16ed9/5

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16ed9/5

17ed9/5 →

Prime factorization	24
Step size	63.5998¢
Octave	19\16ed9/5 (1208.4¢)
Twelfth	30\16ed9/5 (1907.99¢) (→15\8ed9/5)
Consistency limit	10
Distinct consistency limit	3

16 equal divisions of 9/5 (abbreviated 16ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 16 equal parts of about 63.6 ¢ each. Each step represents a frequency ratio of (9/5)^1/16, or the 16th root of 9/5.

16ed9/5 represents the lower bound of the phoenix tuning range. 16ed9/5 benefits from all the desirable properties of phoenix tuning systems.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	63.6	22/21, 23/22
2	127.2	13/12, 14/13, 15/14, 16/15
3	190.799	9/8, 10/9, 19/17, 21/19
4	254.399	7/6, 15/13, 22/19
5	317.999	6/5, 17/14, 23/19
6	381.599	5/4, 21/17
7	445.198	9/7, 13/10, 17/13, 22/17
8	508.798	4/3, 19/14, 23/17
9	572.398	7/5, 18/13
10	635.998	10/7, 13/9
11	699.597	3/2
12	763.197	11/7, 14/9, 17/11, 20/13
13	826.797	8/5, 13/8, 21/13
14	890.397	5/3, 22/13
15	953.997	7/4, 19/11
16	1017.596	9/5

Harmonics

Approximation of harmonics in 16ed9/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.4	+6.0	+16.8	+12.1	+14.4	+2.0	+25.2	+12.1	+20.5	-17.3	+22.8
	Relative (%)	+13.2	+9.5	+26.4	+19.0	+22.7	+3.1	+39.6	+19.0	+32.2	-27.3	+35.9
Steps (reduced)		19 (3)	30 (14)	38 (6)	44 (12)	49 (1)	53 (5)	57 (9)	60 (12)	63 (15)	65 (1)	68 (4)

Approximation of harmonics in 16ed9/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+11.5	+10.4	+18.1	-30.0	-7.8	+20.5	-9.5	+28.9	+8.0	-8.9	-22.3
	Relative (%)	+18.0	+16.3	+28.5	-47.2	-12.2	+32.2	-15.0	+45.4	+12.6	-14.1	-35.1
Steps (reduced)		70 (6)	72 (8)	74 (10)	75 (11)	77 (13)	79 (15)	80 (0)	82 (2)	83 (3)	84 (4)	85 (5)