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


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 ==
With [[3/1|harmonic 3]] less than a cent flat, [[5/1|harmonic 5]] a bit over three cents sharp and [[7/1|7]] less flat than that, 77edo represents an excellent tuning choice for both [[valentine]] (hence also [[Carlos Alpha]]), the {{nowrap|31 & 46}} temperament, and [[starling]], the [[rank-3 temperament]] [[tempering out]] [[126/125]], giving the [[optimal patent val]] for [[11-limit]] valentine and its [[13-limit]] extension [[valentino]], as well as 11-limit starling and [[oxpecker]] temperaments. For desirers of purer/more convincing harmonies of 19, it's also a great choice for [[nestoria]] (the extension of schismic to prime 19) so that ~16:19:24 can be heard to concord in isolation. It also gives the optimal patent val for [[grackle]] and various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 (which gives valentine); it is a very good choice for full-subgroup [[unicorn]]. These are 7-limit [[unicorn family #Alicorn|alicorn]] and 11- and 13-limit [[unicorn family #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 the [[schisma]] (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=
The [[17/1|17]] and [[19/1|19]] are tuned fairly well, making it [[consistent]] to the no-11 [[21-odd-limit]]. The equal temperament tempers out [[256/255]] in the 17-limit; and [[171/170]], [[361/360]], [[513/512]], and [[1216/1215]] in the 19-limit.


{| class="wikitable"
It also does surprisingly well (for its size) in a large range of very high odd-limits (41 to 125 range).
|-
 
! | Degree
=== Prime harmonics ===
! | Cents Value
{{Harmonics in equal|77|columns=9}}
!pions
{{Harmonics in equal|77|columns=10|start=10|collapsed=true|title=Approximation of prime harmonics in 77edo (continued)}}
!7mus
 
! | Approximate Ratios
=== Subsets and supersets ===
Since 77 factors into primes as {{nowrap|7 × 11}}, 77edo contains [[7edo]] and [[11edo]] as subset edos.


