336edt

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336edt

337edt →

Prime factorization	24 × 3 × 7
Step size	5.66058 ¢
Octave	212\336edt (1200.04 ¢) (→ 53\84edt)
Consistency limit	16
Distinct consistency limit	16

336 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 336edt or 336ed3), is a nonoctave tuning system that divides the interval of 3/1 into 336 equal parts of about 5.66 ¢ each. Each step represents a frequency ratio of 3^1/336, or the 336th root of 3.

Theory

336edt is nearly identical to 212edo, but with the perfect twelfth instead of the octave tuned just. The octave is stretched by about 0.0430 cents. Like 212edo, 336edt is consistent to the 16-integer-limit. The stretch is so subtle that most of the prime harmonics tuned flat in 212edo remain flat.

Harmonics

Approximation of harmonics in 336edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.04	+0.00	+0.09	-1.31	+0.04	-0.78	+0.13	+0.00	-1.27	-2.11	+0.09
	Relative (%)	+0.8	+0.0	+1.5	-23.1	+0.8	-13.8	+2.3	+0.0	-22.4	-37.3	+1.5
Steps (reduced)		212 (212)	336 (0)	424 (88)	492 (156)	548 (212)	595 (259)	636 (300)	672 (0)	704 (32)	733 (61)	760 (88)

Approximation of harmonics in 336edt (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-2.63	-0.74	-1.31	+0.17	+2.77	+0.04	+2.67	-1.22	-0.78	-2.07	+0.22	+0.13
	Relative (%)	-46.5	-13.0	-23.1	+3.0	+48.9	+0.8	+47.2	-21.6	-13.8	-36.6	+3.9	+2.3
Steps (reduced)		784 (112)	807 (135)	828 (156)	848 (176)	867 (195)	884 (212)	901 (229)	916 (244)	931 (259)	945 (273)	959 (287)	972 (300)

Subsets and supersets

Since 336 factors into primes as 2⁴ × 3 × 7, 336edt contains subset edts 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, and 168.

See also

• 124edf – relative edf
• 212edo – relative edo