199edo: Difference between revisions

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'''199edo''' is the [[EDO|equal division of the octave]] into 199 parts of 6.0302 cents each. It tempers out 2109375/2097152 (semicomma) and 31381059609/30517578125 ([[15edt|mowgli comma]]) in the 5-limit. Using the patent val, it tempers out 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.
{{EDO intro}}


199edo is the 46th [[prime EDO]].
Using the [[patent val]], the equal temperament [[tempering out|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.


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
=== Odd harmonics ===
[[Category:Prime EDO]]
{{Harmonics in equal|199}}
 
=== Subsets and supersets ===
199edo is the 46th [[prime edo]].

Revision as of 12:59, 15 April 2024

← 198edo 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

Template:EDO intro

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 (%) -40.8 -6.4 +33.6 +18.5 -42.7 -38.8 -47.1 -40.5 -33.8 -7.1 -18.9
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.

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