in the 13-limit
== Intervals ==
|-
{| class="wikitable center-all right-2 left-3"
| colspan="4" style="text-align:right;" | 0
| style="text-align:center;" | 1/1
|-
|-
| style="text-align:right;" | 1
! #
| style="text-align:right;" | 15.584
! Cents
|16.5195
! Approximate ratios*
|19.948 (13.F2B<sub>16</sub>)
! [[Ups and downs notation]]
| style="text-align:center;" | 81/80, 99/98
|-
|-
| style="text-align:right;" | 2
| 0
| style="text-align:right;" | 31.169
| 0.0
|33.039
| 1/1
|39.896 (27.E56<sub>16</sub>)
| {{UDnote|step=0}}
| style="text-align:center;" | 64/63, 49/48
|-
|-
| style="text-align:right;" | 3
| 1
| style="text-align:right;" | 46.753
| 15.6
|49.558
| 81/80, 91/90, 99/98, 105/104
|59.844 (3B.D82<sub>16</sub>)
| {{UDnote|step=1}}
| style="text-align:center;" | 33/32, 36/35
|-
|-
| style="text-align:right;" | 4
| 2
| style="text-align:right;" | 62.338
| 31.2
|66.078
| 49/48, 55/54, 64/63, 65/64, ''100/99''
|79.792 (4F.CAD<sub>16</sub>)
| {{UDnote|step=2}}
| style="text-align:center;" | 28/27, 26/25
|-
|-
| style="text-align:right;" | 5
| 3
| style="text-align:right;" | 77.922
| 46.8
|82.597
| 33/32, 36/35, 40/39, ''45/44'', ''50/49''
|99.74 (63.BD8<sub>16</sub>)
| {{UDnote|step=3}}
| style="text-align:center;" | 21/20, 25/24
|-
|-
| style="text-align:right;" | 6
| 4
| style="text-align:right;" | 93.5065
| 62.3
|99.117
| 26/25, 27/26, 28/27
|119.688 (77.B03<sub>16</sub>)
| {{UDnote|step=4}}
| style="text-align:center;" | 135/128
|-
|-
| style="text-align:right;" | 7
| 5
| style="text-align:right;" | 109.091
| 77.9
|115.636
| 21/20, 22/21, 25/24
|139.636 (8B.A2F<sub>16</sub>)
| {{UDnote|step=5}}
| style="text-align:center;" | 16/15
|-
|-
| style="text-align:right;" | 8
| 6
| style="text-align:right;" | 124.675
| 93.5
|132.156
| 18/17, 19/18, 20/19
|159.584 (9F.95A<sub>16</sub>)
| {{UDnote|step=6}}
| style="text-align:center;" | 15/14
|-
|-
| style="text-align:right;" | 9
| 7
| style="text-align:right;" | 140.26
| 109.1
|148.675
| 16/15, 17/16
|179.5325 (B3.885<sub>16</sub>)
| {{UDnote|step=7}}
| style="text-align:center;" | 13/12
|-
|-
| style="text-align:right;" | 10
| 8
| style="text-align:right;" | 155.844
| 124.7
|165.195
| 14/13, 15/14
|199.4805 (C7.7B<sub>16</sub>)
| {{UDnote|step=8}}
| style="text-align:center;" | 12/11, 11/10
|-
|-
| style="text-align:right;" | 11
| 9
| style="text-align:right;" | 171.429
| 140.3
|181.714
| 13/12
|219.429 (DB.6DB<sub>16</sub>)
| {{UDnote|step=9}}
| style="text-align:center;" | 72/65
|-
|-
| style="text-align:right;" | 12
| 10
| style="text-align:right;" | 187.013
| 155.8
|198.234
| ''11/10'', 12/11
|239.377 (EF.607<sub>16</sub>)
| {{UDnote|step=10}}
| style="text-align:center;" | 10/9
|-
|-
| style="text-align:right;" | 13
| 11
| style="text-align:right;" | 202.597
| 171.4
|214.753
| 21/19
|259.325 (103.532<sub>16</sub>)
| {{UDnote|step=11}}
| style="text-align:center;" | 9/8
|-
|-
| style="text-align:right;" | 14
| 12
| style="text-align:right;" | 218.182
| 187.0
|231.273
| 10/9
|279.273 (117.45D<sub>16</sub>)
| {{UDnote|step=12}}
| style="text-align:center;" | 256/225
|-
|-
| style="text-align:right;" | 15
| 13
| style="text-align:right;" | 233.766
| 202.6
|247.792
| 9/8
|299.221 (12B.388<sub>16</sub>)
| {{UDnote|step=13}}
| style="text-align:center;" | 8/7
|-
|-
| style="text-align:right;" | 16
| 14
| style="text-align:right;" | 249.351
| 218.2
|264.312
| 17/15
|319.169 (13F.2B4<sub>16</sub>)
| {{UDnote|step=14}}
| style="text-align:center;" | 15/13
|-
|-
| style="text-align:right;" | 17
| 15
