17ed5/3

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← 16ed5/317ed5/318ed5/3 →
Prime factorization 17 (prime)
Step size 52.0211¢ 
Octave 23\17ed5/3 (1196.49¢)
(semiconvergent)
Twelfth 37\17ed5/3 (1924.78¢)
Consistency limit 2
Distinct consistency limit 2

17 equal divisions of 5/3 (abbreviated 17ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 17 equal parts of about 52 ¢ each. Each step represents a frequency ratio of (5/3)1/17, or the 17th root of 5/3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 52.021
2 104.042 17/16, 20/19
3 156.063 11/10, 12/11
4 208.084 19/17
5 260.106 7/6, 22/19
6 312.127 6/5, 19/16, 23/19
7 364.148 16/13
8 416.169 14/11, 24/19
9 468.19 17/13
10 520.211 19/14, 23/17
11 572.232 7/5
12 624.253 10/7, 23/16
13 676.274
14 728.295
15 780.317 11/7, 19/12
16 832.338 13/8
17 884.359 5/3

Harmonics

Approximation of harmonics in 17ed5/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.5 +22.8 -7.0 +22.8 +19.3 +12.5 -10.5 -6.4 +19.3 +10.4 +15.8
Relative (%) -6.8 +43.9 -13.5 +43.9 +37.1 +24.1 -20.3 -12.2 +37.1 +19.9 +30.4
Steps
(reduced)
23
(6)
37
(3)
46
(12)
54
(3)
60
(9)
65
(14)
69
(1)
73
(5)
77
(9)
80
(12)
83
(15)
Approximation of harmonics in 17ed5/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -18.7 +9.0 -6.4 -14.1 -15.0 -9.9 +0.6 +15.8 -16.6 +6.9 -18.1
Relative (%) -36.0 +17.4 -12.2 -27.0 -28.8 -19.0 +1.1 +30.4 -32.0 +13.2 -34.8
Steps
(reduced)
85
(0)
88
(3)
90
(5)
92
(7)
94
(9)
96
(11)
98
(13)
100
(15)
101
(16)
103
(1)
104
(2)