39ed9

← 37ed9

39ed9

41ed9 →

Prime factorization	3 × 13
Step size	97.5362¢
Octave	12\39ed9 (1170.43¢) (→4\13ed9)
Twelfth	20\39ed9 (1950.72¢)
Consistency limit	2
Distinct consistency limit	2

Similar to 97.5cET, 39ed9 divides the double tritave, 9/1, into 39 equal steps of approximately 97.5362c. It stands out as a 9.4/3.5/3.7/3.11/3.13/3 subgroup (and equivalently 9.12.15.21.33.39 subgroup) tuning as of the 2*39 subgroups that came down from the 39edt. This is a third-basis subgroup.⁠ ⁠^{[idiosyncratic term ]}

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	97.5
2	195.1	19/17, 29/26
3	292.6	13/11
4	390.1
5	487.7
6	585.2	7/5
7	682.8
8	780.3	11/7
9	877.8	5/3
10	975.4
11	1072.9	13/7
12	1170.4
13	1268	29/14
14	1365.5	11/5
15	1463	7/3
16	1560.6
17	1658.1	13/5
18	1755.7
19	1853.2
20	1950.7
21	2048.3
22	2145.8
23	2243.3	11/3
24	2340.9
25	2438.4
26	2535.9	13/3
27	2633.5
28	2731	29/6
29	2828.5
30	2926.1
31	3023.6
32	3121.2
33	3218.7
34	3316.2
35	3413.8
36	3511.3
37	3608.8
38	3706.4	17/2
39	3803.9

Harmonics

Approximation of harmonics in 39ed9

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-29.6	+48.8	+38.4	+42.2	+19.2	+44.9	+8.8	+0.0	+12.7	+42.7	-10.4
	Relative (%)	-30.3	+50.0	+39.4	+43.3	+19.7	+46.1	+9.1	+0.0	+13.0	+43.8	-10.6
Steps (reduced)		12 (12)	20 (20)	25 (25)	29 (29)	32 (32)	35 (35)	37 (37)	39 (0)	41 (2)	43 (4)	44 (5)

Approximation of harmonics in 39ed9

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+46.1	+15.4	-6.5	-20.7	-28.1	-29.6	-25.6	-16.9	-3.8	+13.2	+33.8
	Relative (%)	+47.3	+15.8	-6.7	-21.3	-28.9	-30.3	-26.3	-17.3	-3.9	+13.5	+34.6
Steps (reduced)		46 (7)	47 (8)	48 (9)	49 (10)	50 (11)	51 (12)	52 (13)	53 (14)	54 (15)	55 (16)	56 (17)

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