395edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 394edo395edo396edo →
Prime factorization 5 × 79
Step size 3.03797¢
Fifth 231\395 (701.772¢)
Semitones (A1:m2) 37:30 (112.4¢ : 91.14¢)
Consistency limit 9
Distinct consistency limit 9

395 equal divisions of the octave (abbreviated 395edo), or 395-tone equal temperament (395tet), 395 equal temperament (395et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 395 equal parts of about 3.04 ¢ each. Each step of 395edo represents a frequency ratio of 21/395, or the 395th root of 2.

Theory

395edo is consistent to the 9-odd-limit. The equal temperament tempers out 32805/32768 in the 5-limit; 4375/4374, 65625/65536, 14348907/14336000, and 40500000/40353607 in the 7-limit; supporting gold and pontiac.

Prime harmonics

Approximation of prime harmonics in 395edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 -0.18 -0.49 +0.29 -1.44 +0.99 +1.37 +0.21 +0.59 +0.30 +0.28
relative (%) +0 -6 -16 +9 -48 +33 +45 +7 +19 +10 +9
Steps
(reduced)
395
(0)
626
(231)
917
(127)
1109
(319)
1366
(181)
1462
(277)
1615
(35)
1678
(98)
1787
(207)
1919
(339)
1957
(377)

Subsets and supersets

Since 395 factors into 5 × 79, 395edo has 5edo and 79edo as its subset edos.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-626 395 [395 626]] 0.0577 0.0577 1.90
2.3.5 32805/32768, [-34 -43 44 [395 626 917]] 0.1089 0.0864 2.84
2.3.5.7 4375/4374, 32805/32768, 40500000/40353607 [395 626 917 1109]] 0.0560 0.1183 3.89
2.3.5.7.11 1375/1372, 4375/4374, 32805/32768, 35937/35840 [395 626 917 1109 1366]] 0.1283 0.1792 5.90

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 164\395 498.23 4/3 Pontiac

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