| Prime factorization
|
24 × 3 × 5
|
| Step size
|
65¢
|
| Octave
|
18\240ed8192 (1170¢) (→3\40ed8192)
|
| Twelfth
|
29\240ed8192 (1885¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
| Special properties
|
|
1 equal division of 65¢ (1ed65c), also known as arithmetic pitch sequence of 65¢ (APS65¢), is an equal nonoctave scale generated by making a continuous chain of intervals of exactly 65¢. It is a good tuning in the 2.3.5.7.11.13.27 subgroup, and is closely related to 37edo and 37ED4. 37 degrees of 1ed65c is exactly 2405¢, which is the 4/1 double octave plus 5¢. Thus, 1ed65c can be seen as a stretched version of 37ed4.
A characteristic pentad of 1ed65c is 8:10:13:14:22 and it's utonal inversion.
Approximation of harmonics in 1ed65c
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
| Error
|
Absolute (¢)
|
-30.0
|
-17.0
|
+5.0
|
+8.7
|
+18.0
|
+11.2
|
-25.0
|
+31.1
|
-21.3
|
+8.7
|
| Relative (%)
|
-46.2
|
-26.1
|
+7.7
|
+13.4
|
+27.8
|
+17.2
|
-38.5
|
+47.8
|
-32.8
|
+13.4
|
| Steps
|
18
|
29
|
37
|
43
|
48
|
52
|
55
|
59
|
61
|
64
|
Intervals
| Degree of 1ed65c
|
Cents Value
|
| 0
|
0
|
| 1
|
65
|
| 2
|
130
|
| 3
|
195
|
| 4
|
260
|
| 5
|
325
|
| 6
|
390
|
| 7
|
455
|
| 8
|
520
|
| 9
|
585
|
| 10
|
650
|
| 11
|
715
|
| 12
|
780
|
| 13
|
845
|
| 14
|
910
|
| 15
|
975
|
| 16
|
1040
|
| 17
|
1105
|
| 18
|
1170
|
| 19
|
1235
|
| 20
|
1300
|
| 21
|
1365
|
| 22
|
1430
|
| 23
|
1495
|
| 24
|
1560
|
| 25
|
1625
|
| 26
|
1690
|
| 27
|
1755
|
| 28
|
1820
|
| 29
|
1885
|
| 30
|
1950
|
| 31
|
2015
|
| 32
|
2080
|
| 33
|
2145
|
| 34
|
2210
|
| 35
|
2275
|
| 36
|
2340
|
| 37
|
2405
|
Music
Slumber of Thought by Chris Vaisvil
Malathion in 65cET by Chris Vaisvil (65cET is an outdated name for this tuning system, standing for "65-cent equal temperament")