2edt: Difference between revisions

(7 intermediate revisions by 6 users not shown)

Line 1:

=== Theory ===

== Theory ==

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.

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.

~~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.~~

=== Harmonics ===

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.~~

== 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]].

~~===Odd harmonics===~~

~~{{Harmonics in equal|2|3|1|intervals=odd}}~~

[[~~Category:Edt~~]]

[[~~Category:Edonoi~~]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
-=== Theory ===
+== Theory ==
+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.
-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.
-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.
+=== Harmonics ===
+{{Harmonics in equal|2|3|1|columns = 14}}
-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.
+== 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]].
-===Odd harmonics===
-{{Harmonics in equal|2|3|1|intervals=odd}}
-[[Category:Edt]]
-[[Category:Edonoi]]