99693edo

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← 99692edo99693edo99694edo →
Prime factorization 32 × 11 × 19 × 53
Special properties
Step size 0.012037¢
Fifth 58317\99693 (701.959¢) (→19439\33231)
Semitones (A1:m2) 9447:7494 (113.7¢ : 90.2¢)
Sharp fifth 58317\99693 (701.959¢) (→19439\33231)
Flat fifth 58316\99693 (701.947¢)
Major 2nd 16940\99693 (203.906¢) (→1540\9063)
Consistency limit 7
Distinct consistency limit 7

99693 equal divisions of the octave (99693edo) is the tuning that divides the octave into 99693 equal steps of about 0.012 cents. It is notable for being the edo below 100000 with the lowest maximum error, using direct approximation for each harmonic, for the first 547 harmonics (547 being the 100th prime number).

Theory

Approximation of odd harmonics in 99693 EDO
Odd harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error absolute (¢) +0.004 +0.000 +0.004 -0.004 -0.001 +0.001 +0.004 -0.005 +0.004 -0.004 -0.006 +0.001 +0.000 +0.004 +0.004
relative (%) +33 +2 +37 -33 -12 +6 +36 -43 +36 -30 -46 +4 +0 +30 +31
Steps (reduced) 158010 (58317) 231480 (32094) 279874 (80488) 316019 (16940) 344881 (45802) 368908 (69829) 389490 (90411) 407491 (8719) 423489 (24717) 437883 (39111) 450967 (52195) 462960 (64188) 474029 (75257) 484307 (85535) 493899 (95127)