7ed5/2: Difference between revisions
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Llywelyn, not necessarily semaja |
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=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|7|5|2|columns=11}} | {{Harmonics in equal|7|5|2|columns=11}} | ||
{{Harmonics in equal|7|5|2|columns=12|start=12|collapsed=true|Approximation of harmonics in 7ed5/2 (continued)}} | {{Harmonics in equal|7|5|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 7ed5/2 (continued)}} | ||
== Intervals == | == Intervals == | ||
Latest revision as of 14:27, 27 May 2026
| ← 6ed5/2 | 7ed5/2 | 8ed5/2 → |
7 equal divisions of 5/2 (abbreviated 7ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 7 equal parts of about 227 ¢ each. Each step represents a frequency ratio of (5/2)1/7, or the 7th root of 5/2.
Theory
7ed5/2 corresponds to 5.2953…edo. It can function as a generator chain for the llywelyn temperament. Its patent val tempers out the same 5-limit commas as 5edo, but the mapping of 7 and higher prime harmonics differs.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -66.9 | -89.0 | +92.8 | -66.9 | +70.7 | +30.4 | +25.9 | +48.6 | +92.8 | -72.2 | +3.8 |
| Relative (%) | -29.5 | -39.3 | +40.9 | -29.5 | +31.2 | +13.4 | +11.4 | +21.4 | +40.9 | -31.9 | +1.7 | |
| Steps (reduced) |
5 (5) |
8 (1) |
11 (4) |
12 (5) |
14 (0) |
15 (1) |
16 (2) |
17 (3) |
18 (4) |
18 (4) |
19 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +91.8 | -36.5 | +70.7 | -41.1 | +80.6 | -18.4 | -112.0 | +25.9 | -58.6 | +87.5 | +10.5 | -63.2 |
| Relative (%) | +40.5 | -16.1 | +31.2 | -18.1 | +35.6 | -8.1 | -49.4 | +11.4 | -25.9 | +38.6 | +4.6 | -27.9 | |
| Steps (reduced) |
20 (6) |
20 (6) |
21 (0) |
21 (0) |
22 (1) |
22 (1) |
22 (1) |
23 (2) |
23 (2) |
24 (3) |
24 (3) |
24 (3) | |
Intervals
| # | Cents | Approximated ratio |
|---|---|---|
| 1 | 227 | 8/7, 25/22 |
| 2 | 453 | 13/10 |
| 3 | 680 | 65/44 |
| 4 | 906 | 22/13 |
| 5 | 1133 | 25/13 |
| 6 | 1360 | 11/5, 35/16 |
| 7 | 1586 | 5/2 |