2edt: Difference between revisions

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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.
+{{EDO intro}}
-==Factoids about 2EDT==
+=== Theory ===
-[[26/15]] and 45/26 are [[Nearest just interval|good rational representations]] of the square root of 3.
-EDT is closely related to the [[Very high accuracy temperaments|monzismic temperament]], which tempers out |54 -37 2&gt;, the monzisma.
+As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5.
+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.
+One step of 2edt is close to the optimal TE generator of [[Very high accuracy temperaments|monzismic temperament]], which tempers out {{monzo|54 -37 2}}, the monzisma.
+===Odd harmonics===
+{{Harmonics in equal|2|3|1|intervals=odd}}
 [[Category:Edt]]
 [[Category:Edonoi]]