99693edo

← 99692edo

99693edo

99694edo →

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 99693edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23	25	27	29	31	33	35	37	39	41	43	45	47	49	51	53	55	57	59	61	63	65	67	69	71	73	75	77	79	81	83	85	87	89	91	93	95	97	99	101	103	105	107	109	111	113	115	117	119	123	125	127
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	+0.003	+0.005	-0.000	+0.005	-0.005	+0.005	-0.004	+0.004	-0.003	-0.001	+0.005	-0.001	-0.004	-0.004	+0.000	+0.000	+0.001	+0.004	-0.002	+0.003	-0.002	+0.005	+0.003	+0.002	+0.004	+0.002	-0.005	-0.004	-0.004	+0.005	-0.004	+0.005	-0.001	-0.005	-0.001	-0.004	-0.003	-0.001	+0.005	+0.004	-0.001	-0.005	-0.003	-0.001	-0.001	+0.001	+0.001
	Relative (%)	+33.3	+2.2	+36.6	-33.3	-11.6	+6.3	+35.6	-43.3	+36.2	-30.1	-46.2	+4.5	+0.0	+30.1	+30.7	+21.7	+38.8	-3.4	+39.7	-43.2	+38.8	-31.1	+37.4	-26.8	-10.0	+42.6	-9.4	-30.4	-33.4	+0.3	+3.3	+8.6	+37.0	-12.9	+26.0	-18.0	+37.8	+24.9	+18.6	+33.4	+19.4	-41.1	-36.6	-29.3	+42.9	-35.9	+38.5	-11.1	-45.0	-7.7	-29.7	-27.8	-6.8	+40.0	+29.9	-10.1	-44.0	-27.0	-6.7	-9.9	+6.7	+5.8
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)	502891 (4426)	511354 (12889)	519346 (20881)	526918 (28453)	534110 (35645)	540961 (42496)	547499 (49034)	553754 (55289)	559747 (61282)	565501 (67036)	571034 (72569)	576361 (77896)	581498 (83033)	586458 (87993)	591253 (92788)	595893 (97428)	600388 (2230)	604747 (6589)	608977 (10819)	613087 (14929)	617082 (18924)	620970 (22812)	624755 (26597)	628443 (30285)	632039 (33881)	635547 (37389)	638971 (40813)	642316 (44158)	645585 (47427)	648782 (50624)	651908 (53750)	654969 (56811)	657965 (59807)	660900 (62742)	663777 (65619)	666597 (68439)	669363 (71205)	672077 (73919)	674741 (76583)	677356 (79198)	679924 (81766)	682447 (84289)	684927 (86769)	687365 (89207)	692120 (93962)	694440 (96282)	696723 (98565)