18ed6

← 17ed6

18ed6

19ed6 →

Prime factorization	2 × 32
Step size	172.331 ¢
Octave	7\18ed6 (1206.32 ¢) (semiconvergent)
Twelfth	11\18ed6 (1895.64 ¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	5

18 equal divisions of the 6th harmonic (abbreviated 18ed6) is a nonoctave tuning system that divides the interval of 6/1 into 18 equal parts of about 172 ¢ each. Each step represents a frequency ratio of 6^1/18, or the 18th root of 6.

18ed6 is close to 7edo, but with the 7/1 rather than the 2/1 being just, which stretches octaves by about 6.32 cents.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	172.3	10/9, 11/10, 21/19
2	344.7	11/9, 16/13
3	517	19/14, 23/17
4	689.3	3/2
5	861.7	18/11
6	1034	9/5, 11/6, 20/11
7	1206.3	2/1
8	1378.6	11/5, 20/9
9	1551	22/9
10	1723.3	19/7
11	1895.6	3/1
12	2068	10/3
13	2240.3	11/3
14	2412.6	4/1
15	2585
16	2757.3
17	2929.6
18	3102	6/1

Harmonics

Approximation of harmonics in 18ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.3	-6.3	+12.6	-29.0	+0.0	+77.8	+18.9	-12.6	-22.7	-15.4	+6.3
	Relative (%)	+3.7	-3.7	+7.3	-16.8	+0.0	+45.1	+11.0	-7.3	-13.2	-8.9	+3.7
Steps (reduced)		7 (7)	11 (11)	14 (14)	16 (16)	18 (0)	20 (2)	21 (3)	22 (4)	23 (5)	24 (6)	25 (7)

Approximation of harmonics in 18ed6

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+40.1	+84.1	-35.3	+25.3	-79.7	-6.3	+72.4	-16.4	+71.5	-9.1	-86.0
	Relative (%)	+23.3	+48.8	-20.5	+14.7	-46.2	-3.7	+42.0	-9.5	+41.5	-5.3	-49.9
Steps (reduced)		26 (8)	27 (9)	27 (9)	28 (10)	28 (10)	29 (11)	30 (12)	30 (12)	31 (13)	31 (13)	31 (13)

See also

• 7edo – relative EDO
• 11edt – relative ED3