| Prime factorization
|
52
|
| Step size
|
33.3236 ¢
|
| Octave
|
36\25edϕ (1199.65 ¢)
(convergent)
|
| Twelfth
|
57\25edϕ (1899.45 ¢)
(semiconvergent)
|
| Consistency limit
|
8
|
| Distinct consistency limit
|
8
|
25 equal divisions of acoustic phi (25edϕ) is the nonoctave tuning system derived by dividing acoustic phi into 25 equal steps of 33.32 ¢ each. It corresponds to 36edo with an octave compression of about 0.35 cents. Like 36edo, it is consistent to the 8-integer-limit.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1
|
| 1
|
33.3
|
|
| 2
|
66.6
|
23/22, 24/23
|
| 3
|
100
|
16/15, 17/16, 18/17, 19/18, 20/19
|
| 4
|
133.3
|
13/12, 14/13
|
| 5
|
166.6
|
11/10, 21/19, 23/21
|
| 6
|
199.9
|
9/8, 19/17, 26/23
|
| 7
|
233.3
|
8/7, 23/20, 25/22
|
| 8
|
266.6
|
7/6
|
| 9
|
299.9
|
19/16
|
| 10
|
333.2
|
17/14, 23/19
|
| 11
|
366.6
|
16/13, 21/17, 26/21
|
| 12
|
399.9
|
19/15, 24/19
|
| 13
|
433.2
|
9/7, 23/18
|
| 14
|
466.5
|
17/13, 21/16
|
| 15
|
499.9
|
4/3
|
| 16
|
533.2
|
15/11, 19/14, 23/17, 26/19
|
| 17
|
566.5
|
18/13
|
| 18
|
599.8
|
17/12, 24/17
|
| 19
|
633.1
|
13/9, 23/16
|
| 20
|
666.5
|
19/13, 22/15
|
| 21
|
699.8
|
3/2
|
| 22
|
733.1
|
23/15, 26/17
|
| 23
|
766.4
|
14/9
|
| 24
|
799.8
|
19/12
|
| 25
|
833.1
|
13/8, 21/13
|
Harmonics
Approximation of harmonics in 1ed33.3236c
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
| Error
|
Absolute (¢)
|
-0.4
|
-2.5
|
-0.7
|
+12.9
|
-2.9
|
-3.1
|
-1.1
|
-5.0
|
+12.5
|
+14.1
|
-3.2
|
-8.5
|
-3.5
|
+10.4
|
-1.4
|
| Relative (%)
|
-1.1
|
-7.5
|
-2.1
|
+38.6
|
-8.6
|
-9.4
|
-3.2
|
-15.1
|
+37.6
|
+42.4
|
-9.6
|
-25.5
|
-10.5
|
+31.1
|
-4.2
|
| Step
|
36
|
57
|
72
|
84
|
93
|
101
|
108
|
114
|
120
|
125
|
129
|
133
|
137
|
141
|
144
|