114edo: Difference between revisions

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'''114edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 114 parts, each of 10.52632 [[cent|cent]]s. In the [[5-limit|5-limit]] it [[tempering_out|tempers out]] 2048/2025, in the [[7-limit|7-limit]] 245/243, in the [[11-limit|11-limit]] 121/120 ~~and~~ 176/175, in the [[13-limit|13-limit]] 196/195 and 325/324, in the [[17-limit|17-limit]] 136/135 and 154/153, in the [[19-limit|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family|shrutar temperament]]; it is in fact the [[Optimal_patent_val|optimal patent val]] for [[Shrutar|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.

'''114edo''' is the [[Equal_division_of_the_octave|equal division of the octave]] into 114 parts, each of 10.52632 [[cent|cent]]s. In the [[5-limit|5-limit]] it [[tempering_out|tempers out]] 2048/2025, in the [[7-limit|7-limit]] 245/243, in the [[11-limit|11-limit]] 121/120, 176/175 and and 117440512/117406179, in the [[13-limit|13-limit]] 196/195 and 325/324, in the [[17-limit|17-limit]] 136/135 and 154/153, in the [[19-limit|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family|shrutar temperament]]; it is in fact the [[Optimal_patent_val|optimal patent val]] for [[Shrutar|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.

===Period of 19-limit Shrutar===

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	'''114edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 114 parts, each of 10.52632 [[cent\|cent]]s. In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120 ~~and~~ 176/175, in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.		'''114edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 114 parts, each of 10.52632 [[cent\|cent]]s. In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and and 117440512/117406179, in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.

	===Period of 19-limit Shrutar===		===Period of 19-limit Shrutar===