25ed7/3

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25ed7/3

26ed7/3 →

Prime factorization	52
Step size	58.6748¢
Octave	20\25ed7/3 (1173.5¢) (→4\5ed7/3)
Twelfth	32\25ed7/3 (1877.59¢)
Consistency limit	3
Distinct consistency limit	3

25 equal divisions of 7/3 (abbreviated 25ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 25 equal parts of about 58.7 ¢ each. Each step represents a frequency ratio of (7/3)^1/25, or the 25th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	58.675
2	117.35	15/14
3	176.025	10/9
4	234.699
5	293.374	13/11, 25/21
6	352.049
7	410.724
8	469.399	17/13
9	528.074	23/17
10	586.748	7/5
11	645.423	19/13
12	704.098	3/2
13	762.773	14/9, 17/11
14	821.448
15	880.123	5/3
16	938.797	19/11
17	997.472	23/13, 25/14
18	1056.147
19	1114.822
20	1173.497
21	1232.172
22	1290.846	21/10
23	1349.521
24	1408.196	9/4
25	1466.871	7/3

Harmonics

Approximation of harmonics in 25ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-26.5	-24.4	+5.7	-28.6	+7.8	-24.4	-20.8	+10.0	+3.6	+14.6	-18.7
	Relative (%)	-45.2	-41.5	+9.7	-48.7	+13.3	-41.5	-35.5	+17.0	+6.1	+24.9	-31.9
Steps (reduced)		20 (20)	32 (7)	41 (16)	47 (22)	53 (3)	57 (7)	61 (11)	65 (15)	68 (18)	71 (21)	73 (23)

Approximation of harmonics in 25ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+18.8	+7.8	+5.7	+11.3	+23.7	-16.5	+7.2	-22.9	+10.0	-11.9	+28.5
	Relative (%)	+32.0	+13.3	+9.7	+19.3	+40.4	-28.2	+12.3	-39.1	+17.0	-20.3	+48.5
Steps (reduced)		76 (1)	78 (3)	80 (5)	82 (7)	84 (9)	85 (10)	87 (12)	88 (13)	90 (15)	91 (16)	93 (18)