| style="text-align:right;" | 264.935
| 233.8
|280.831
| 8/7
|339.117 (153.1DF<sub>16</sub>)
| {{UDnote|step=15}}
| style="text-align:center;" | 7/6
|-
|-
| style="text-align:right;" | 18
| 16
| style="text-align:right;" | 280.5195
| 249.4
|297.351
| 15/13, 22/19
|359.065 (167.10A<sub>16</sub>)
| {{UDnote|step=16}}
| style="text-align:center;" | 33/28
|-
|-
| style="text-align:right;" | 19
| 17
| style="text-align:right;" | 296.104
| 264.9
|313.87
| 7/6
|379.013 (17B.035<sub>16</sub>)
| {{UDnote|step=17}}
| style="text-align:center;" | 32/27, 13/11
|-
|-
| style="text-align:right;" | 20
| 18
| style="text-align:right;" | 311.688
| 280.5
|330.39
| 20/17
|398.961 (18E.F6<sub>16</sub>)
| {{UDnote|step=18}}
| style="text-align:center;" | 6/5
|-
|-
| style="text-align:right;" | 21
| 19
| style="text-align:right;" | 327.273
| 296.1
|346.909
| 13/11, 19/16, 32/27
|418.909 (1A2.E8B<sub>16</sub>)
| {{UDnote|step=19}}
| style="text-align:center;" | 98/81
|-
|-
| style="text-align:right;" | 22
| 20
| style="text-align:right;" | 342.857
| 311.7
|363.429
| 6/5
|438.857 (1B6.DB7<sub>16</sub>)
| {{UDnote|step=20}}
| style="text-align:center;" | 11/9, 39/32
|-
|-
| style="text-align:right;" | 23
| 21
| style="text-align:right;" | 358.442
| 327.3
|379.948
| 98/81
|458.805 (1CA.CE2<sub>16</sub>)
| {{UDnote|step=21}}
| style="text-align:center;" | 16/13
|-
|-
| style="text-align:right;" | 24
| 22
| style="text-align:right;" | 374.026
| 342.9
|396.4675
| 11/9, 17/14
|478.753 (1DE.C0D<sub>16</sub>)
| {{UDnote|step=22}}
| style="text-align:center;" | 56/45, 26/21
|-
|-
| style="text-align:right;" | 25
| 23
| style="text-align:right;" | 389.61
| 358.4
|412.987
| 16/13, 21/17
|498.701 (1F2.B388<sub>16</sub>)
| {{UDnote|step=23}}
| style="text-align:center;" | 5/4
|-
|-
| style="text-align:right;" | 26
| 24
| style="text-align:right;" | 405.195
| 374.0
|429.5065
| 26/21, 56/45
|518.649 (206.A64<sub>16</sub>)
| {{UDnote|step=24}}
| style="text-align:center;" | 33/26, 81/64
|-
|-
| style="text-align:right;" | 27
| 25
| style="text-align:right;" | 420.779
| 389.6
|446.026
| 5/4
|538.597 (21A.98F<sub>16</sub>)
| {{UDnote|step=25}}
| style="text-align:center;" | 14/11, 32/25
|-
|-
| style="text-align:right;" | 28
| 26
| style="text-align:right;" | 436.364
| 405.2
|462.5455
| 19/15, 24/19, 33/26
|558.5455 (22E.8BA<sub>16</sub>)
| {{UDnote|step=26}}
| style="text-align:center;" | 9/7
|-
|-
| style="text-align:right;" | 29
| 27
| style="text-align:right;" | 451.948
| 420.8
|479.065
| 14/11, 32/25
|578.4935 (242.7E5<sub>16</sub>)
| {{UDnote|step=27}}
| style="text-align:center;" | 13/10
|-
|-
| style="text-align:right;" | 30
| 28
| style="text-align:right;" | 467.5325
| 436.4
|495.584
| 9/7
|598.442 (256.711<sub>16</sub>)
| {{UDnote|step=28}}
| style="text-align:center;" | 21/16
|-
|-
| style="text-align:right;" | 31
| 29
| style="text-align:right;" | 483.117
| 451.9
|512.104
| 13/10
|618.39 (26A.63C<sub>16</sub>)
| {{UDnote|step=29}}
| style="text-align:center;" | 120/91
|-
|-
| style="text-align:right;" | 32
| 30
| style="text-align:right;" | 498.701
| 467.5
|528.623
| 17/13, 21/16
|638.338 (27E.567<sub>16</sub>)
| {{UDnote|step=30}}
| style="text-align:center;" | 4/3
|-
|-
| style="text-align:right;" | 33
| 31
| style="text-align:right;" | 514.286
| 483.1
|545.143
| 120/91
|658.286 (292.492<sub>16</sub>)
| {{UDnote|step=31}}
| style="text-align:center;" | 27/20
|-
|-
| style="text-align:right;" | 34
| 32
| style="text-align:right;" | 529.87
| 498.7
|561.662
| 4/3
|678.234 (2A6.3BD8<sub>16</sub>)
| {{UDnote|step=32}}
