99693edo

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99693edo
Prime factorization 32 × 11 × 19 × 53
Step size 0.012037¢
Fifth 58317\99693 = 701.959¢
Major 2nd 16941\99693 = 203.918¢
Minor 2nd 7494\99693 = 90.205¢
Augmented 1sn 9447\99693 = 113.713¢

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 99693edo
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)