105edo: Difference between revisions
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105edo gives the [[Optimal_patent_val|optimal patent val]] for 11-limit meantone (ie huygens rather than meanpop) and provides a good tuning in the 13-limit, though [[74edo|74edo]] is in that case the optimal patent val. 105 is highly composite, being the product 3*5*7 of the three smallest odd primes, with other divisors being 15, 21 and 35. As the common multiple of these three primes closest to 100, 105 is a perfect substitute for it when a "[[cent|cent]]" is desired to include them all. | 105edo gives the [[Optimal_patent_val|optimal patent val]] for 11-limit meantone (ie huygens rather than meanpop) and provides a good tuning in the 13-limit, though [[74edo|74edo]] is in that case the optimal patent val. 105 is highly composite, being the product 3*5*7 of the three smallest odd primes, with other divisors being 15, 21 and 35. As the common multiple of these three primes closest to 100, 105 is a perfect substitute for it when a "[[cent|cent]]" is desired to include them all. | ||
== 105edo close-up == | |||
<pre>C . . . . . . C# . . Db . . . . . . D</pre> | |||
[[Category:edo]] | [[Category:edo]] | ||
[[Category:huygens]] | [[Category:huygens]] | ||
[[Category:meantone]] | [[Category:meantone]] | ||
[[Category:theory]] | [[Category:theory]] | ||
Revision as of 18:09, 26 September 2018
105edo is the equal division of the octave into 105 equal parts of 11.429 cents each. It is most notable as a tuning of meantone and in particular higher limit extensions of meantone, tempering out 81/80 in the 5-limit; 81/80, 126/125 and hence 225/224 in the 7-limit; 99/98, 176/175 and 441/440 in the 11-limit; and if we want to push that far, 144/143 in the 13-limit. This is the sharper fifth mapping (aka "huygens") of 11-limit meantone.
105edo gives the optimal patent val for 11-limit meantone (ie huygens rather than meanpop) and provides a good tuning in the 13-limit, though 74edo is in that case the optimal patent val. 105 is highly composite, being the product 3*5*7 of the three smallest odd primes, with other divisors being 15, 21 and 35. As the common multiple of these three primes closest to 100, 105 is a perfect substitute for it when a "cent" is desired to include them all.
105edo close-up
C . . . . . . C# . . Db . . . . . . D