| Prime factorization
|
n/a
|
| Step size
|
84.4672¢
|
| Octave
|
14\1ed21/20 (1182.54¢)
|
| Twelfth
|
23\1ed21/20 (1942.75¢)
|
| Consistency limit
|
2
|
| Distinct consistency limit
|
1
|
| Special properties
|
|
1 equal division of 21/20 (1ed21/20), also known as ambitonal sequence of 21/20 (AS21/20) or 21/20 equal-step tuning, is the equal multiplication of the 21/20 septimal chromatic semitone of 84.467 cents. As such, every interval is a subset of 7-limit just inotation.
It is equal to approximately 14.2067 EDO, and as a result of tethering between compressed 14 and heavily stretched 15 it is quite xenharmonic in its sound. Nonetheless, it is quite a useful scale because it is related to nautilus, sextilififths and floral temperaments.
Harmonics
1ed21/20 offers a good approximation of the no-3s 11-limit, and of the no-3s, no-13s, no-59s 73-limit. It could be used as a dual-fifth tuning.
Approximation of prime harmonics in 1ed21/20
| Harmonic
|
2
|
3
|
5
|
7
|
11
|
13
|
17
|
19
|
23
|
29
|
31
|
| Error
|
Absolute (¢)
|
-17.5
|
+40.8
|
+1.1
|
+9.9
|
-12.4
|
+36.2
|
-5.9
|
-29.5
|
-22.4
|
-1.3
|
-32.3
|
| Relative (%)
|
-20.7
|
+48.3
|
+1.3
|
+11.7
|
-14.7
|
+42.9
|
-6.9
|
-34.9
|
-26.5
|
-1.6
|
-38.3
|
| Step
|
14
|
23
|
33
|
40
|
49
|
53
|
58
|
60
|
64
|
69
|
70
|
(contd.)
| Harmonic
|
37
|
41
|
43
|
47
|
53
|
59
|
61
|
67
|
71
|
73
|
79
|
| Error
|
Absolute (¢)
|
-0.8
|
-9.6
|
-7.5
|
+7.4
|
-31.7
|
+36.1
|
-21.6
|
-15.1
|
-31.1
|
+5.3
|
+37.5
|
| Relative (%)
|
-0.9
|
-11.3
|
-8.9
|
+8.8
|
-37.5
|
+42.7
|
-25.6
|
-17.9
|
-36.8
|
+6.3
|
+44.4
|
| Step
|
74
|
76
|
77
|
79
|
81
|
84
|
84
|
86
|
87
|
88
|
90
|