4edf: Difference between revisions
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Rework interval table, including removing irrelevant stuff |
Move the only nontrivial sentence to the theory section |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} It corresponds to 6.8380[[edo]]. | {{ED intro}} It corresponds to 6.8380[[edo]]. | ||
== Theory == | |||
4edf is related to the [[tetracot]] temperament, which [[tempering out|tempers out]] [[20000/19683]] in the 5-limit. | |||
=== Harmonics === | |||
{{Harmonics in equal|4|3|2}} | |||
== Intervals == | == Intervals == | ||
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|- | |- | ||
| 0 | | 0 | ||
| 0. | | 0.0 | ||
| C | | C | ||
|- | |- | ||
Latest revision as of 06:09, 10 May 2024
| ← 3edf | 4edf | 5edf → |
(semiconvergent)
(semiconvergent)
4 equal divisions of the perfect fifth (abbreviated 4edf or 4ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 4 equal parts of about 175 ¢ each. Each step represents a frequency ratio of (3/2)1/4, or the 4th root of 3/2. It corresponds to 6.8380edo.
Theory
4edf is related to the tetracot temperament, which tempers out 20000/19683 in the 5-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +28.4 | +28.4 | +56.8 | +21.5 | +56.8 | -34.5 | +85.3 | +56.8 | +49.9 | +60.4 | +85.3 |
| Relative (%) | +16.2 | +16.2 | +32.4 | +12.3 | +32.4 | -19.7 | +48.6 | +32.4 | +28.5 | +34.4 | +48.6 | |
| Steps (reduced) |
7 (3) |
11 (3) |
14 (2) |
16 (0) |
18 (2) |
19 (3) |
21 (1) |
22 (2) |
23 (3) |
24 (0) |
25 (1) | |
Intervals
| # | Cents | Tetratonic Notation |
|---|---|---|
| 0 | 0.0 | C |
| 1 | 175.5 | D |
| 2 | 351.0 | E |
| 3 | 526.5 | F |
| 4 | 702.0 | C |
| 5 | 877.4 | D |
| 6 | 1052.9 | E |
| 7 | 1228.4 | F |
| 8 | 1403.9 | C |
| 9 | 1579.4 | D |
| 10 | 1754.9 | E |
| 11 | 1930.4 | F |
| 12 | 2105.9 | C |
| 13 | 2281.4 | D |
| 14 | 2456.8 | E |