16ed5

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16ed5

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Prime factorization	24
Step size	174.145¢
Octave	7\16ed5 (1219.01¢) (semiconvergent)
Twelfth	11\16ed5 (1915.59¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	4

16 equal divisions of the 5th harmonic (abbreviated 16ed5) is a nonoctave tuning system that divides the interval of 5/1 into 16 equal parts of about 174 ¢ each. Each step represents a frequency ratio of 5^1/16, or the 16th root of 5.

16ed5 is a strong no-2s, no-13s, no-29s 41-limit tuning. Alternatively, it could include 2s, but the equave might need to be compressed to make the 2/1 and 4/1 more in tune.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	174.145	10/9, 11/10, 19/17, 21/19, 23/21
2	348.289	11/9, 17/14, 21/17, 23/19
3	522.434	15/11, 19/14, 23/17
4	696.578	3/2
5	870.723	5/3, 18/11, 23/14
6	1044.868	11/6, 20/11
7	1219.012	2/1
8	1393.157	9/4, 20/9
9	1567.301	5/2, 22/9
10	1741.446	11/4, 19/7
11	1915.591	3/1
12	2089.735	10/3
13	2263.88	11/3
14	2438.024
15	2612.169	9/2
16	2786.314	5/1

Harmonics

Approximation of prime harmonics in 16ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+19.0	+13.6	+0.0	-60.1	+28.2	-86.9	-28.9	-47.3	-29.8	-82.8	-24.1
	Relative (%)	+10.9	+7.8	+0.0	-34.5	+16.2	-49.9	-16.6	-27.2	-17.1	-47.5	-13.8
Steps (reduced)		7 (7)	11 (11)	16 (0)	19 (3)	24 (8)	25 (9)	28 (12)	29 (13)	31 (15)	33 (1)	34 (2)

Approximation of prime harmonics in 16ed5

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+17.9	+14.3	-68.2	-48.0	-81.9	+80.8	+23.0	+34.8	-65.6	+60.4	-76.3
	Relative (%)	+10.3	+8.2	-39.1	-27.6	-47.0	+46.4	+13.2	+20.0	-37.7	+34.7	-43.8
Steps (reduced)		36 (4)	37 (5)	37 (5)	38 (6)	39 (7)	41 (9)	41 (9)	42 (10)	42 (10)	43 (11)	43 (11)