 15/14
| 15/14
|-
|-
| style="text-align:right;" | 9
| 9
| style="text-align:right;" | 140.26
| 140.260
| style="text-align:center;" | 13/12
| 13/12
|-
|-
| style="text-align:right;" | 10
| 10
| style="text-align:right;" | 155.844
| 155.844
| style="text-align:center;" | 12/11, 11/10
| 12/11, 11/10
|-
|-
| style="text-align:right;" | 11
| 11
| style="text-align:right;" | 171.429
| 171.429
| style="text-align:center;" | 72/65
| 72/65
|-
|-
| style="text-align:right;" | 12
| 12
| style="text-align:right;" | 187.013
| 187.013
| style="text-align:center;" | 10/9
| 10/9
|-
|-
| style="text-align:right;" | 13
| 13
| style="text-align:right;" | 202.597
| 202.597
| style="text-align:center;" | 9/8
| 9/8
|-
|-
| style="text-align:right;" | 14
| 14
| style="text-align:right;" | 218.182
| 218.182
| style="text-align:center;" | 256/225
| 256/225
|-
|-
| style="text-align:right;" | 15
| 15
| style="text-align:right;" | 233.766
| 233.766
| style="text-align:center;" | 8/7
| 8/7
|-
|-
| style="text-align:right;" | 16
| 16
| style="text-align:right;" | 249.351
| 249.351
| style="text-align:center;" | 15/13
| 15/13
|-
|-
| style="text-align:right;" | 17
| 17
| style="text-align:right;" | 264.935
| 264.935
| style="text-align:center;" | 7/6
| 7/6
|-
|-
| style="text-align:right;" | 18
| 18
| style="text-align:right;" | 280.5195
| 280.519
| style="text-align:center;" | 33/28
| 33/28
|-
|-
| style="text-align:right;" | 19
| 19
| style="text-align:right;" | 296.104
| 296.104
| style="text-align:center;" | 32/27, 13/11
| 32/27, 13/11
|-
|-
| style="text-align:right;" | 20
| 20
| style="text-align:right;" | 311.688
| 311.688
| style="text-align:center;" | 6/5
| 6/5
|-
|-
| style="text-align:right;" | 21
| 21
| style="text-align:right;" | 327.273
| 327.273
| style="text-align:center;" | 98/81
| 98/81
|-
|-
| style="text-align:right;" | 22
| 22
| style="text-align:right;" | 342.857
| 342.857
| style="text-align:center;" | 11/9, 39/32
| 11/9, 39/32
|-
|-
| style="text-align:right;" | 23
| 23
| style="text-align:right;" | 358.442
| 358.442
| style="text-align:center;" | 16/13
| 16/13
|-
|-
| style="text-align:right;" | 24
| 24
| style="text-align:right;" | 374.026
| 374.026
| style="text-align:center;" | 56/45, 26/21
| 56/45, 26/21
|-
|-
| style="text-align:right;" | 25
| 25
| style="text-align:right;" | 389.61
| 389.610
| style="text-align:center;" | 5/4
| 5/4
|-
|-
| style="text-align:right;" | 26
| 26
| style="text-align:right;" | 405.195
| 405.195
| style="text-align:center;" | 33/26, 81/64
| 33/26, 81/64
|-
|-
| style="text-align:right;" | 27
| 27
| style="text-align:right;" | 420.779
| 420.779
| style="text-align:center;" | 14/11, 32/25
| 14/11, 32/25
|-
|-
| style="text-align:right;" | 28
| 28
| style="text-align:right;" | 436.364
| 436.364
| style="text-align:center;" | 9/7
| 9/7
|-
|-
| style="text-align:right;" | 29
| 29
| style="text-align:right;" | 451.948
| 451.948
| style="text-align:center;" | 13/10
| 13/10
|-
|-
| style="text-align:right;" | 30
| 30
| style="text-align:right;" | 467.5325
| 467.532
| style="text-align:center;" | 21/16
| 21/16
|-
|-
| style="text-align:right;" | 31
| 31
| style="text-align:right;" | 483.117
| 483.117
| style="text-align:center;" | 120/91
| 120/91
|-
|-
| style="text-align:right;" | 32
| 32
| style="text-align:right;" | 498.701
| 498.701
| style="text-align:center;" | 4/3
| 4/3
|-
|-
| style="text-align:right;" | 33
| 33
| style="text-align:right;" | 514.286
| 514.286
| style="text-align:center;" | 27/20
| 27/20
|-
|-
| style="text-align:right;" | 34
| 34
| style="text-align:right;" | 529.87
| 529.870
| style="text-align:center;" | 49/36
| 49/36
|-
|-
| style="text-align:right;" | 35
| 35
| style="text-align:right;" | 545.4545
| 545.455
| style="text-align:center;" | 11/8, 15/11
| 11/8, 15/11
|-
|-
| style="text-align:right;" | 36
| 36
| style="text-align:right;" | 561.039
| 561.039
| style="text-align:center;" | 18/13
| 18/13
|-
|-
| style="text-align:right;" | 37
| 37
| style="text-align:right;" | 576.623
| 576.623
| style="text-align:center;" | 7/5
| 7/5
|-
|-
| style="text-align:right;" | 38
| 38
| style="text-align:right;" | 592.208
| 592.208
| style="text-align:center;" | 45/32
| 45/32
|-
|-
| style="text-align:right;" | 39
| 39
| style="text-align:right;" | 607.792
| 607.792
| style="text-align:center;" | 64/45
| 64/45
|-
|-
| style="text-align:right;" | 40
| 40
| style="text-align:right;" | 623.377
| 623.377
| style="text-align:center;" | 10/7
| 10/7
|-
|-
| style="text-align:right;" | 41
| 41
| style="text-align:right;" | 638.961
| 638.961
| style="text-align:center;" | 13/9
| 13/9
|-
|-
| style="text-align:right;" | 42
| 42
| style="text-align:right;" | 654.5455
| 654.545
| style="text-align:center;" | 16/11, 22/15
| 16/11, 22/15
|-
|-
| style="text-align:right;" | 43
| 43
| style="text-align:right;" | 670.13
| 670.130
