634edo

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← 633edo634edo635edo →
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 634-tone equal temperament (634tet), 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 of 634edo 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 +13 -10 +14 -28 -8 -45 -19 +6 +4 +4
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