| style="text-align:center;" | 49/36
|-
|-
| style="text-align:right;" | 35
| 33
| style="text-align:right;" | 545.4545
| 514.3
|578.182
| 27/20
|698.182 (2BA.2E9<sub>16</sub>)
| {{UDnote|step=33}}
| style="text-align:center;" | 11/8, 15/11
|-
|-
| style="text-align:right;" | 36
| 34
| style="text-align:right;" | 561.039
| 529.9
|594.701
| 19/14
|718.13 (2CE.214<sub>16</sub>)
| {{UDnote|step=34}}
| style="text-align:center;" | 18/13
|-
|-
| style="text-align:right;" | 37
| 35
| style="text-align:right;" | 576.623
| 545.5
|611.221
| 11/8, ''15/11'', 26/19
|738.078 (2E2.13F<sub>16</sub>)
| {{UDnote|step=35}}
| style="text-align:center;" | 7/5
|-
|-
| style="text-align:right;" | 38
| 36
| style="text-align:right;" | 592.208
| 561.0
|627.74
| 18/13
|758.026 (2F6.06A<sub>16</sub>)
| {{UDnote|step=36}}
| style="text-align:center;" | 45/32
|-
|-
| style="text-align:right;" | 39
| 37
| style="text-align:right;" | 607.792
| 576.6
|644.26
| 7/5
|777.974 (309.F96<sub>16</sub>)
| {{UDnote|step=37}}
| style="text-align:center;" | 64/45
|-
|-
| style="text-align:right;" | 40
| 38
| style="text-align:right;" | 623.377
| 592.2
|660.779
| 24/17, 38/27, 45/32
|797.922 (31D.EC1<sub>16</sub>)
| {{UDnote|step=38}}
| style="text-align:center;" | 10/7
|-
|-
| style="text-align:right;" | 41
| …
| style="text-align:right;" | 638.961
| …
|677.299
| …
|817.87 (331.DEC<sub>16</sub>)
| style="text-align:center;" | 13/9
|-
| style="text-align:right;" | 42
| style="text-align:right;" | 654.5455
|693.818
|837.818 (345.D17<sub>16</sub>)
| style="text-align:center;" | 16/11, 22/15
|-
| style="text-align:right;" | 43
| style="text-align:right;" | 670.13
|710.338
|857.766 (359.C428<sub>16</sub>)
| style="text-align:center;" | 72/49
|-
| style="text-align:right;" | 44
| style="text-align:right;" | 685.714
|726.857
|877.714 (36D.B6E<sub>16</sub>)
| style="text-align:center;" | 40/27
|-
| style="text-align:right;" | 45
| style="text-align:right;" | 701.299
|743.377
|897.662 (381.A99<sub>16</sub>)
| style="text-align:center;" | 3/2
|-
| style="text-align:right;" | 46
| style="text-align:right;" | 716.883
|759.896
|917.61 (395.9C4<sub>16</sub>)
| style="text-align:center;" | 91/60
|-
| style="text-align:right;" | 47
| style="text-align:right;" | 732.4675
|776.416
|937.558 (3A9.8EF<sub>16</sub>)
| style="text-align:center;" | 32/21
|-
| style="text-align:right;" | 48
| style="text-align:right;" | 748.052
|792.935
|957.5065 (3BD.81B<sub>16</sub>)
| style="text-align:center;" | 20/13
|-
| style="text-align:right;" | 49
| style="text-align:right;" | 763.636
|809.4545
|977.4545 (3D1.746<sub>16</sub>)
| style="text-align:center;" | 14/9
|-
| style="text-align:right;" | 50
| style="text-align:right;" | 779.221
|825.974
|997.403 (3E5.671<sub>16</sub>)
| style="text-align:center;" | 11/7, 25/16
|-
| style="text-align:right;" | 51
| style="text-align:right;" | 794.805
|842.4935
|1017.351 (3F9.59C<sub>16</sub>)
| style="text-align:center;" | 52/33, 128/81
|-
| style="text-align:right;" | 52
| style="text-align:right;" | 810.39
|859.013
|1037.299 (40D.4C78<sub>16</sub>)
| style="text-align:center;" | 8/5
|-
| style="text-align:right;" | 53
| style="text-align:right;" | 825.974
|875.5325
|1057.247 (421.3F3<sub>16</sub>)
| style="text-align:center;" | 45/28, 21/13
|-
| style="text-align:right;" | 54
| style="text-align:right;" | 841.558
|892.052
|1077.195 (435.31E<sub>16</sub>)
| style="text-align:center;" | 13/8
|-
| style="text-align:right;" | 55
| style="text-align:right;" | 857.143
|908.571
