3edt

From Xenharmonic Wiki
Revision as of 13:44, 24 May 2023 by Eliora (talk | contribs) (a lot of temperaments have 3/1 reached in 3 generators, elaborate)
Jump to navigation Jump to search
← 2edt 3edt 4edt →
Prime factorization 3 (prime)
Step size 633.985 ¢ 
Octave 2\3edt (1267.97 ¢)
(convergent)
Consistency limit 4
Distinct consistency limit 3

3EDT, if the attempt is made to use it as an actual scale, would divide the tritave into three equal parts, each of size 633.9850 cents, which is to say 3^(1/3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out 9/8 as well as 2edo.

Theory

75/52 is a good rational representation of the cube root of 3.

Relationship to octave temperaments

3EDT is closely related to any rank-2 octavated temperament which takes 3 generators to reach the 3rd harmonic, of which there's a notable amount of.

Simple octave temperaments

Fractional-octave temperaments