10ed8/3: Difference between revisions
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== Theory == | == Theory == | ||
10ed8/3 can be seen as a very compressed version of [[7edo]]. The [[octave stretching|octave compression]] results in a more accurate perfect fourth, at the expense of the fifth, which becomes a sharp [[Mavila]] fifth. | 10ed8/3 can be seen as a very compressed version of [[7edo]]. The [[octave stretching|octave compression]] results in a more accurate perfect fourth, at the expense of the fifth, which becomes a sharp [[Mavila]] fifth. | ||
== Intervals == | |||
{{Interval table}} | |||
==Music== | ==Music== | ||
'''Cole''' | '''Cole''' | ||
* [[Media:10ed8_3 improv.mp3|10ed8/3 improv]] | * [[Media:10ed8_3 improv.mp3|10ed8/3 improv]] | ||
Revision as of 23:18, 17 March 2025
| ← 9ed8/3 | 10ed8/3 | 11ed8/3 → |
(semiconvergent)
10 equal divisions of 8/3 (abbreviated 10ed8/3) is a nonoctave tuning system that divides the interval of 8/3 into 10 equal parts of about 170 ¢ each. Each step represents a frequency ratio of (8/3)1/10, or the 10th root of 8/3.
Theory
10ed8/3 can be seen as a very compressed version of 7edo. The octave compression results in a more accurate perfect fourth, at the expense of the fifth, which becomes a sharp Mavila fifth.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 169.8 | 9/8, 10/9, 11/10, 12/11, 13/12, 19/17, 21/19 |
| 2 | 339.6 | 6/5, 11/9, 16/13, 17/14, 21/17 |
| 3 | 509.4 | 4/3, 15/11, 19/14 |
| 4 | 679.2 | 3/2, 16/11, 19/13, 22/15 |
| 5 | 849 | 13/8, 18/11, 21/13 |
| 6 | 1018.8 | 9/5, 11/6, 16/9, 20/11 |
| 7 | 1188.6 | 2/1 |
| 8 | 1358.4 | 11/5, 13/6, 20/9 |
| 9 | 1528.2 | 12/5, 17/7, 19/8, 22/9 |
| 10 | 1698 | 8/3, 19/7, 21/8 |
Music
Cole