Ed13
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Ed13 means Division of the Thirteenth Harmonic (13/1) into n equal parts.
Division of the thirteenth harmonic into n equal parts
The thirteenth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3 triskaidecataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with triskaidecatave equivalence, this fact shapes one's musical approach dramatically. The thirteenth harmonic causes the ideal chromatic scale to "break down" after the tritave:
| Unison | m2 | M2 | m3 | M3 | P4 | A4
d5 |
P5 | m6 | M6 | m7 | M7 | P8 | m9 | M9 | m10 | M10 | P11 | A11
d12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1/1 | 16/15 15/14 |
10/9 9/8 8/7 |
7/6 6/5 |
5/4 | 4/3 | 7/5 | 3/2 | 8/5 | 5/3 | 7/4 9/5 |
11/6 13/7 15/8 |
2/1 | 15/7 13/6 |
11/5 9/4 |
7/3 12/5 |
5/2 13/5 |
8/3 11/4 |
14/5 17/6 |
| P12 | m13 | M13 | m14 | M14 | P15 | m16 | M16 | m17 | M17 | P18 | A18
d19 |
P19 | m20 | M20 | m21 | M21 | P22 | |
| 3/1 | 16/5 13/4 |
10/3 17/5 |
7/2 18/5 |
11/3 15/4 |
4/1 | 17/4 13/3 |
9/2 | 14/3 | 5/1 | 16/3 11/2 |
28/5 17/3 |
6/1 | 13/2 | 20/3 | 7/1 | 15/2 | 8/1 | |