14edt

← 13edt

14edt

15edt →

Prime factorization	2 × 7
Step size	135.854 ¢
Octave	9\14edt (1222.69 ¢)
Consistency limit	7
Distinct consistency limit	6

14 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 14edt or 14ed3), is a nonoctave tuning system that divides the interval of 3/1 into 14 equal parts of about 136 ¢ each. Each step represents a frequency ratio of 3^1/14, or the 14th root of 3.

Theory

14edt is the simplest edt with a distinct form for each rotation of the antilambda scale. It can be seen as 9edo with significantly stretched octaves (~23 ¢) and may be used as a tuning for Pelog.

Harmonics

Approximation of harmonics in 14edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+22.7	+0.0	+45.4	+66.6	+22.7	+27.5	-67.8	+0.0	-46.5	+60.2	+45.4
	Relative (%)	+16.7	+0.0	+33.4	+49.0	+16.7	+20.3	-49.9	+0.0	-34.3	+44.3	+33.4
Steps (reduced)		9 (9)	14 (0)	18 (4)	21 (7)	23 (9)	25 (11)	26 (12)	28 (0)	29 (1)	31 (3)	32 (4)

Approximation of harmonics in 14edt (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+42.7	+50.2	+66.6	-45.1	-14.2	+22.7	+64.9	-23.9	+27.5	-53.0	+5.9	-67.8
	Relative (%)	+31.4	+37.0	+49.0	-33.2	-10.5	+16.7	+47.8	-17.6	+20.3	-39.0	+4.3	-49.9
Steps (reduced)		33 (5)	34 (6)	35 (7)	35 (7)	36 (8)	37 (9)	38 (10)	38 (10)	39 (11)	39 (11)	40 (12)	40 (12)

Subsets and supersets

Since 14 factors into primes as 2 × 7, 14edt has subset edts 2edt and 7edt.

Intervals

#	Cents	Hekts	Notation[clarification needed]
1	136	93	Cp/D\\
2	272	186	D
3	408	279	E
4	543	371	Ep/F\\
5	679	464	F
6	815	557	G
7	951	650	Gp/H\\
8	1087	743	H
9	1223	836	J
10	1359	929	Jp/A\\
11	1494	1021	A
12	1630	1114	Ap/B\\
13	1766	1207	B
14	1902	1300	C

See also

• 9edo – relative edo
• 23ed6 – relative ed6
• 32ed12 – relative ed12

Todo: expand