|1097.143 (449.249<sub>16</sub>)
| style="text-align:center;" | 18/11, 64/39
|-
| style="text-align:right;" | 56
| style="text-align:right;" | 872.727
|925.091
|1117.091 (45D.174<sub>16</sub>)
| style="text-align:center;" | 81/49
|-
| style="text-align:right;" | 57
| style="text-align:right;" | 888.312
|941.61
|1137.039 (471.0A<sub>16</sub>)
| style="text-align:center;" | 5/3
|-
| style="text-align:right;" | 58
| style="text-align:right;" | 903.896
|958.13
|1156.987 (484.FCB<sub>16</sub>)
| style="text-align:center;" | 27/16, 22/13
|-
| style="text-align:right;" | 59
| style="text-align:right;" | 919.4805
|974.649
|1176.935 (498.EF6<sub>16</sub>)
| style="text-align:center;" | 56/33
|-
| style="text-align:right;" | 60
| style="text-align:right;" | 935.065
|991.169
|1196.883 (4AC.E21<sub>16</sub>)
| style="text-align:center;" | 12/7
|-
| style="text-align:right;" | 61
| style="text-align:right;" | 950.649
|1007.688
|1216.831 (4C0.D4C<sub>16</sub>)
| style="text-align:center;" | 26/15
|-
| style="text-align:right;" | 62
| style="text-align:right;" | 966.234
|1024.208
|1236.77 (4D4.C78<sub>16</sub>)
| style="text-align:center;" | 7/4
|-
| style="text-align:right;" | 63
| style="text-align:right;" | 981.818
|1040.727
|1256.727 (4E8.BA3<sub>16</sub>)
| style="text-align:center;" | 225/128
|-
| style="text-align:right;" | 64
| style="text-align:right;" | 997.403
|1057.247
|1276.675 (4FC.ACE<sub>16</sub>)
| style="text-align:center;" | 16/9
|-
| style="text-align:right;" | 65
| style="text-align:right;" | 1012.987
|1073.766
|1296.623 (510.9F9<sub>16</sub>)
| style="text-align:center;" | 9/5
|-
| style="text-align:right;" | 66
| style="text-align:right;" | 1028.571
|1090.285
|1316.571 (524.924<sub>16</sub>)
| style="text-align:center;" | 65/36
|-
| style="text-align:right;" | 67
| style="text-align:right;" | 1044.156
|1106.805
|1336.5195 (538.85<sub>16</sub>)
| style="text-align:center;" | 11/6, 20/11
|-
| style="text-align:right;" | 68
| style="text-align:right;" | 1059.74
|1123.325
|1356.4675 (54C.77B<sub>16</sub>)
| style="text-align:center;" | 24/13
|-
| style="text-align:right;" | 69
| style="text-align:right;" | 1075.325
|1139.844
|1376.416 (560.6A6<sub>16</sub>)
| style="text-align:center;" | 28/15
|-
| style="text-align:right;" | 70
| style="text-align:right;" | 1090.909
|1156.364
|1396.364 (574.5D1<sub>16</sub>)
| style="text-align:center;" | 15/8
|-
| style="text-align:right;" | 71
| style="text-align:right;" | 1106.4935
|1172.883
|1416.312 (588.4FD<sub>16</sub>)
| style="text-align:center;" | 256/135
|-
| style="text-align:right;" | 72
| style="text-align:right;" | 1122.078
|1189.403
|1436.26 (59C.426<sub>16</sub>)
| style="text-align:center;" | 40/21, 48/25
|-
| style="text-align:right;" | 73
| style="text-align:right;" | 1137.662
|1205.922
|1456.208 (5B0.353<sub>16</sub>)
| style="text-align:center;" | 27/14, 25/13
|-
| style="text-align:right;" | 74
| style="text-align:right;" | 1153.247
|1222.442
|1476.156 (5C4.27E<sub>16</sub>)
| style="text-align:center;" | 64/33, 35/18
|-
| style="text-align:right;" | 75
| style="text-align:right;" | 1168.831
|1238.961
|1496.104 (5D8.1AA<sub>16</sub>)
| style="text-align:center;" | 63/32, 96/49
|-
| style="text-align:right;" | 76
| style="text-align:right;" | 1184.416
|1255.4805
|1516.052 (5EC.0D5<sub>16</sub>)
| style="text-align:center;" | 160/81, 196/99
|-
| style="text-align:right;" | 77
| style="text-align:right;" | 1200
|1272
|1536 (600<sub>16</sub>)
| style="text-align:center;" | 2/1
|}
|}
<nowiki/>* As a 19-limit temperament


