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| Prime factorization
|
n/a
|
| Step size
|
381.972¢
|
| Octave
|
3\1ed697/559 (1145.92¢)
(convergent)
|
| Twelfth
|
5\1ed697/559 (1909.86¢)
(convergent)
|
| Consistency limit
|
7
|
| Distinct consistency limit
|
1
|
| Special properties
|
|
π-edo, 1ed21/π, or APS(1/π oct) is a nonoctave equal-step tuning in which π steps occur per octave. It does not approximate any simple harmonics well, except for the 3rd harmonic. In fact, it is nearly identical to 5edt. This lends the tuning to use with custom inharmonic timbres. It has the potential to facilitate music far removed from any conventional harmonic or melodic traditions.
Harmonics
Approximation of harmonics in π-edo
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Error
|
Absolute (¢)
|
-54.1
|
+7.9
|
-108.2
|
-112.5
|
-46.2
|
+68.9
|
-162.3
|
+15.8
|
-166.6
|
+50.4
|
-100.3
|
| Relative (%)
|
-14.2
|
+2.1
|
-28.3
|
-29.5
|
-12.1
|
+18.0
|
-42.5
|
+4.1
|
-43.6
|
+13.2
|
-26.2
|
| Steps
|
3
|
5
|
6
|
7
|
8
|
9
|
9
|
10
|
10
|
11
|
11
|