50ed12

← 49ed12

50ed12

51ed12 →

Prime factorization	2 × 52
Step size	86.0391 ¢
Octave	14\50ed12 (1204.55 ¢) (→ 7\25ed12)
Twelfth	22\50ed12 (1892.86 ¢) (→ 11\25ed12)
Consistency limit	7
Distinct consistency limit	5

50 equal divisions of the 12th harmonic (abbreviated 50ed12) is a nonoctave tuning system that divides the interval of 12/1 into 50 equal parts of about 86 ¢ each. Each step represents a frequency ratio of 12^1/50, or the 50th root of 12.

Interval table

Steps	Cents	Approximate ratios
0	0	1/1
1	86	20/19, 21/20, 22/21
2	172.1	21/19, 31/28, 32/29
3	258.1	22/19
4	344.2	11/9, 28/23
5	430.2	9/7
6	516.2	27/20, 31/23
7	602.3	17/12, 24/17
8	688.3
9	774.4
10	860.4	23/14, 28/17
11	946.4	19/11, 31/18
12	1032.5	20/11, 29/16
13	1118.5	21/11
14	1204.5	2/1
15	1290.6	19/9
16	1376.6	31/14
17	1462.7	7/3
18	1548.7	22/9
19	1634.7	18/7
20	1720.8	27/10
21	1806.8	17/6
22	1892.9
23	1978.9	22/7
24	2064.9	23/7
25	2151
26	2237
27	2323.1	23/6
28	2409.1
29	2495.1
30	2581.2	31/7
31	2667.2	14/3
32	2753.3
33	2839.3	31/6
34	2925.3
35	3011.4
36	3097.4	6/1
37	3183.4
38	3269.5
39	3355.5
40	3441.6
41	3527.6	23/3
42	3613.6
43	3699.7	17/2
44	3785.7
45	3871.8	28/3
46	3957.8
47	4043.8	31/3
48	4129.9
49	4215.9
50	4302	12/1

Harmonics

Approximation of harmonics in 50ed12

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.5	-9.1	+9.1	-33.1	-4.5	-13.3	+13.6	-18.2	-28.5	-21.4	+0.0
	Relative (%)	+5.3	-10.6	+10.6	-38.4	-5.3	-15.5	+15.9	-21.1	-33.1	-24.9	+0.0
Steps (reduced)		14 (14)	22 (22)	28 (28)	32 (32)	36 (36)	39 (39)	42 (42)	44 (44)	46 (46)	48 (48)	50 (0)