469edo

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← 468edo469edo470edo →
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 2.559 ¢ 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 (%) -35 +2 +35 +31 -47 +49 -33 -2 -28 +0 +45
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