# 469edo

 ← 468edo 469edo 470edo →
Prime factorization 7 × 67
Step size 2.55864¢
Fifth 274\469 (701.066¢)
Semitones (A1:m2) 42:37 (107.5¢ : 94.67¢)
Dual sharp fifth 275\469 (703.625¢)
Dual flat fifth 274\469 (701.066¢)
Dual major 2nd 80\469 (204.691¢)
Consistency limit 5
Distinct consistency limit 5

469 equal divisions of the octave (abbreviated 469edo or 469ed2), also called 469-tone equal temperament (469tet) or 469 equal temperament (469et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 469 equal parts of about 2.56 ¢ each. Each step represents a frequency ratio of 21/469, or the 469th root of 2.

## Theory

469et is only consistent to the 5-odd-limit and the error of the harmonic 3 is quite large. It can be considered for the 2.9.5.7.13.17 subgroup, tempering out 2601/2600, 7616/7605, 5832/5831, 60112/60025 and 265625/264992. It supports gravity and french decimal.

### Odd harmonics

Approximation of odd harmonics in 469edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.89 +0.04 +0.90 +0.78 -1.21 +1.26 -0.85 -0.05 -0.71 +0.01 +1.15
Relative (%) -34.7 +1.6 +35.1 +30.5 -47.3 +49.4 -33.2 -2.0 -27.8 +0.3 +44.9
Steps
(reduced)
743
(274)
1089
(151)
1317
(379)
1487
(80)
1622
(215)
1736
(329)
1832
(425)
1917
(41)
1992
(116)
2060
(184)
2122
(246)

### Subsets and supersets

Since 469 factors into 7 × 67, 469edo has 7edo and 67edo as its subset edos. 938edo, which doubles it, gives a good correction to the harmonics 3 and 5.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [1487 -469 [469 1487]] -0.1232 0.1232 4.82
2.9.5 [38 -1 -15, [13 -29 34 [469 1487 1089]] -0.0879 0.1122 4.39