1448edo

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← 1447edo1448edo1449edo →
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

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

Approximation of prime harmonics in 1448edo
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.