3edf: Difference between revisions

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== Factoids about 3edf ==
== Factoids about 3edf ==
3edf's step size is close to the [[slendric]] temperament, which tempers out 1029/1024 in the 2.3.7 subgroup.
3edf's step size is close to the [[slendric]] temperament, which tempers out 1029/1024 in the 2.3.7 subgroup. It can be used as a slendric tuning. It also works well as a tuning for


== Intervals ==
{| class="wikitable center-all"
{| class="wikitable center-all"
! #
! #

Revision as of 20:47, 24 May 2025

← 2edf 3edf 4edf →
Prime factorization 3 (prime)
Step size 233.985 ¢ 
Octave 5\3edf (1169.93 ¢)
(convergent)
Twelfth 8\3edf (1871.88 ¢)
(convergent)
Consistency limit 10
Distinct consistency limit 4

3edf, if the attempt is made to use it as an actual scale, would divide the just perfect fifth into three equal parts, each of size 233.985 cents, which is to say (3/2)1/3 as a frequency ratio. It corresponds to 5.1285 edo. If we want to consider it to be a temperament, it tempers out 16/15, 21/20, 28/27, 81/80, and 256/243 as well as 5edo.

Factoids about 3edf

3edf's step size is close to the slendric temperament, which tempers out 1029/1024 in the 2.3.7 subgroup. It can be used as a slendric tuning. It also works well as a tuning for

# Cents Approximate JI Ratios
1 233.99 8/7
2 467.97 55/42
3 701.96 exact 3/2

Music