2edt: Difference between revisions

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'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[27/25]], equating 5/3 with 9/5.

==~~Factoids about 2EDT~~==

== Theory ==

[[26/15]] ~~and 45~~/~~26 are~~ [[~~Nearest just interval|good rational representations~~]] of the ~~square root~~ of 3.

As a temperament in the [[3.5 subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5. Because of this, it is related to the [[bug]] temperament. In fact, removing octaves from the [[bug]] temperament results in a 3.5 interpretation of 2edt.

~~2EDT~~ is ~~closely related to the~~ [[~~Very high accuracy temperaments|monzismic temperament~~]], ~~which~~ tempers out ~~|54 -37~~ 2~~>~~, the ~~monzisma~~.

Since [[26/15]] is a [[convergent]] of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma.

[[~~Category:Edt~~]]

=== Harmonics ===

[[~~Category:Edonoi~~]]

== Relationship to octave temperaments ==

One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[semaphore]] and [[monzismic]].

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 {{Infobox ET}}
-'''2EDT''', if the attempt is made to use it as an actual scale, would divide the [[3/1|tritave]] into two equal parts, each of size 950.9775 cents, which is to say sqrt(3) as a frequency ratio. If we want to consider it to be a temperament, it tempers out [[27/25]], equating 5/3 with 9/5.
+{{ED intro}}
-==Factoids about 2EDT==
+== Theory ==
-[[26/15]] and 45/26 are [[Nearest just interval|good rational representations]] of the square root of 3.
+As a temperament in the [[3.5 subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5. Because of this, it is related to the [[bug]] temperament. In fact, removing octaves from the [[bug]] temperament results in a 3.5 interpretation of 2edt.
-EDT is closely related to the [[Very high accuracy temperaments|monzismic temperament]], which tempers out |54 -37 2&gt;, the monzisma.
+Since [[26/15]] is a [[convergent]] of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma.
-[[Category:Edt]]
+=== Harmonics ===
-[[Category:Edonoi]]
+{{Harmonics in equal|2|3|1|columns = 14}}
+== Relationship to octave temperaments ==
+One step of 2edt can represent the generator for any rank-2 octavated temperament which takes 2 generators to reach the 3rd harmonic, such as [[semaphore]] and [[monzismic]].