3ed5

← 2ed5

3ed5

4ed5 →

Prime factorization	3 (prime)
Step size	928.771¢
Octave	1\3ed5 (928.771¢) (semiconvergent)
Twelfth	2\3ed5 (1857.54¢) (convergent)
Consistency limit	3
Distinct consistency limit	2

3 equal divisions of the 5th harmonic (abbreviated 3ed5) is a nonoctave tuning system that divides the interval of 5/1 into 3 equal parts of about 929 ¢ each. Each step represents a frequency ratio of 5^1/3, or the 3rd root of 5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1, 14/13, 15/14, 18/17, 19/18, 20/19
1	928.771	5/3, 9/5, 11/6, 17/10, 18/11, 19/11, 19/12, 20/11
2	1857.542	3/1, 11/4, 14/5, 17/6
3	2786.314	5/1, 14/3, 19/4

Harmonics

Approximation of harmonics in 3ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-271	-44	+386	+0	-316	+346	+115	-89	-271	-436	+342
	Relative (%)	-29.2	-4.8	+41.6	+0.0	-34.0	+37.3	+12.4	-9.6	-29.2	-47.0	+36.8
Steps (reduced)		1 (1)	2 (2)	3 (0)	3 (0)	3 (0)	4 (1)	4 (1)	4 (1)	4 (1)	4 (1)	5 (2)

Approximation of harmonics in 3ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+203	+75	-44	-156	-261	-360	-454	+386	+302	+221	+144
	Relative (%)	+21.9	+8.1	-4.8	-16.8	-28.1	-38.8	-48.8	+41.6	+32.5	+23.8	+15.5
Steps (reduced)		5 (2)	5 (2)	5 (2)	5 (2)	5 (2)	5 (2)	5 (2)	6 (0)	6 (0)	6 (0)	6 (0)