1448edo
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Prime factorization
23 × 181
Step size
0.828729¢
Fifth
847\1448 (701.934¢)
Semitones (A1:m2)
137:109 (113.5¢ : 90.33¢)
Consistency limit
15
Distinct consistency limit
15
Special properties
| ← 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 | -3 | -15 | -5 | -26 | -24 | +35 | +0 | -12 | -36 | +32 | |
| 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.