=Linear temperaments=
== Notation ==


{| class="wikitable"
=== Ups and downs notation ===
|-
 
! | Periods
77edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc.
{{Sharpness-sharp7a}}
 
Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used:
{{Sharpness-sharp7}}
 
=== Sagittal notation ===
==== Evo flavor ====
<imagemap>
File:77-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 591 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 220 106 [[64/63]]
rect 220 80 340 106 [[33/32]]
default [[File:77-EDO_Evo_Sagittal.svg]]
</imagemap>
 
==== Revo flavor ====
<imagemap>
File:77-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 543 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 220 106 [[64/63]]
rect 220 80 340 106 [[33/32]]
default [[File:77-EDO_Revo_Sagittal.svg]]
</imagemap>
 
== Approximation to JI ==
=== Zeta peak index ===
{{ZPI
| zpi = 414
| steps = 76.9918536925042
| step size = 15.5860645308353
| tempered height = 8.194847
| pure height = 8.145298
| integral = 1.311364
| gap = 17.029289
| octave = 1200.12696887432
| consistent = 10
| distinct = 10
}}


per Octave
== Regular temperament properties ==
! | Generator
{| class="wikitable center-4 center-5 center-6"
! | Temperaments
|-
|-
| style="text-align:right;" | 1
! rowspan="2" | [[Subgroup]]
| style="text-align:right;" | 1\77
! rowspan="2" | [[Comma list]]
| |
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
| style="text-align:right;" | 1
! [[TE error|Absolute]] (¢)
| style="text-align:right;" | 2\77
! [[TE simple badness|Relative]] (%)
| |
|-
|-
| style="text-align:right;" | 1
| 2.3
| style="text-align:right;" | 3\77
| {{monzo| -122 77 }}
| |  
| {{mapping| 77 122 }}
| +0.207
| 0.207
| 1.33
|-
|-
| style="text-align:right;" | 1
| 2.3.5
| style="text-align:right;" | 4\77
| 32805/32768, 1594323/1562500
| | [[Unicorn|Unicorn]]/alicorn/camahueto/qilin
| {{mapping| 77 122 179 }}
| −0.336
| 0.785
| 5.04
|-
|-
| style="text-align:right;" | 1
| 2.3.5.7
| style="text-align:right;" | 5\77
| 126/125, 1029/1024, 10976/10935
| | [[Valentine|Valentine]]
| {{mapping| 77 122 179 216 }}
| −0.021
| 0.872
| 5.59
|-
|-
| style="text-align:right;" | 1
| 2.3.5.7.11
| style="text-align:right;" | 6\77
| 121/120, 126/125, 176/175, 10976/10935
| |  
| {{mapping| 77 122 179 216 266 }}
| +0.322
| 1.039
| 6.66
|-
|-
| style="text-align:right;" | 1
| 2.3.5.7.11.13
| style="text-align:right;" | 8\77
| 121/120, 126/125, 176/175, 196/195, 676/675
| |
| {{mapping| 77 122 179 216 266 285 }}
|-
| +0.222
| style="text-align:right;" | 1
| 0.974
| style="text-align:right;" | 9\77
| 6.25
| | [[Tsaharuk|Tsaharuk]]
|}
|-
 
