467edo

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← 466edo467edo468edo →
Prime factorization 467 (prime)
Step size 2.56959¢
Fifth 273\467 (701.499¢)
Semitones (A1:m2) 43:36 (110.5¢ : 92.51¢)
Consistency limit 9
Distinct consistency limit 9

467 equal divisions of the octave (abbreviated 467edo or 467ed2), also called 467-tone equal temperament (467tet) or 467 equal temperament (467et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 467 equal parts of about 2.570 ¢ each. Each step represents a frequency ratio of 21/467, or the 467th root of 2.

Theory

467edo is consistent to the 9-odd-limit with harmonics 3, 5, and 7 all tuned flat. Using the patent val, the equal temperament tempers out 4375/4374, 2100875/2097152, 5250987/5242880, and [-16 4 9 -4 in the 7-limit. It supports mitonic and counterkleismic, supplying the optimal patent val for the latter.

In the 11-limit, the 467e val scores much better than the patent val. The 467e val tempers out 1375/1372, 24057/24010, 35937/35840, and 41503/41472, and in the 13-limit, 625/624, 729/728, 1716/1715, and 2200/2197. The patent val tempers out 540/539, 6250/6237, 12005/11979, and 14700/14641, and in the 13-limit, 625/624, 729/728, and 2080/2079.

In the 17-limit, it supplies the optimal patent val for the rank-6 temperament tempering out 375/374.

Odd harmonics

Approximation of odd harmonics in 467edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -0.46 -0.87 -0.09 -0.91 +1.14 -0.27 +1.24 +0.40 +0.56 -0.55 +1.28
relative (%) -18 -34 -3 -35 +45 -11 +48 +15 +22 -21 +50
Steps
(reduced)
740
(273)
1084
(150)
1311
(377)
1480
(79)
1616
(215)
1728
(327)
1825
(424)
1909
(41)
1984
(116)
2051
(183)
2113
(245)

Subsets and supersets

467edo is the 91st prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-740 467 [467 740]] 0.1439 0.1439 5.38
2.3.5 [-36 11 8, [-16 35 -17 [467 740 1084]] 0.2215 0.1608 6.02
2.3.5.7 4375/4374, 2100875/2097152, [-16 4 9 -4 [467 740 1084 1311]] 0.1741 0.1617 6.05

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 71\467 182.441 10/9 Mitonic
1 123\467 316.060 6/5 Counterhanson

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Music

Francium