# 465edo

 ← 464edo 465edo 466edo →
Prime factorization 3 × 5 × 31
Step size 2.58065¢
Fifth 272\465 (701.935¢)
Semitones (A1:m2) 44:35 (113.5¢ : 90.32¢)
Consistency limit 5
Distinct consistency limit 5

465 equal divisions of the octave (abbreviated 465edo or 465ed2), also called 465-tone equal temperament (465tet) or 465 equal temperament (465et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 465 equal parts of about 2.58 ¢ each. Each step represents a frequency ratio of 21/465, or the 465th root of 2.

## Theory

465edo is only consistent to the 5-odd-limit, and the errors of harmonics beyond 3 tend to be quite large. It can be considered for the 2.3.5.11.13.17 subgroup, tempering out 936/935, 1377/1375, 71874/71825, 131648/131625 and 225000/224939. It supports counterschismic in the 5-limit, and birds and belobog in the 7-limit using the patent val.

### Prime harmonics

Approximation of prime harmonics in 465edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.02 +0.78 -1.08 +0.94 +0.76 +0.85 -0.74 -1.18 +0.10 +0.77
Relative (%) +0.0 -0.8 +30.3 -42.0 +36.4 +29.6 +33.0 -28.6 -45.6 +3.9 +29.9
Steps
(reduced)
465
(0)
737
(272)
1080
(150)
1305
(375)
1609
(214)
1721
(326)
1901
(41)
1975
(115)
2103
(243)
2259
(399)
2304
(444)

### Subsets and supersets

Since 465 factors into 3 × 5 × 31, 465edo has subset edos 3, 5, 15, 31, 93, and 155. 930edo, which doubles it, gives a good correction to the harmonic 7.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-737 465 [465 737]] +0.0062 0.0062 0.24
2.3.5 [25 15 -21, [-22 30 -11 [465 737 1080]] -0.1083 0.1619 6.27

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 193\465 498.06 4/3 Counterschismic
5 322\465
(43\465)
830.97
(110.97)
80/49
(15/14)
Qintosec (465)

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