# 634edo

 ← 633edo 634edo 635edo →
Prime factorization 2 × 317
Step size 1.89274¢
Fifth 371\634 (702.208¢)
Semitones (A1:m2) 61:47 (115.5¢ : 88.96¢)
Consistency limit 9
Distinct consistency limit 9

634 equal divisions of the octave (abbreviated 634edo or 634ed2), also called 634-tone equal temperament (634tet) or 634 equal temperament (634et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 634 equal parts of about 1.89 ¢ each. Each step represents a frequency ratio of 21/634, or the 634th root of 2.

## Theory

634edo is a good 13-limit and no-17 higher-limit system. The equal temperament tempers out [-53 10 16 (kwazy comma) and [33 -34 9 (countritonic comma) in the 5-limit; 420175/419904 (wizma), 703125/702464 (meter), and 33554432/33480783 (garischisma) in the 7-limit; 9801/9800, 19712/19683, 41503/41472 in the 11-limit; 1716/1715, 2080/2079, 4096/4095, 4225/4224, 14641/14625, and 31250/31213 in the 13-limit.

### Prime harmonics

Approximation of prime harmonics in 634edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.253 -0.194 +0.259 -0.529 -0.149 -0.854 -0.352 +0.117 +0.076 +0.075
Relative (%) +0.0 +13.4 -10.2 +13.7 -28.0 -7.9 -45.1 -18.6 +6.2 +4.0 +4.0
Steps
(reduced)
634
(0)
1005
(371)
1472
(204)
1780
(512)
2193
(291)
2346
(444)
2591
(55)
2693
(157)
2868
(332)
3080
(544)
3141
(605)

### Subsets and supersets

Since 634 factors into 2 × 317, 634edo has 2edo and 317edo as its subsets.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [1005 -634 [634 1005]] -0.0799 0.0799 4.22
2.3.5 [-53 10 16, [33 -34 9 [634 1005 1472]] -0.0254 0.1009 5.33
2.3.5.7 420175/419904, 703125/702464, 33554432/33480783 [634 1005 1472 1780]] -0.0422 0.0921 4.86
2.3.5.7.11 9801/9800, 19712/19683, 41503/41472, 703125/702464 [634 1005 1472 1780 2193]] -0.0031 0.1135 6.00
2.3.5.7.11.13 1716/1715, 2080/2079, 4096/4095, 14641/14625, 31250/31213 [634 1005 1472 1780 2193 2346]] +0.0041 0.1048 5.54

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 241\634 456.15 125/96 Qak
1 263\634 497.79 4/3 Gary
1 311\634 588.64 [-14 15 -4 Countritonic (5-limit)
2 86\634 162.78 1125/1024 Kwazy

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