| style="text-align:center;" | 72/49
| 72/49
|-
|-
| style="text-align:right;" | 44
| 44
| style="text-align:right;" | 685.714
| 685.714
| style="text-align:center;" | 40/27
| 40/27
|-
|-
| style="text-align:right;" | 45
| 45
| style="text-align:right;" | 701.299
| 701.299
| style="text-align:center;" | 3/2
| 3/2
|-
|-
| style="text-align:right;" | 46
| 46
| style="text-align:right;" | 716.883
| 716.883
| style="text-align:center;" | 91/60
| 91/60
|-
|-
| style="text-align:right;" | 47
| 47
| style="text-align:right;" | 732.4675
| 732.468
| style="text-align:center;" | 32/21
| 32/21
|-
|-
| style="text-align:right;" | 48
| 48
| style="text-align:right;" | 748.052
| 748.052
| style="text-align:center;" | 20/13
| 20/13
|-
|-
| style="text-align:right;" | 49
| 49
| style="text-align:right;" | 763.636
| 763.636
| style="text-align:center;" | 14/9
| 14/9
|-
|-
| style="text-align:right;" | 50
| 50
| style="text-align:right;" | 779.221
| 779.221
| style="text-align:center;" | 11/7, 25/16
| 11/7, 25/16
|-
|-
| style="text-align:right;" | 51
| 51
| style="text-align:right;" | 794.805
| 794.805
| style="text-align:center;" | 52/33, 128/81
| 52/33, 128/81
|-
|-
| style="text-align:right;" | 52
| 52
| style="text-align:right;" | 810.39
| 810.390
| style="text-align:center;" | 8/5
| 8/5
|-
|-
| style="text-align:right;" | 53
| 53
| style="text-align:right;" | 825.974
| 825.974
| style="text-align:center;" | 45/28, 21/13
| 45/28, 21/13
|-
|-
| style="text-align:right;" | 54
| 54
| style="text-align:right;" | 841.558
| 841.558
| style="text-align:center;" | 13/8
| 13/8
|-
|-
| style="text-align:right;" | 55
| 55
| style="text-align:right;" | 857.143
| 857.143
| style="text-align:center;" | 18/11, 64/39
| 18/11, 64/39
|-
|-
| style="text-align:right;" | 56
| 56
| style="text-align:right;" | 872.727
| 872.727
| style="text-align:center;" | 81/49
| 81/49
|-
|-
| style="text-align:right;" | 57
| 57
| style="text-align:right;" | 888.312
| 888.312
| style="text-align:center;" | 5/3
| 5/3
|-
|-
| style="text-align:right;" | 58
| 58
| style="text-align:right;" | 903.896
| 903.896
| style="text-align:center;" | 27/16, 22/13
| 27/16, 22/13
|-
|-
| style="text-align:right;" | 59
| 59
| style="text-align:right;" | 919.4805
| 919.481
| style="text-align:center;" | 56/33
| 56/33
|-
|-
| style="text-align:right;" | 60
| 60
| style="text-align:right;" | 935.065
| 935.065
| style="text-align:center;" | 12/7
| 12/7
|-
|-
| style="text-align:right;" | 61
| 61
| style="text-align:right;" | 950.649
| 950.649
| style="text-align:center;" | 26/15
| 26/15
|-
|-
| style="text-align:right;" | 62
| 62
| style="text-align:right;" | 966.234
| 966.234
| style="text-align:center;" | 7/4
| 7/4
|-
|-
| style="text-align:right;" | 63
| 63
| style="text-align:right;" | 981.818
| 981.818
| style="text-align:center;" | 225/128
| 225/128
|-
|-
| style="text-align:right;" | 64
| 64
| style="text-align:right;" | 997.403
| 997.403
| style="text-align:center;" | 16/9
| 16/9
|-
|-
| style="text-align:right;" | 65
| 65
| style="text-align:right;" | 1012.987
| 1012.987
| style="text-align:center;" | 9/5
| 9/5
|-
|-
| style="text-align:right;" | 66
| 66
| style="text-align:right;" | 1028.571
| 1028.571
| style="text-align:center;" | 65/36
| 65/36
|-
|-
| style="text-align:right;" | 67
| 67
| style="text-align:right;" | 1044.156
| 1044.156
| style="text-align:center;" | 11/6, 20/11
| 11/6, 20/11
|-
|-
| style="text-align:right;" | 68
| 68
| style="text-align:right;" | 1059.74
| 1059.740
| style="text-align:center;" | 24/13
| 24/13
|-
|-
| style="text-align:right;" | 69
| 69
| style="text-align:right;" | 1075.325
| 1075.325
| style="text-align:center;" | 28/15
| 28/15
|-
|-
| style="text-align:right;" | 70
| 70
| style="text-align:right;" | 1090.909
| 1090.909
| style="text-align:center;" | 15/8
| 15/8
|-
|-
| style="text-align:right;" | 71
| 71
| style="text-align:right;" | 1106.4935
| 1106.494
| style="text-align:center;" | 256/135
| 256/135
|-
|-
| style="text-align:right;" | 72
| 72
| style="text-align:right;" | 1122.078
| 1122.078
| style="text-align:center;" | 40/21, 48/25
| 40/21, 48/25
|-
|-
| style="text-align:right;" | 73
| 73
| style="text-align:right;" | 1137.662
| 1137.662
| style="text-align:center;" | 27/14, 25/13
| 27/14, 25/13
|-
|-
| style="text-align:right;" | 74
| 74
| style="text-align:right;" | 1153.247
| 1153.247
| style="text-align:center;" | 64/33, 35/18
| 64/33, 35/18
|-
|-
| style="text-align:right;" | 75
| 75
| style="text-align:right;" | 1168.831
| 1168.831
| style="text-align:center;" | 63/32, 96/49
| 63/32, 96/49
|-
|-
| style="text-align:right;" | 76
| 76
| style="text-align:right;" | 1184.416
| 1184.416
| style="text-align:center;" | 160/81, 196/99
| 160/81, 196/99
|-
|-
| style="text-align:right;" | 77
| 77
| style="text-align:right;" | 1200
| 1200.000
| style="text-align:center;" | 2/1
| 2/1
|}
|}


