2edt: Difference between revisions

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Mitigate the silly trivial statements. Switch to integer harmonics for the table
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== Theory ==
== Theory ==
As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5.
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.


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.
=== Harmonics ===
{{Harmonics in equal|2|3|1}}


===Odd harmonics===
== Relationship to octave temperaments ==
{{Harmonics in equal|2|3|1|intervals=odd}}
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 [[monzismic]].


[[Category:Edt]]
[[Category:Edt]]
[[Category:Edonoi]]
[[Category:Edonoi]]