7 equal divisions of acoustic phi (6edϕ) is the nonoctave tuning system derived by dividing acoustic phi into 7 equal steps of 119 ¢ each. It corresponds to 10edo with an octave compression of 9.87 cents.
| Prime factorization
|
7 (prime)
|
| Step size
|
119.013 ¢
|
| Octave
|
10\7edϕ (1190.13 ¢)
(convergent)
|
| Twelfth
|
16\7edϕ (1904.21 ¢)
(convergent)
|
| Consistency limit
|
9
|
| Distinct consistency limit
|
5
|
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1
|
| 1
|
119
|
12/11, 13/12, 14/13, 15/14, 16/15, 17/16, 18/17, 19/18, 21/20
|
| 2
|
238
|
7/6, 8/7, 9/8, 13/11, 15/13, 17/15, 19/17, 20/17
|
| 3
|
357
|
5/4, 6/5, 11/9, 16/13, 17/14, 21/17
|
| 4
|
476.1
|
4/3, 9/7, 13/10, 17/13, 21/16
|
| 5
|
595.1
|
7/5, 10/7, 11/8, 13/9, 17/12, 18/13
|
| 6
|
714.1
|
3/2, 14/9, 17/11, 20/13
|
| 7
|
833.1
|
5/3, 8/5, 11/7, 13/8, 18/11, 19/12, 21/13
|
Harmonics
Approximation of harmonics in 1ed119.013c
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
| Error
|
Absolute (¢)
|
-9.9
|
+2.3
|
-19.7
|
-49.0
|
-7.6
|
-36.5
|
-29.6
|
+4.5
|
-58.9
|
+14.1
|
-17.5
|
-37.0
|
-46.3
|
-46.8
|
-39.5
|
| Relative (%)
|
-8.3
|
+1.9
|
-16.6
|
-41.2
|
-6.4
|
-30.6
|
-24.9
|
+3.8
|
-49.5
|
+11.9
|
-14.7
|
-31.1
|
-38.9
|
-39.3
|
-33.2
|
| Step
|
10
|
16
|
20
|
23
|
26
|
28
|
30
|
32
|
33
|
35
|
36
|
37
|
38
|
39
|
40
|
Music