77edo: Difference between revisions

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'''77 equal temperament''', '''77-tET''' or '''77-EDO''' divides the octave into 77 steps of size 15.5844 [[cent|cents]] each.

== 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&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]].

With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7/4|7/4s]] less flat than that, 77edo represents an excellent tuning choice for both [[valentine]], the 31&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]], [[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.

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+'''77 equal temperament''', '''77-tET''' or '''77-EDO''' divides the octave into 77 steps of size 15.5844 [[cent|cents]] each.
 == Theory ==
--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]].
+With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7/4|7/4s]] less flat than that, 77edo 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]].
 et 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.