Prime factorization

3^{2} × 11 × 19 × 53

Step size

0.012037¢

Fifth

58317\99693 (701.959¢) (→19439\33231)

Semitones (A1:m2)

9447:7494 (113.7¢ : 90.2¢)

Dual sharp fifth

58317\99693 (701.959¢) (→19439\33231)

Dual flat fifth

58316\99693 (701.947¢)

Dual 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)