=Linear temperaments=
== Linear temperaments ==


{| class="wikitable"
{| class="wikitable center-all left-3"
|-
|-
! | Periods
! Periods<br>per Octave
 
! Generator
per Octave
! Temperaments
! | Generator
! | Temperaments
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 1\77
| 1\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 2\77
| 2\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 3\77
| 3\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 4\77
| 4\77
| | [[Unicorn|Unicorn]]/alicorn/camahueto/qilin
| [[Unicorn]]/alicorn/camahueto/qilin
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 5\77
| 5\77
| | [[Valentine|Valentine]]
| [[Valentine]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 6\77
| 6\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 8\77
| 8\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 9\77
| 9\77
| | [[Tsaharuk|Tsaharuk]]
| [[Tsaharuk]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 10\77
| 10\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 12\77
| 12\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 13\77
| 13\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 15\77
| 15\77
| | [[guiron|Guiron]]
| [[Guiron]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 16\77
| 16\77
| | [[Hemischis|Hemischis]]
| [[Hemischis]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 17\77
| 17\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 18\77
| 18\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 19\77
| 19\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 20\77
| 20\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 23\77
| 23\77
| | Restles ([http://x31eq.com/cgi-bin/rt.cgi?ets=87+%26+77&limit=13 77&amp;87])
| [[Restles]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 24\77
| 24\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 25\77
| 25\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 26\77
| 26\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 27\77
| 27\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 29\77
| 29\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 30\77
| 30\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 31\77
| 31\77
| | [[Hemiseven|Hemiseven]]
| [[Hemiseven]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 32\77
| 32\77
| | [[Hendecatonic|Hendecatonic]], [[Grackle|grackle]]
| [[Hendecatonic]], [[grackle]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 34\77
| 34\77
| | Mabila ([http://x31eq.com/cgi-bin/rt.cgi?ets=34_43&limit=5 34&amp;43])
| Mabila ([http://x31eq.com/cgi-bin/rt.cgi?ets=34_43&limit=5 34&amp;43])
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 36\77
| 36\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 37\77
| 37\77
| |  
|  
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 38\77
| 38\77
| |  
|  
|-
|-
| style="text-align:right;" | 7
| 7
| style="text-align:right;" | 1\77
| 1\77
| | "[[TemperamentOrphanage|Absurdity]]" ([http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5 7&amp;84])
| "[[TemperamentOrphanage|Absurdity]]" ([http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5 7&amp;84])
|-
|-
| style="text-align:right;" | 7
| 7
| style="text-align:right;" | 2\77
| 2\77
| |  
|  
|-
|-
| style="text-align:right;" | 7
| 7
| style="text-align:right;" | 3\77
| 3\77
| |  
|  
|-
|-
| style="text-align:right;" | 7
| 7
| style="text-align:right;" | 4\77
| 4\77
| |  
|  
|-
|-
| style="text-align:right;" | 7
| 7
| style="text-align:right;" | 5\77
| 5\77
| |  
|  
|-
|-
| style="text-align:right;" | 11
| 11
| style="text-align:right;" | 1\77
| 1\77
| |  
|  
|-
|-
| style="text-align:right;" | 11
| 11
| style="text-align:right;" | 2\77
| 2\77
| |  
|  
|-
|-
| style="text-align:right;" | 11
| 11
| style="text-align:right;" | 3\77
| 3\77
| |  
|  
|}
|}


