| Prime factorization
|
n/a
|
| Step size
|
1200 ¢
|
| Fifth
|
1\1 (1200 ¢)
|
| Semitones (A1:m2)
|
3:-2 (3600 ¢ : -2400 ¢)
|
| Dual sharp fifth
|
1\1 (1200 ¢)
|
| Dual flat fifth
|
0\1 (0 ¢)
|
| Dual major 2nd
|
0\1 (0 ¢)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
1
|
| Special properties
|
|
1 equal division of the octave (abbreviated 1edo or 1ed2), also called 1-tone equal temperament (1tet) or 1 equal temperament (1et) when viewed under a regular temperament perspective, is the tuning system that uses equal steps of 2/1 (one octave), or exactly 1200 ¢.
Notation
A. All A.
Theory
All intervals are either tempered out or mapped to the octave.
Intervals
| Steps
|
Cents
|
Approximate ratios
|
Ups and downs notation
(Dual flat fifth 0\1)
|
Ups and downs notation
(Dual sharp fifth 1\1)
|
| 0
|
0
|
1/1, 4/3, 5/3, 5/4, 7/6, 8/7, 10/7, 11/6, 11/7, 11/8, 11/10, 13/9, 13/12, 14/9, 14/13, 15/13, 15/14, 16/9, 16/13, 16/15, 17/9, 17/12, 17/13, 17/14, 17/15, 17/16, 19/9, 19/12, 19/13, 19/14, 19/15, 19/16, 19/17, 20/9, 20/13, 20/17, 20/19
|
D, E, F, A, B, C
|
D, E, F, G, B, C
|
| 1
|
1200
|
2/1, 3/2, 5/2, 6/5, 7/3, 7/4, 7/5, 8/3, 8/5, 9/7, 9/8, 10/3, 11/3, 11/4, 11/5, 12/7, 12/11, 13/6, 13/7, 13/8, 13/10, 13/11, 14/11, 15/7, 15/8, 15/11, 16/7, 16/11, 17/6, 17/7, 17/8, 17/10, 17/11, 18/13, 18/17, 19/6, 19/7, 19/8, 19/10, 19/11, 20/7, 20/11
|
G, D
|
A, D
|
Harmonics
Approximation of prime harmonics in 1edo
| Harmonic
|
2
|
3
|
5
|
7
|
11
|
13
|
17
|
19
|
23
|
29
|
31
|
37
|
41
|
43
|
47
|
53
|
59
|
61
|
67
|
71
|
| Error
|
Absolute (¢)
|
+0
|
+498
|
-386
|
+231
|
-551
|
+359
|
-105
|
-298
|
+572
|
+170
|
+55
|
-251
|
-429
|
-512
|
+534
|
+326
|
+141
|
+83
|
-79
|
-180
|
| Relative (%)
|
+0.0
|
+41.5
|
-32.2
|
+19.3
|
-45.9
|
+30.0
|
-8.7
|
-24.8
|
+47.6
|
+14.2
|
+4.6
|
-20.9
|
-35.8
|
-42.6
|
+44.5
|
+27.2
|
+11.7
|
+6.9
|
-6.6
|
-15.0
|
| Step
|
1
|
2
|
2
|
3
|
3
|
4
|
4
|
4
|
5
|
5
|
5
|
5
|
5
|
5
|
6
|
6
|
6
|
6
|
6
|
6
|
Approximation of prime harmonics in 1edo
| Harmonic
|
73
|
79
|
83
|
89
|
97
|
101
|
103
|
107
|
109
|
113
|
127
|
131
|
137
|
139
|
149
|
151
|
157
|
163
|
167
|
173
|
| Error
|
Absolute (¢)
|
-228
|
-365
|
-450
|
-571
|
+480
|
+410
|
+376
|
+310
|
+278
|
+216
|
+14
|
-40
|
-118
|
-143
|
-263
|
-286
|
-354
|
-418
|
-460
|
-522
|
| Relative (%)
|
-19.0
|
-30.4
|
-37.5
|
-47.6
|
+40.0
|
+34.2
|
+31.3
|
+25.9
|
+23.2
|
+18.0
|
+1.1
|
-3.3
|
-9.8
|
-11.9
|
-21.9
|
-23.8
|
-29.5
|
-34.9
|
-38.4
|
-43.5
|
| Step
|
6
|
6
|
6
|
6
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|
7
|