| Prime factorization
|
24 × 3
|
| Step size
|
125¢
|
| Octave
|
10\48ed32 (1250¢) (→5\24ed32)
|
| Twelfth
|
15\48ed32 (1875¢) (→5\16ed32)
|
| Consistency limit
|
2
|
| Distinct consistency limit
|
2
|
| Special properties
|
|
1 equal division of 125¢ (1ed125c), also known as arithmetic pitch sequence of 125¢ (APS125¢), is a nonoctave tuning using equal steps of 125 cents each. This could be considered as dividing the approximate perfect fourth of 500 cents into 4 equal parts, making it very slightly compressed 4ed4/3. It is equivalent to 9.6edo, and is a subset of 48edo (every fifth step). Therefore, it can be regarded as 48ed32.
Approximation of harmonics in 1ed125c
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
| Error
|
Absolute (¢)
|
+50.0
|
-27.0
|
-25.0
|
-36.3
|
+23.0
|
+6.2
|
+25.0
|
-53.9
|
+13.7
|
-26.3
|
| Relative (%)
|
+40.0
|
-21.6
|
-20.0
|
-29.1
|
+18.4
|
+4.9
|
+20.0
|
-43.1
|
+10.9
|
-21.1
|
| Steps
|
10
|
15
|
19
|
22
|
25
|
27
|
29
|
30
|
32
|
33
|
Intervals
| ordinal number
|
cents
|
interval name
|
| 0
|
0
|
unison
|
| 1
|
125
|
2/3-tone, trienthird
|
| 2
|
250
|
semifourth
|
| 3
|
375
|
narrow perde segah, marvelous major third, near just major third
|
| 4
|
500
|
perfect fourth
|
| 5
|
625
|
pental diminished fifth, classic diminshed fifth
|
| 6
|
750
|
septendecimal subminor sixth
|
| 7
|
875
|
major sixth
|
| 8
|
1000
|
Pythagorean minor seventh
|
| 9
|
1125
|
classic (5-limit) diminished octave.
|
| 10
|
1250
|
|
| 11
|
1375
|
|
| 12
|
1500
|
|
| 13
|
1625
|
|
| 14
|
1750
|
|
| 15
|
1875
|
|
| 16
|
2000
|
|
Scala file
! E:\cakewalk\scales\125cent.scl
!
125 cent tuning
4
!
125.00000
250.00000
375.00000
500.00000
Music