3edt: Difference between revisions
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a lot of temperaments have 3/1 reached in 3 generators, elaborate |
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'''3EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1|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]]. | '''3EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1|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 [[Nearest just interval|good rational representation]] of the cube root of 3. | 75/52 is a [[Nearest just interval|good rational representation]] of the cube root of 3. | ||
3EDT is closely related to the [[ | == 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 === | |||
* [[Liese]] | |||
* [[Triton]] | |||
* [[Tricot]] | |||
=== Fractional-octave temperaments === | |||
* [[Augene]], [[augmented]], [[august]] - can be seen as a superset of [[3edo]] and 3edt | |||
* [[Soviet ferris wheel]] - [[20edo]] and 3edt | |||
* [[Akjayland]] - [[21edo]] and 3edt | |||
* [[Oganesson]] - [[118edo]] and 3edt | |||
[[Category:Edt]] | [[Category:Edt]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 13:44, 24 May 2023
| ← 2edt | 3edt | 4edt → |
(convergent)
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.