332edo

 ← 331edo 332edo 333edo →
Prime factorization 22 × 83
Step size 3.61446¢
Fifth 194\332 (701.205¢) (→97\166)
Semitones (A1:m2) 30:26 (108.4¢ : 93.98¢)
Consistency limit 7
Distinct consistency limit 7

332 equal divisions of the octave (abbreviated 332edo or 332ed2), also called 332-tone equal temperament (332tet) or 332 equal temperament (332et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 332 equal parts of about 3.61 ¢ each. Each step represents a frequency ratio of 21/332, or the 332nd root of 2.

Theory

332edo is consistent to the 7-odd-limit. The equal temperament tempers out 2401/2400, 19683/19600, 118098/117649, and 29360128/29296875 in the 7-limit. It provides the optimal patent val for 11-, 13-, and 17-limit sedia.

Prime harmonics

Approximation of prime harmonics in 332edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.75 +0.43 -0.15 +1.69 +1.64 -0.14 -1.13 +0.64 +0.54 +0.75
Relative (%) +0.0 -20.8 +12.0 -4.2 +46.9 +45.4 -3.8 -31.2 +17.7 +15.0 +20.7
Steps
(reduced)
332
(0)
526
(194)
771
(107)
932
(268)
1149
(153)
1229
(233)
1357
(29)
1410
(82)
1502
(174)
1613
(285)
1645
(317)

Subsets and supersets

Since 332 factors into 22 × 83, 332edo has subset edos 2, 4, 83, and 166.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3.5 [-13 17 -6, [-53 10 16 [332 526 771]] 0.0955 0.2778 7.69
2.3.5.7 2401/2400, 19683/19600, 29360128/29296875 [332 526 771 932]] 0.0851 0.2412 6.67

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 33\332 119.28 15/14 Septidiasemi
1 75\332 271.08 1024/875 Quasiorwell
1 127\332 459.04 125/96 Majvam
1 143\332 516.87 27/20 Gravity
2 143\332
(23\332)
516.87
(83.13)
27/20
(21/20)
Harry
2 45\332 162.65 1125/1024 Kwazy

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