1448edo: Difference between revisions
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The | {{Infobox ET}} | ||
{{ED intro}} | |||
The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1448}} | {{Harmonics in equal|1448}} | ||
[[Category: | === Subsets and supersets === | ||
Since 1448 factors into {{factorization|1448}}, it has subset edos 2, 4, 8, 181, 362, and 724. | |||
[[Category:Thor]] | |||
[[Category:Donar]] | |||
Latest revision as of 17:04, 18 February 2025
| ← 1447edo | 1448edo | 1449edo → |
1448 equal divisions of the octave (abbreviated 1448edo or 1448ed2), also called 1448-tone equal temperament (1448tet) or 1448 equal temperament (1448et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1448 equal parts of about 0.829 ¢ each. Each step represents a frequency ratio of 21/1448, or the 1448th root of 2.
The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 subgroup system. It is a zeta peak edo, and provides the optimal patent val for donar. A basis for the 13-limit commas is {3025/3024, 4225/4224, 4375/4374, 140625/140608, 823680/823543}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.021 | -0.126 | -0.041 | -0.213 | -0.196 | +0.293 | +0.001 | -0.098 | -0.295 | +0.268 |
| Relative (%) | +0.0 | -2.6 | -15.2 | -5.0 | -25.7 | -23.7 | +35.4 | +0.1 | -11.8 | -35.6 | +32.4 | |
| Steps (reduced) |
1448 (0) |
2295 (847) |
3362 (466) |
4065 (1169) |
5009 (665) |
5358 (1014) |
5919 (127) |
6151 (359) |
6550 (758) |
7034 (1242) |
7174 (1382) | |
Subsets and supersets
Since 1448 factors into 23 × 181, it has subset edos 2, 4, 8, 181, 362, and 724.