17ed11/5

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← 16ed11/517ed11/518ed11/5 →
Prime factorization 17 (prime)
Step size 80.2944¢ 
Octave 15\17ed11/5 (1204.42¢)
(semiconvergent)
Twelfth 24\17ed11/5 (1927.06¢)
Consistency limit 8
Distinct consistency limit 4

17 equal divisions of 11/5 (abbreviated 17ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 17 equal parts of about 80.3 ¢ each. Each step represents a frequency ratio of (11/5)1/17, or the 17th root of 11/5.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 80.294 21/20, 22/21, 23/22, 24/23
2 160.589 11/10, 12/11, 23/21
3 240.883 8/7, 23/20
4 321.177 6/5, 17/14
5 401.472 5/4, 14/11
6 481.766 4/3, 17/13, 21/16
7 562.061 11/8
8 642.355 16/11, 19/13, 23/16
9 722.649 23/15
10 802.944 8/5
11 883.238 5/3
12 963.532 7/4
13 1043.827 11/6, 20/11
14 1124.121 21/11, 23/12
15 1204.415 2/1
16 1284.71 21/10, 23/11
17 1365.004 11/5, 20/9, 24/11

Harmonics

Approximation of harmonics in 17ed11/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.4 +25.1 +8.8 +24.0 +29.5 +3.5 +13.2 -30.1 +28.4 +24.0 +33.9
Relative (%) +5.5 +31.3 +11.0 +29.9 +36.8 +4.4 +16.5 -37.5 +35.4 +29.9 +42.3
Steps
(reduced)
15
(15)
24
(7)
30
(13)
35
(1)
39
(5)
42
(8)
45
(11)
47
(13)
50
(16)
52
(1)
54
(3)
Approximation of harmonics in 17ed11/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -24.3 +8.0 -31.2 +17.7 -7.0 -25.7 -39.0 +32.8 +28.6 +28.4 +31.7
Relative (%) -30.3 +9.9 -38.9 +22.0 -8.7 -32.0 -48.5 +40.9 +35.7 +35.4 +39.5
Steps
(reduced)
55
(4)
57
(6)
58
(7)
60
(9)
61
(10)
62
(11)
63
(12)
65
(14)
66
(15)
67
(16)
68
(0)