5ed5

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5ed5

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Prime factorization	5 (prime)
Step size	557.263 ¢
Octave	2\5ed5 (1114.53 ¢) (semiconvergent)
Twelfth	3\5ed5 (1671.79 ¢)
Consistency limit	5
Distinct consistency limit	3

5 equal divisions of the 5th harmonic (abbreviated 5ed5) is a nonoctave tuning system that divides the interval of 5/1 into 5 equal parts of about 557 ¢ each. Each step represents a frequency ratio of 5^1/5, or the 5th root of 5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	557.3	4/3, 7/5, 10/7, 11/8, 15/11, 19/14
2	1114.5	11/6, 13/7, 15/8, 19/10, 21/11
3	1671.8	8/3, 13/5, 19/7, 21/8
4	2229.1	7/2, 11/3, 15/4
5	2786.3	5/1

Harmonics

Approximation of harmonics in 5ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-85	-230	-171	+0	+242	-25	-256	+97	-85	-250	+156
	Relative (%)	-15.3	-41.3	-30.7	+0.0	+43.4	-4.5	-46.0	+17.4	-15.3	-44.9	+28.0
Steps (reduced)		2 (2)	3 (3)	4 (4)	5 (0)	6 (1)	6 (1)	6 (1)	7 (2)	7 (2)	7 (2)	8 (3)

Approximation of harmonics in 5ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+18	-111	-230	+215	+110	+11	-82	-171	-255	+221	+144
	Relative (%)	+3.2	-19.9	-41.3	+38.6	+19.8	+2.1	-14.7	-30.7	-45.8	+39.7	+25.9
Steps (reduced)		8 (3)	8 (3)	8 (3)	9 (4)	9 (4)	9 (4)	9 (4)	9 (4)	9 (4)	10 (0)	10 (0)