4ed5/2: Difference between revisions
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{{ED intro}} | {{ED intro}} | ||
== Harmonics == | == Intervals == | ||
{{Harmonics in equal|4|5|2}} | {| class="wikitable" | ||
|+ | |||
!Steps | |||
!Cents | |||
!JI approximation (2.5.31) | |||
|- | |||
|0 | |||
|0 | |||
|1/1 | |||
|- | |||
|1 | |||
|396.58 | |||
|5/4, 31/25 | |||
|- | |||
|2 | |||
|793.15 | |||
|8/5 | |||
|- | |||
|3 | |||
|1189.74 | |||
|2/1 | |||
|- | |||
|4 | |||
|1586.31 | |||
|5/2, 62/25 | |||
|} | |||
==Harmonics== | |||
{{Harmonics in equal|4|5|2|intervals=prime}} | |||
{{stub}} | {{stub}} | ||
Revision as of 17:04, 16 December 2024
| ← 3ed5/2 | 4ed5/2 | 5ed5/2 → |
(convergent)
4 equal divisions of 5/2 (abbreviated 4ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 4 equal parts of about 397 ¢ each. Each step represents a frequency ratio of (5/2)1/4, or the 4th root of 5/2.
Intervals
| Steps | Cents | JI approximation (2.5.31) |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 396.58 | 5/4, 31/25 |
| 2 | 793.15 | 8/5 |
| 3 | 1189.74 | 2/1 |
| 4 | 1586.31 | 5/2, 62/25 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10 | +81 | -10 | -196 | -186 | -78 | -146 | +58 | +124 | +119 | +4 |
| Relative (%) | -2.6 | +20.4 | -2.6 | -49.5 | -46.8 | -19.7 | -36.8 | +14.6 | +31.2 | +30.0 | +0.9 | |
| Steps (reduced) |
3 (3) |
5 (1) |
7 (3) |
8 (0) |
10 (2) |
11 (3) |
12 (0) |
13 (1) |
14 (2) |
15 (3) |
15 (3) | |
|
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