| Prime factorization
|
n/a
|
| Step size
|
2400 ¢
|
| Octave
|
1\1ed4 (2400 ¢)
|
| Twelfth
|
1\1ed4 (2400 ¢)
|
| Consistency limit
|
1
|
| Distinct consistency limit
|
1
|
| Special properties
|
|
1 equal division of the 4th harmonic (abbreviated 1ed4) is a nonoctave tuning system that uses equal steps of 4/1, or exactly 2400 ¢.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
| 0
|
0
|
1/1, 3/2, 5/2, 5/3, 7/2, 7/3, 7/5, 9/4, 10/9, 11/4, 11/6, 11/9, 11/10, 13/4, 13/6, 13/9, 13/10, 13/11, 14/9, 14/11, 14/13, 15/4, 15/11, 15/13, 15/14, 17/4, 17/6, 17/9, 17/10, 17/11, 17/13, 17/14, 17/15, 19/4, 19/6, 19/9, 19/10, 19/11, 19/13, 19/14, 19/15, 19/17
|
| 1
|
2400
|
2/1, 3/1, 4/3, 5/1, 6/5, 7/1, 9/2, 9/5, 9/7, 10/3, 10/7, 11/2, 11/3, 11/5, 11/7, 12/11, 13/2, 13/3, 13/5, 13/7, 14/3, 14/5, 15/2, 15/7, 17/2, 17/3, 17/5, 17/7, 18/11, 18/13, 18/17, 19/2, 19/3, 19/5, 19/7, 20/9, 20/11, 20/13, 20/17, 20/19
|
Harmonics
Approximation of harmonics in 1ed4
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Error
|
Absolute (¢)
|
+1200
|
+498
|
+0
|
-386
|
-702
|
-969
|
+1200
|
+996
|
+814
|
+649
|
+498
|
| Relative (%)
|
+50.0
|
+20.8
|
+0.0
|
-16.1
|
-29.2
|
-40.4
|
+50.0
|
+41.5
|
+33.9
|
+27.0
|
+20.8
|
| Step
|
1
|
1
|
1
|
1
|
1
|
1
|
2
|
2
|
2
|
2
|
2
|
Approximation of harmonics in 1ed4
| Harmonic
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
| Error
|
Absolute (¢)
|
+359
|
+231
|
+112
|
+0
|
-105
|
-204
|
-298
|
-386
|
-471
|
-551
|
-628
|
| Relative (%)
|
+15.0
|
+9.6
|
+4.7
|
+0.0
|
-4.4
|
-8.5
|
-12.4
|
-16.1
|
-19.6
|
-23.0
|
-26.2
|
| Step
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
2
|
