121edo: Difference between revisions
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121edo 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]] for 13-limit [[grendel]] temperament. It is [[consistent]] through to the [[19-odd-limit]] and uniquely consistent to the [[15-odd-limit]]. | 121edo 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]] for 13-limit [[grendel]] temperament. It is [[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]], because it tempers out 325/324 it allows [[marveltwin chords]], because it tempers out 640/637 it allows [[huntmic chords]], because it tempers out 352/351 it allows [[minthmic chords]], because it tempers out 364/363 it allows [[ | Because it tempers out 540/539 it allows [[swetismic chords]], because it tempers out 325/324 it allows [[marveltwin chords]], because it tempers out 640/637 it allows [[huntmic chords]], because it tempers out 352/351 it allows [[major minthmic chords]], because it tempers out 364/363 it allows [[minor minthmic chords]], because it tempers out 676/675 it allows [[island chords]] and because it tempers out 1575/1573 it allows [[nicolic chords]]. 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. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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Since 121 is part of the Fibonacci sequence beginning with 5 and 12, 121edo closely approximates peppermint temperament. This makes it suitable for neo-Gothic tunings. | Since 121 is part of the Fibonacci sequence beginning with 5 and 12, 121edo closely approximates peppermint temperament. This makes it suitable for neo-Gothic tunings. | ||
[[Category:Grendel]] | [[Category:Grendel]] | ||
[[Category:Quintupole]] | [[Category:Quintupole]] | ||