121edo: Difference between revisions

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The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374 and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the [[Optimal_patent_val|optimal patent val]] for 13-limit [[Mirkwai_clan|grendel temperament]]. It is [[consistent|consistent]] through to the 19 odd limit and uniquely consistent to the 15 odd limit.

The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each and being the square closest to division of the octave by the Germanic [https://en.wikipedia.org/wiki/Long_hundred long hundred], it has a unit step which is the quadratic (fine) relative cent of [[1edo]]. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374 and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the [[Optimal_patent_val|optimal patent val]] for 13-limit [[Mirkwai_clan|grendel temperament]]. It is [[consistent|consistent]] through to the 19 odd limit and uniquely consistent to the 15 odd limit.

Because it tempers out 540/539 it allows [[swetismic_chords|swetismic chords]], because it tempers out 325/324 it allows [[marveltwin_triad|marveltwin chords]], because it tempers out 640/637 it allows [[huntmic_chords|huntmic chords]], because it tempers out 352/351 it allows [[minthmic_chords|minthmic chords]], because it tempers out 364/363 it allows [[gentle_chords|gentle chords]], because it tempers out 676/675 it allows [[island_tetrad|island chords]] and because it tempers out 1575/1573 it allows the [[nicolic_tetrad|nicolic tetrad]]. That makes for a very flexible system, and since this suite of commas defines 13-limit 121et, it is a system only associated with 121.

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	The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374 and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the [[Optimal_patent_val\|optimal patent val]] for 13-limit [[Mirkwai_clan\|grendel temperament]]. It is [[consistent\|consistent]] through to the 19 odd limit and uniquely consistent to the 15 odd limit.		The 121 equal temperament divides the octave into 121 equal steps of 9.917 cents each and being the square closest to division of the octave by the Germanic [https://en.wikipedia.org/wiki/Long_hundred long hundred], it has a unit step which is the quadratic (fine) relative cent of [[1edo]]. It has a distinctly sharp tendency, in that the odd primes from 3 to 19 all have sharp tunings. It tempers out 15625/15552 in the 5-limit; 4000/3969, 6144/6125, 10976/10935 in the 7-limit; 540/539, 896/891 and 1375/1372 in the 11-limit; 325/324, 352/351, 364/363 and 625/624 in the 13-limit; 256/255, 375/374 and 442/441 in the 17-limit; 190/189 and 361/360 in the 19-limit. It also serves as the [[Optimal_patent_val\|optimal patent val]] for 13-limit [[Mirkwai_clan\|grendel temperament]]. It is [[consistent\|consistent]] through to the 19 odd limit and uniquely consistent to the 15 odd limit.

	Because it tempers out 540/539 it allows [[swetismic_chords\|swetismic chords]], because it tempers out 325/324 it allows [[marveltwin_triad\|marveltwin chords]], because it tempers out 640/637 it allows [[huntmic_chords\|huntmic chords]], because it tempers out 352/351 it allows [[minthmic_chords\|minthmic chords]], because it tempers out 364/363 it allows [[gentle_chords\|gentle chords]], because it tempers out 676/675 it allows [[island_tetrad\|island chords]] and because it tempers out 1575/1573 it allows the [[nicolic_tetrad\|nicolic tetrad]]. That makes for a very flexible system, and since this suite of commas defines 13-limit 121et, it is a system only associated with 121.		Because it tempers out 540/539 it allows [[swetismic_chords\|swetismic chords]], because it tempers out 325/324 it allows [[marveltwin_triad\|marveltwin chords]], because it tempers out 640/637 it allows [[huntmic_chords\|huntmic chords]], because it tempers out 352/351 it allows [[minthmic_chords\|minthmic chords]], because it tempers out 364/363 it allows [[gentle_chords\|gentle chords]], because it tempers out 676/675 it allows [[island_tetrad\|island chords]] and because it tempers out 1575/1573 it allows the [[nicolic_tetrad\|nicolic tetrad]]. That makes for a very flexible system, and since this suite of commas defines 13-limit 121et, it is a system only associated with 121.