6ed5/3

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

← 5ed5/3

6ed5/3

7ed5/3 →

Prime factorization	2 × 3
Step size	147.393¢
Octave	8\6ed5/3 (1179.14¢) (→4\3ed5/3)
Twelfth	13\6ed5/3 (1916.11¢) (convergent)
Consistency limit	7
Distinct consistency limit	2
Special properties	Highly composite

6 equal divisions of 5/3 (abbreviated 6ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 6 equal parts of about 147 ¢ each. Each step represents a frequency ratio of (5/3)^1/6, or the 6th root of 5/3. One step of this tuning system is extremely close to 49/45, differing by a mere 0.035 cents; this is the basis of Izar temperament.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	147.4	10/9, 11/10, 12/11, 13/12, 14/13, 15/14, 17/16, 18/17, 19/18, 21/19
2	294.8	6/5, 7/6, 11/9, 13/11, 15/13, 17/14, 20/17
3	442.2	4/3, 5/4, 9/7, 13/10, 14/11, 17/13, 19/15
4	589.6	7/5, 10/7, 11/8, 13/9, 15/11, 16/11, 17/12, 18/13
5	737	3/2, 11/7, 14/9, 17/11, 20/13
6	884.4	5/3, 12/7, 13/8, 17/10, 18/11, 21/13

Harmonics

Approximation of harmonics in 6ed5/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-20.9	+14.2	-41.7	+14.2	-6.7	+21.2	-62.6	+28.3	-6.7	-24.3	-27.6
	Relative (%)	-14.1	+9.6	-28.3	+9.6	-4.5	+14.4	-42.4	+19.2	-4.5	-16.5	-18.7
Steps (reduced)		8 (2)	13 (1)	16 (4)	19 (1)	21 (3)	23 (5)	24 (0)	26 (2)	27 (3)	28 (4)	29 (5)

Approximation of harmonics in 6ed5/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.7	+0.4	+28.3	+64.0	-41.0	+7.5	+61.2	-27.6	+35.4	-45.2	+25.3
	Relative (%)	-12.7	+0.2	+19.2	+43.4	-27.8	+5.1	+41.6	-18.7	+24.0	-30.6	+17.1
Steps (reduced)		30 (0)	31 (1)	32 (2)	33 (3)	33 (3)	34 (4)	35 (5)	35 (5)	36 (0)	36 (0)	37 (1)