# 475edo

 ← 474edo 475edo 476edo →
Prime factorization 52 × 19
Step size 2.52632¢
Fifth 278\475 (702.316¢)
Semitones (A1:m2) 46:35 (116.2¢ : 88.42¢)
Consistency limit 5
Distinct consistency limit 5

475 equal divisions of the octave (abbreviated 475edo or 475ed2), also called 475-tone equal temperament (475tet) or 475 equal temperament (475et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 475 equal parts of about 2.53 ¢ each. Each step represents a frequency ratio of 21/475, or the 475th root of 2.

## Theory

475edo is only consistent to the 5-odd-limit. The equal temperament tempers out [-14 -19 19 (enneadeca) and [47 -15 -10 (quintosec comma) in the 5-limit. In the 7-limit, the 475d val supports enneadecal and the patent val supports cotoneum.

It can be considered for the 2.3.5.11.13.19.23 subgroup, tempering out 2376/2375, 3250/3249, 11132/11115, 11979/11960, 14300/14283 and 42757/42750.

### Prime harmonics

Approximation of prime harmonics in 475edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.36 +0.21 -1.25 -0.58 +0.74 +1.15 +0.59 +0.78 +1.16 -0.61
Relative (%) +0.0 +14.3 +8.4 -49.4 -23.0 +29.1 +45.5 +23.4 +30.8 +45.9 -24.3
Steps
(reduced)
475
(0)
753
(278)
1103
(153)
1333
(383)
1643
(218)
1758
(333)
1942
(42)
2018
(118)
2149
(249)
2308
(408)
2353
(453)

### Subsets and supersets

Since 475 factors into 52 × 19, 475edo has subset edos 5, 19, 25, and 95. 950edo, 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 [753 -475 [475 753]] -0.1138 0.1138 4.50
2.3.5 [-14 -19 19, [47 -15 -10 [475 753 1103]] -0.1064 0.0935 3.70

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 157\475 396.63 98304/78125 Squarschmidt
5 329\475
(44\475)
831.16
(111.16)
160/99
(16/15)
Quintosec
19 197\475
(3\475)
497.68
(7.58)
4/3
(225/224)