12ed5

← 11ed5

12ed5

13ed5 →

Prime factorization	22 × 3 (highly composite)
Step size	232.193 ¢
Octave	5\12ed5 (1160.96 ¢)
Twelfth	8\12ed5 (1857.54 ¢) (→ 2\3ed5)
Consistency limit	6
Distinct consistency limit	4

Division of the 5th harmonic into 12 equal parts (12ed5) is related to the mothra temperament and the quadrawell temperament. The step size about 232.1928 cents, corresponding to 5.1681 edo, very nearly every 6th step of 31edo. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	232.1928	8/7
2	464.3856	17/13
3	696.5784		meantone fifth (pseudo-3/2)
4	928.7712	65/38
5	1160.9640	45/23
6	1393.1569	38/17, 85/38	meantone major second plus an octave
7	1625.3497	23/9
8	1857.5425	38/13
9	2089.7353		meantone major sixth plus an octave (pseudo-10/3)
10	2321.9281	65/17
11	2554.1209	35/8
12	2786.3137	exact 5/1	just major third plus two octaves

Harmonics

Approximation of harmonics in 12ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-39	-44	-78	+0	-83	+114	+115	-89	-39	+28	+110
	Relative (%)	-16.8	-19.1	-33.6	+0.0	-35.9	+49.1	+49.6	-38.3	-16.8	+12.1	+47.2
Steps (reduced)		5 (5)	8 (8)	10 (10)	12 (0)	13 (1)	15 (3)	16 (4)	16 (4)	17 (5)	18 (6)	19 (7)

Approximation of harmonics in 12ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-29	+75	-44	+76	-29	+104	+11	-78	+70	-11	-88
	Relative (%)	-12.4	+32.3	-19.1	+32.8	-12.4	+44.9	+4.6	-33.6	+30.0	-4.7	-37.8
Steps (reduced)		19 (7)	20 (8)	20 (8)	21 (9)	21 (9)	22 (10)	22 (10)	22 (10)	23 (11)	23 (11)	23 (11)