75edo: Difference between revisions

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'''75edo''' divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for [[Tetracot_family|tetracot temperament]]. In the 7-limit, it tenpers 225/224 and 1728/1715. In the 11-limit, 75e val scores lower in [[badness]] than the [[patent val]], tempers 100/99 and 243/242, in the 13-limit, it tempers 325/324 and 512/507, in the 17-limit, it tempers 120/119 and 256/255, in the 19-limit, it tempers 190/189 and 250/247.

'''75edo''' divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for [[Tetracot_family|tetracot temperament]]. In the 7-limit, it tenpers 225/224 and 1728/1715. In the 11-limit, 75e val scores lower in [[badness]] than the [[patent val]], tempers 100/99 and 243/242, whereas the patent val tempers out 99/98 and 121/120. In the 13-limit, it tempers 325/324 and 512/507, in the 17-limit, it tempers 120/119 and 256/255, in the 19-limit, it tempers 190/189 and 250/247.

It provides the optimal patent val for the [[M&N_temperaments|12&51 temperament]] in the 7-limit and the [[M&N_temperaments|31&44 temperament]] in the 19-limit.

Revision as of 22:12, 16 February 2022 view source Gud2228 (talk \| contribs) autopatrolled, emailconfirmed 227 edits No edit summary Tags: Visual edit Mobile edit Mobile web edit ← Older edit		Revision as of 22:18, 16 February 2022 view source Gud2228 (talk \| contribs) autopatrolled, emailconfirmed 227 edits No edit summary Tags: Visual edit Mobile edit Mobile web edit Newer edit →
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	'''75edo''' divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for [[Tetracot_family\|tetracot temperament]]. In the 7-limit, it tenpers 225/224 and 1728/1715. In the 11-limit, 75e val scores lower in [[badness]] than the [[patent val]], tempers 100/99 and 243/242, in the 13-limit, it tempers 325/324 and 512/507, in the 17-limit, it tempers 120/119 and 256/255, in the 19-limit, it tempers 190/189 and 250/247.		'''75edo''' divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for [[Tetracot_family\|tetracot temperament]]. In the 7-limit, it tenpers 225/224 and 1728/1715. In the 11-limit, 75e val scores lower in [[badness]] than the [[patent val]], tempers 100/99 and 243/242, whereas the patent val tempers out 99/98 and 121/120. In the 13-limit, it tempers 325/324 and 512/507, in the 17-limit, it tempers 120/119 and 256/255, in the 19-limit, it tempers 190/189 and 250/247.

	It provides the optimal patent val for the [[M&N_temperaments\|12&51 temperament]] in the 7-limit and the [[M&N_temperaments\|31&44 temperament]] in the 19-limit.		It provides the optimal patent val for the [[M&N_temperaments\|12&51 temperament]] in the 7-limit and the [[M&N_temperaments\|31&44 temperament]] in the 19-limit.