62ed6

← 61ed6

62ed6

63ed6 →

Prime factorization	2 × 31
Step size	50.0315 ¢
Octave	24\62ed6 (1200.76 ¢) (→ 12\31ed6)
Twelfth	38\62ed6 (1901.2 ¢) (→ 19\31ed6)
Consistency limit	6
Distinct consistency limit	6

62 equal divisions of the 6th harmonic (abbreviated 62ed6) is a nonoctave tuning system that divides the interval of 6/1 into 62 equal parts of about 50 ¢ each. Each step represents a frequency ratio of 6^1/62, or the 62nd root of 6.

Theory

62ed6 is nearly identical to 24edo (quarter-tone tuning), but with the 6th harmonic rather than the octave being just, which stretches the octave by about 0.757 cents. Like 24edo, 62ed6 is consistent to the 6-integer-limit.

Harmonics

Approximation of harmonics in 62ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.8	-0.8	+1.5	+15.5	+0.0	-16.7	+2.3	-1.5	+16.2	+1.3	+0.8
	Relative (%)	+1.5	-1.5	+3.0	+30.9	+0.0	-33.4	+4.5	-3.0	+32.4	+2.6	+1.5
Steps (reduced)		24 (24)	38 (38)	48 (48)	56 (56)	62 (0)	67 (5)	72 (10)	76 (14)	80 (18)	83 (21)	86 (24)

Approximation of harmonics in 62ed6 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+12.3	-16.0	+14.7	+3.0	-1.9	-0.8	+5.7	+17.0	-17.5	+2.1	-24.9	+1.5
	Relative (%)	+24.5	-31.9	+29.4	+6.1	-3.7	-1.5	+11.4	+33.9	-34.9	+4.1	-49.7	+3.0
Steps (reduced)		89 (27)	91 (29)	94 (32)	96 (34)	98 (36)	100 (38)	102 (40)	104 (42)	105 (43)	107 (45)	108 (46)	110 (48)

Subsets and supersets

Since 62 factors into primes as 2 × 31, 62ed6 contains subset ed6's 2ed6 and 31ed6.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	50	33/32, 34/33, 35/34
2	100.1	18/17, 35/33
3	150.1	12/11
4	200.1	9/8
5	250.2	15/13, 22/19
6	300.2	19/16, 31/26
7	350.2	11/9, 27/22
8	400.3	24/19, 34/27
9	450.3	13/10, 22/17, 35/27
10	500.3	4/3
11	550.3	11/8
12	600.4	17/12, 24/17
13	650.4	16/11, 35/24
14	700.4	3/2
15	750.5	17/11
16	800.5	27/17, 35/22
17	850.5	18/11, 31/19
18	900.6	32/19
19	950.6	26/15
20	1000.6
21	1050.7	11/6
22	1100.7	17/9
23	1150.7	33/17, 35/18
24	1200.8	2/1
25	1250.8	33/16, 35/17
26	1300.8	17/8
27	1350.9	24/11, 35/16
28	1400.9	9/4
29	1450.9	30/13
30	1500.9	19/8, 31/13
31	1551	22/9, 27/11
32	1601
33	1651	13/5
34	1701.1	8/3
35	1751.1	11/4
36	1801.1	17/6
37	1851.2	32/11, 35/12
38	1901.2	3/1
39	1951.2	34/11
40	2001.3	35/11
41	2051.3
42	2101.3
43	2151.4
44	2201.4
45	2251.4	11/3
46	2301.5	34/9
47	2351.5	35/9
48	2401.5	4/1
49	2451.5	33/8
50	2501.6	17/4
51	2551.6	35/8
52	2601.6	9/2
53	2651.7
54	2701.7	19/4
55	2751.7
56	2801.8
57	2851.8	26/5
58	2901.8	16/3
59	2951.9	11/2
60	3001.9	17/3
61	3051.9	35/6
62	3102	6/1

See also

• 14edf – relative edf
• 24edo – relative edo
• 38edt – relative edt
• 56ed5 – relative ed5
• 86ed12 – relative ed12
• 198ed304 – close to the zeta-optimized tuning for 24edo