18ed7/4

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 17ed7/4

18ed7/4

19ed7/4 →

Prime factorization	2 × 32
Step size	53.8237¢
Octave	22\18ed7/4 (1184.12¢) (→11\9ed7/4)
Twelfth	35\18ed7/4 (1883.83¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	3

18 equal divisions of 7/4 (abbreviated 18ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 18 equal parts of about 53.8 ¢ each. Each step represents a frequency ratio of (7/4)^1/18, or the 18th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	53.824
2	107.647	15/14
3	161.471	11/10, 21/19, 23/21
4	215.295	9/8, 17/15
5	269.118	20/17
6	322.942	17/14, 23/19
7	376.766	21/17
8	430.589	14/11, 22/17
9	484.413	4/3
10	538.237	15/11, 19/14, 23/17
11	592.06	7/5
12	645.884	19/13, 22/15
13	699.708	3/2
14	753.531	17/11, 23/15
15	807.355
16	861.179	23/14
17	915.002	17/10
18	968.826

Harmonics

Approximation of harmonics in 18ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-15.9	-18.1	+22.1	+12.5	+19.8	+22.1	+6.2	+17.6	-3.4	-6.9	+3.9
	Relative (%)	-29.5	-33.7	+41.0	+23.3	+36.8	+41.0	+11.5	+32.6	-6.2	-12.8	+7.3
Steps (reduced)		22 (4)	35 (17)	45 (9)	52 (16)	58 (4)	63 (9)	67 (13)	71 (17)	74 (2)	77 (5)	80 (8)

Approximation of harmonics in 18ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+26.8	+6.2	-5.6	-9.7	-7.0	+1.7	+15.7	-19.2	+3.9	-22.8	+7.9
	Relative (%)	+49.9	+11.5	-10.4	-18.0	-13.0	+3.1	+29.2	-35.8	+7.3	-42.3	+14.7
Steps (reduced)		83 (11)	85 (13)	87 (15)	89 (17)	91 (1)	93 (3)	95 (5)	96 (6)	98 (8)	99 (9)	101 (11)