=Music=
== Music ==
 
''[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3 Star 1-GrimaldiA+Bmod]'' by [[Joel_Grant_Taylor|Joel Grant Taylor]]


''[http://micro.soonlabel.com/star/20120830-77et-star.mp3 77et Star]'' by [[Chris_Vaisvil|Chris Vaisvil]]
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3 Star 1-GrimaldiA+Bmod]'' by [[Joel Grant Taylor]]
* ''[http://micro.soonlabel.com/star/20120830-77et-star.mp3 77et Star]'' by [[Chris Vaisvil]]
* ''[http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 A Seed Planted]'' by [[Jake Freivald]], in an [http://soonlabel.com/xenharmonic/archives/1391 organ version] of Claudi Meneghin.


''[http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 A Seed Planted]'' A Seed Planted by Jake Freivald, in an [http://soonlabel.com/xenharmonic/archives/1391 organ version] of Claudi Meneghin.
[[Category:edo]]
[[Category:edo]]
[[Category:listen]]
[[Category:listen]]

Revision as of 06:16, 23 August 2020

Theory

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 Approximate Ratios
in the 13-limit
0 0.000 1/1
1 15.584 81/80, 99/98
2 31.169 64/63, 49/48
3 46.753 33/32, 36/35
4 62.338 28/27, 26/25
5 77.922 21/20, 25/24
6 93.506 135/128
7 109.091 16/15
8 124.675 15/14
9 140.260 13/12
10 155.844 12/11, 11/10
11 171.429 72/65
12 187.013 10/9
13 202.597 9/8
14 218.182 256/225
15 233.766 8/7
16 249.351 15/13
17 264.935 7/6
18 280.519 33/28
19 296.104 32/27, 13/11
20 311.688 6/5
21 327.273 98/81
22 342.857 11/9, 39/32
23 358.442 16/13
24 374.026 56/45, 26/21
25 389.610 5/4
26 405.195 33/26, 81/64
27 420.779 14/11, 32/25
28 436.364 9/7
29 451.948 13/10
30 467.532 21/16
31 483.117 120/91
32 498.701 4/3
33 514.286 27/20
34 529.870 49/36
35 545.455 11/8, 15/11
36 561.039 18/13
37 576.623 7/5
38 592.208 45/32
39 607.792 64/45
40 623.377 10/7
41 638.961 13/9
42 654.545 16/11, 22/15
43 670.130 72/49
44 685.714 40/27
45 701.299 3/2
46 716.883 91/60
47 732.468 32/21
48 748.052 20/13
49 763.636 14/9
50 779.221 11/7, 25/16
51 794.805 52/33, 128/81
52 810.390 8/5
53 825.974 45/28, 21/13
54 841.558 13/8
55 857.143 18/11, 64/39
56 872.727 81/49
57 888.312 5/3
58 903.896 27/16, 22/13
59 919.481 56/33
60 935.065 12/7
61 950.649 26/15
62 966.234 7/4
63 981.818 225/128
64 997.403 16/9
65 1012.987 9/5
66 1028.571 65/36
67 1044.156 11/6, 20/11
68 1059.740 24/13
69 1075.325 28/15
70 1090.909 15/8
71 1106.494 256/135
72 1122.078 40/21, 48/25
73 1137.662 27/14, 25/13
74 1153.247 64/33, 35/18
75 1168.831 63/32, 96/49
76 1184.416 160/81, 196/99
77 1200.000 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
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

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