74edo

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74edo

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Prime factorization	2 × 37
Step size	16.2162 ¢
Fifth	43\74 (697.297 ¢)
Semitones (A1:m2)	5:7 (81.08 ¢ : 113.5 ¢)
Consistency limit	5
Distinct consistency limit	5

74edo divides the octave into 74 equal parts of size 16.216 cents each. It is most notable as a meantone tuning, tempering out 81/80 in the 5-limit; 81/80 and 126/125 (and hence 225/224) in the 7-limit; 99/98, 176/175 and 441/440 in the 11-limit; and 144/143 and 847/845 in the 13-limit. Discarding 847/845 from that gives 13-limit meantone, aka 13-limit huygens, for which 74edo gives the optimal patent val; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.

74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.

Music

• Twinkle canon – 74 edo by Claudi Meneghin ^{[dead link]}