25ed7/4

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

← 24ed7/4

25ed7/4

26ed7/4 →

Prime factorization	52
Step size	38.753¢
Octave	31\25ed7/4 (1201.34¢) (semiconvergent)
Twelfth	49\25ed7/4 (1898.9¢) (semiconvergent)
Consistency limit	12
Distinct consistency limit	3

25 equal divisions of 7/4 (abbreviated 25ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 25 equal parts of about 38.8 ¢ each. Each step represents a frequency ratio of (7/4)^1/25, or the 25th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	38.753
2	77.506	20/19, 21/20, 22/21, 23/22, 24/23, 25/24, 26/25
3	116.259	14/13, 15/14, 16/15, 17/16
4	155.012	11/10, 12/11, 23/21, 25/23
5	193.765	9/8, 10/9, 19/17
6	232.518	8/7, 23/20, 25/22
7	271.271	7/6, 20/17
8	310.024	6/5, 25/21
9	348.777	11/9, 16/13
10	387.53	5/4
11	426.283	9/7, 14/11, 23/18
12	465.036	13/10, 17/13, 21/16, 25/19
13	503.789	4/3
14	542.543	11/8, 15/11, 26/19
15	581.296	7/5
16	620.049	10/7, 23/16
17	658.802	16/11, 19/13, 22/15, 25/17
18	697.555	3/2
19	736.308	20/13, 23/15, 26/17
20	775.061	11/7, 14/9, 25/16
21	813.814	8/5
22	852.567	13/8, 18/11, 23/14
23	891.32	5/3
24	930.073	12/7, 17/10
25	968.826	7/4

Harmonics

Approximation of harmonics in 25ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.3	-3.1	+2.7	+3.9	-1.7	+2.7	+4.0	-6.1	+5.2	-4.7	-0.4
	Relative (%)	+3.5	-7.9	+6.9	+10.1	-4.4	+6.9	+10.4	-15.8	+13.5	-12.2	-0.9
Steps (reduced)		31 (6)	49 (24)	62 (12)	72 (22)	80 (5)	87 (12)	93 (18)	98 (23)	103 (3)	107 (7)	111 (11)

Approximation of harmonics in 25ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.1	+4.0	+0.8	+5.4	+16.7	-4.8	+17.9	+6.6	-0.4	-3.4	-2.8
	Relative (%)	+41.5	+10.4	+2.2	+13.9	+43.0	-12.3	+46.2	+17.0	-0.9	-8.8	-7.4
Steps (reduced)		115 (15)	118 (18)	121 (21)	124 (24)	127 (2)	129 (4)	132 (7)	134 (9)	136 (11)	138 (13)	140 (15)