105edo

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, as it is the highest edo that strictly fulfils both criteria of meantone - ie, all intervals can be reached by stacking it's best fifth, and stacking four of them equals it's best major third. It tempers 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 (i. e. (14+1)*14/2) of the three smallest odd primes, with other divisors being 15, 21 and 35. As the common multiple of these three primes and the triangular number closest to 100, 105 is a perfect substitute for it when a "cent" is desired to include them all or be a triangular number.

105edo close-up

C . . Dbb B## . . C# . . Db . . . C## . . D