18ed5/4

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18ed5/4

19ed5/4 →

Prime factorization	2 × 32
Step size	21.4619¢
Octave	56\18ed5/4 (1201.86¢) (→28\9ed5/4)
Twelfth	89\18ed5/4 (1910.11¢)
Consistency limit	8
Distinct consistency limit	4

18 equal divisions of 5/4 (abbreviated 18ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 18 equal parts of about 21.5 ¢ each. Each step represents a frequency ratio of (5/4)^1/18, or the 18th root of 5/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	21.462
2	42.924
3	64.386	22/21
4	85.847	19/18, 20/19, 21/20, 23/22, 24/23
5	107.309	16/15, 17/16, 18/17
6	128.771	13/12, 14/13, 15/14
7	150.233	11/10, 23/21
8	171.695	10/9, 21/19
9	193.157	19/17
10	214.619	9/8, 17/15
11	236.081	8/7, 22/19, 23/20
12	257.542	7/6, 15/13
13	279.004	20/17
14	300.466	13/11, 19/16
15	321.928	6/5, 23/19
16	343.39	17/14
17	364.852	16/13, 21/17
18	386.314	5/4

Harmonics

Approximation of harmonics in 18ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.86	+8.15	+3.73	+3.73	+10.02	+0.69	+5.59	-5.16	+5.59	-9.18	-9.58
	Relative (%)	+8.7	+38.0	+17.4	+17.4	+46.7	+3.2	+26.1	-24.0	+26.1	-42.8	-44.6
Steps (reduced)		56 (2)	89 (17)	112 (4)	130 (4)	145 (1)	157 (13)	168 (6)	177 (15)	186 (6)	193 (13)	200 (2)

Approximation of harmonics in 18ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	+2.55	-9.58	+7.46	+9.81	-3.29	+10.41	+7.46	+8.84	-7.31	+1.58
	Relative (%)	+9.7	+11.9	-44.6	+34.8	+45.7	-15.3	+48.5	+34.8	+41.2	-34.1	+7.4
Steps (reduced)		207 (9)	213 (15)	218 (2)	224 (8)	229 (13)	233 (17)	238 (4)	242 (8)	246 (12)	249 (15)	253 (1)