| style="text-align:right;" | 1
=== Rank-2 temperaments ===
| style="text-align:right;" | 10\77
{| class="wikitable center-all left-5"
| |
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 12\77
| |
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 13\77
| |
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 15\77
| | [[guiron|Guiron]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 16\77
| | [[Hemischis|Hemischis]]
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 17\77
| |
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 18\77
| |
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 19\77
| |
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 20\77
| |
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 23\77
| | Restles ([http://x31eq.com/cgi-bin/rt.cgi?ets=87+%26+77&limit=13 77&amp;87])
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 24\77
| |
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 25\77
| |
|-
| style="text-align:right;" | 1
| style="text-align:right;" | 26\77
| |
|-
|-
| style="text-align:right;" | 1
! Periods<br>per 8ve
| style="text-align:right;" | 27\77
! Generator*
| |
! Cents*
! Associated<br>ratio*
! Temperament
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 29\77
| 4\77
| |  
| 62.3
| 28/27
| [[Unicorn]] / alicorn (77e) / camahueto (77) / qilin (77)
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 30\77
| 5\77
| |  
| 77.9
| 21/20
| [[Valentine]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 31\77
| 9\77
| | [[Hemiseven|Hemiseven]]
| 140.3
| 13/12
| [[Tsaharuk]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 32\77
| 15\77
| | [[Hendecatonic|Hendecatonic]], [[Grackle|grackle]]
| 233.8
| 8/7
| [[Guiron]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 34\77
| 16\77
| | Mabila ([http://x31eq.com/cgi-bin/rt.cgi?ets=34_43&limit=5 34&amp;43])
| 249.4
| 15/13
| [[Hemischis]] (77e)
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 36\77
| 20\77
| |  
| 311.7
| 6/5
| [[Oolong]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 37\77
| 23\77
| |  
| 358.4
| 16/13
| [[Restles]]
|-
|-
| style="text-align:right;" | 1
| 1
| style="text-align:right;" | 38\77
| 31\77
| |  
| 483.1
| 45/34
| [[Hemiseven]]
|-
|-
| style="text-align:right;" | 7
| 1
| style="text-align:right;" | 1\77
| 32\77
| | "[[TemperamentOrphanage|Absurdity]]" ([http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5 7&amp;84])
| 498.7
| 4/3
| [[Grackle]]
|-
|-
| style="text-align:right;" | 7
| 1
| style="text-align:right;" | 2\77
| 34\77
| |  
| 529.9
| 512/375
| [[Tuskaloosa]] / [[muscogee]]
|-
|-
| style="text-align:right;" | 7
| 1
| style="text-align:right;" | 3\77
| 36\77
| |  
| 561.0
| 18/13
| [[Demivalentine]]
|-
|-
| style="text-align:right;" | 7
| 7
| style="text-align:right;" | 4\77
| 32\77<br>(1\77)
| |  
| 498.7<br>(15.6)
| 4/3<br>(81/80)
| [[Absurdity]]
|-
|-
| style="text-align:right;" | 7
| 11
| style="text-align:right;" | 5\77
| 32\77<br>(3\77)
| |
| 498.7<br>(46.8)
|-
| 4/3<br>(36/35)
| style="text-align:right;" | 11
| [[Hendecatonic]]
| style="text-align:right;" | 1\77
| |
|-
| style="text-align:right;" | 11
| style="text-align:right;" | 2\77
| |
|-
| style="text-align:right;" | 11
| style="text-align:right;" | 3\77
| |
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Instruments ==
=== Skip fretting ===
'''Skip fretting system 77 9 11''' is a [[skip fretting]] system that tunes strings 11\77 apart, with frets placed at intervals of 9\77, or 8.555...-edo. All examples on this page are for 7-string [[guitar]].
; Intervals
0\77=1/1: string 2 open
77\77=2/1: string 7 fret 11
45\77=3/2: string 2 fret 5
25\77=5/4: string 1 fret 4
62\77=7/4: string 6 fret 2
35\77=11/8: string 4 fret 10
54\77=13/8: string 2 fret 6
7\77=17/16: string 1 fret 2
19\77=19/16: string 5 fret 7
40\77=23/16: string 4 fret 2
; Chords
x00030x: Neutral 9th (saj6, v5)
=== Keyboards ===
[[Lumatone mapping for 77edo|Lumatone mappings for 77edo]] are available.
== Music ==
; [[Bryan Deister]
* [https://www.youtube.com/shorts/wSZez2KgP2U ''microtonal improvisation in 77edo''] (2025)


=Music=
; [[Jake Freivald]]
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3 ''A Seed Planted'']{{dead link}}, in an [https://web.archive.org/web/20190412162407/http://soonlabel.com/xenharmonic/archives/1391 organ version] of [[Claudi Meneghin]].


''[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]]
; [[Joel Grant Taylor]]
* [https://web.archive.org/web/20201127015546/http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3 ''Star 1-GrimaldiA+Bmod'']


''[http://micro.soonlabel.com/star/20120830-77et-star.mp3 77et Star]'' by [[Chris_Vaisvil|Chris Vaisvil]]
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/star/20120830-77et-star.mp3 ''77et Star'']


''[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:Listen]]
[[Category:edo]]
[[Category:Star]]
[[Category:listen]]
[[Category:Starling]]
[[Category:star]]
[[Category:Valentine]]
[[Category:starling]]
[[Category:valentine]]
Retrieved from "https://en.xen.wiki/w/77edo"