2ed5

2 equal divisions of the 5th harmonic (abbreviated 2ed5) is a nonoctave tuning system that divides the interval of 5/1 into 2 equal parts of about 1390 ¢ each. Each step represents a frequency ratio of 5^1/2, or the square root of 5.

← 1ed5

2ed5

3ed5 →

Prime factorization	2 (prime) (highly composite)
Step size	1393.16 ¢
Octave	1\2ed5 (1393.16 ¢) (convergent)
Twelfth	1\2ed5 (1393.16 ¢) (semiconvergent)
Consistency limit	2
Distinct consistency limit	2

Theory

Odd harmonics

Approximation of harmonics in 2ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+193	-509	+386	+0	-316	-583	+579	+376	+193	+28	-122
	Relative (%)	+13.9	-36.5	+27.7	+0.0	-22.7	-41.8	+41.6	+27.0	+13.9	+2.0	-8.8
Steps (reduced)		1 (1)	1 (1)	2 (0)	2 (0)	2 (0)	2 (0)	3 (1)	3 (1)	3 (1)	3 (1)	3 (1)

Interval table

Steps	Cents	Approximate Ratios
0	0	1/1
1	1393.157	9/4
2	2786.314	5/1