1 equal division of 17/16 (abbreviated 1ed17/16) is a nonoctave tuning system that uses equal steps of 17/16, or about 105 ¢.
| Prime factorization
|
n/a
|
| Step size
|
104.955 ¢
|
| Octave
|
11\1ed17/16 (1154.51 ¢)
|
| Twelfth
|
18\1ed17/16 (1889.2 ¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
Harmonics
Approximation of harmonics in 1ed17/16
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Error
|
Absolute (¢)
|
-45.5
|
-12.8
|
+14.0
|
+47.5
|
+46.7
|
-10.3
|
-31.5
|
-25.5
|
+2.0
|
+46.9
|
+1.2
|
| Relative (%)
|
-43.3
|
-12.2
|
+13.3
|
+45.2
|
+44.5
|
-9.8
|
-30.0
|
-24.3
|
+1.9
|
+44.7
|
+1.2
|
| Step
|
11
|
18
|
23
|
27
|
30
|
32
|
34
|
36
|
38
|
40
|
41
|
Approximation of harmonics in 1ed17/16 (continued)
| Harmonic
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
| Error
|
Absolute (¢)
|
-32.4
|
+49.2
|
+34.7
|
+27.9
|
+27.9
|
+33.9
|
+45.3
|
-43.5
|
-23.0
|
+1.4
|
+29.4
|
| Relative (%)
|
-30.9
|
+46.9
|
+33.1
|
+26.6
|
+26.6
|
+32.3
|
+43.2
|
-41.4
|
-21.9
|
+1.3
|
+28.0
|
| Step
|
42
|
44
|
45
|
46
|
47
|
48
|
49
|
49
|
50
|
51
|
52
|
Note that this tuning is fairly close to 18edt, although by patent val mapping 18edt maps ~17/16 inconsistently to 2\18edt instead of 1\18edt, while 1ed17/16 maps its own equave even more inconsistently, to 3\1ed17/16.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0.0
|
1/1
|
| 1
|
105.0
|
16/15, 17/16, 18/17
|
| 2
|
209.9
|
9/8, 26/23, 17/15
|
| 3
|
314.9
|
6/5
|
| 4
|
419.8
|
14/11, 23/18
|
| 5
|
524.8
|
19/14, 23/17, 27/20
|
| 6
|
629.7
|
13/9, 23/16
|
| 7
|
734.7
|
23/15, 26/17, 32/21
|
| 8
|
839.6
|
13/8, 21/13, 34/21
|
| 9
|
945.6
|
19/11, 26/15
|
| 10
|
1049.6
|
11/6
|
| 11
|
1154.5
|
35/18, 39/20
|
| 12
|
1259.5
|
35/17, 33/16, 27/13
|
Instruments
Music
See also
