199edt

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← 198edt199edt200edt →
Prime factorization 199 (prime)
Step size 9.55756¢ 
Octave 126\199edt (1204.25¢)
Consistency limit 2
Distinct consistency limit 2

199 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 199edt or 199ed3), is a nonoctave tuning system that divides the interval of 3/1 into 199 equal parts of about 9.56 ¢ each. Each step represents a frequency ratio of 31/199, or the 199th root of 3.

Harmonics

Approximation of harmonics in 199edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.25 +0.00 -1.05 +4.49 +4.25 -4.56 +3.20 +0.00 -0.81 -3.34 -1.05
Relative (%) +44.5 +0.0 -11.0 +47.0 +44.5 -47.8 +33.5 +0.0 -8.5 -34.9 -11.0
Steps
(reduced)
126
(126)
199
(0)
251
(52)
292
(93)
325
(126)
352
(153)
377
(178)
398
(0)
417
(19)
434
(36)
450
(52)
Approximation of harmonics in 199edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +3.74 -0.31 +4.49 -2.10 -1.93 +4.25 -3.33 +3.44 -4.56 +0.92 +0.42
Relative (%) +39.1 -3.3 +47.0 -22.0 -20.1 +44.5 -34.9 +36.0 -47.8 +9.6 +4.4
Steps
(reduced)
465
(67)
478
(80)
491
(93)
502
(104)
513
(115)
524
(126)
533
(135)
543
(145)
551
(153)
560
(162)
568
(170)