# 467edo

 ← 466edo 467edo 468edo →
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 2.57 ¢ 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 (%) -17.7 -34.0 -3.5 -35.5 +44.5 -10.5 +48.2 +15.5 +21.8 -21.2 +49.7
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

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