199edo

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199edo

200edo →

Prime factorization	199 (prime)
Step size	6.03015¢
Fifth	116\199 (699.497¢)
Semitones (A1:m2)	16:17 (96.48¢ : 102.5¢)
Dual sharp fifth	117\199 (705.528¢)
Dual flat fifth	116\199 (699.497¢)
Dual major 2nd	34\199 (205.025¢)
Consistency limit	5
Distinct consistency limit	5

199 equal divisions of the octave (abbreviated 199edo or 199ed2), also called 199-tone equal temperament (199tet) or 199 equal temperament (199et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 199 equal parts of about 6.03 ¢ each. Each step represents a frequency ratio of 2^1/199, or the 199th root of 2.

Using the patent val, the equal temperament tempers out 2109375/2097152 (semicomma) and 31381059609/30517578125 (mowgli comma) in the 5-limit; 225/224 and 1728/1715 in the 7-limit; 243/242, 2420/2401, 3025/3024, and 161051/160000 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 2704/2695 in the 13-limit. Using the 199bef val, it tempers out 245/243, 65536/64827, and 390625/387072 in the 7-limit; 1375/1372, 2560/2541, 5632/5625, and 6875/6804 in the 11-limit; 364/363, 640/637, 676/675, 1625/1617, and 3200/3159 in the 13-limit. Using the 199d val, it tempers out 3136/3125, 33075/32768, and 177147/175000 in the 7-limit; 243/242, 385/384, 3773/3750, and 12005/11979 in the 11-limit; 351/350, 847/845, 1287/1280, and 1575/1573 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 199edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	-2.46	-0.38	+2.03	+1.12	-2.57	-2.34	-2.84	-2.44	-2.04	-0.43	-1.14
	relative (%)	-41	-6	+34	+18	-43	-39	-47	-41	-34	-7	-19
Steps (reduced)		315 (116)	462 (64)	559 (161)	631 (34)	688 (91)	736 (139)	777 (180)	813 (17)	845 (49)	874 (78)	900 (104)

Subsets and supersets

199edo is the 46th prime edo.