| Prime factorization
|
32 × 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)
|