2edt: Difference between revisions
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== Theory == | == Theory == | ||
As a temperament in the 3.5 | 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. | ||
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 === | ||
{{Harmonics in equal|2|3|1}} | {{Harmonics in equal|2|3|1|columns = 14}} | ||
== Relationship to octave temperaments == | == 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 [[ | 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]]. | ||
[[ | |||