User:MisterShafXen/7ed13

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7ed13

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Prime factorization	7 (prime)
Step size	634.361 ¢
Octave	2\7ed13 (1268.72 ¢) (semiconvergent)
Twelfth	3\7ed13 (1903.08 ¢) (convergent)
Consistency limit	4
Distinct consistency limit	3

7 equal divisions of the 13th harmonic (abbreviated 7ed13) is a nonoctave tuning system that divides the interval of 13/1 into 7 equal parts of about 634 ¢ each. Each step represents a frequency ratio of 13^1/7, or the 7th root of 13.

Intervals

Steps	Cents	Approximate ratios	Ups and downs notation
0	0	1/1	D
1	100	15/14, 16/15, 17/16, 18/17, 19/18, 20/19, 21/20, 22/21	D♯, E♭
2	200	9/8, 10/9, 17/15, 19/17, 21/19	E
3	300	6/5, 19/16, 20/17	F
4	400	5/4, 14/11, 19/15, 23/18	F♯, G♭
5	500	4/3, 23/17	G
6	600	7/5, 10/7, 17/12, 23/16	G♯, A♭
7	700	3/2	A
8	800	8/5, 11/7, 19/12	A♯, B♭
9	900	5/3, 17/10	B
10	1000	9/5, 16/9, 23/13	C
11	1100	15/8, 17/9, 19/10, 21/11, 23/12	C♯, D♭
12	1200	2/1	D

Harmonics

Approximation of harmonics in 7ed13

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+69	+1	+137	-249	+70	-197	+206	+2	-180	+289	+139
	Relative (%)	+10.8	+0.2	+21.7	-39.2	+11.0	-31.1	+32.5	+0.4	-28.4	+45.6	+21.8
Steps (reduced)		2 (2)	3 (3)	4 (4)	4 (4)	5 (5)	5 (5)	6 (6)	6 (6)	6 (6)	7 (0)	7 (0)

Approximation of harmonics in 7ed13

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0	-128	-248	+275	+170	+71	-23	-111	-196	-276	+281
	Relative (%)	+0.0	-20.2	-39.1	+43.3	+26.8	+11.2	-3.6	-17.6	-30.9	-43.6	+44.3
Steps (reduced)		7 (0)	7 (0)	7 (0)	8 (1)	8 (1)	8 (1)	8 (1)	8 (1)	8 (1)	8 (1)	9 (2)