Ploidacot/Alpha-dicot: Difference between revisions
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{{Breadcrumb}} | {{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=1|Cots=2|Pergen=[P8, P4/2]|Forms=5, 9, 14|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' means the same thing and is unused. | ||
'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' means the same thing and is unused. | |||
Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals. | Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals. | ||
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|minor third | |minor third | ||
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|perfect fourth | |perfect fourth | ||
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|perfect fifth | |perfect fifth | ||
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|A | |A | ||
|major sixth | |major sixth | ||
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=== Barbados === | === Barbados === | ||
Here, the generator actually is 26/15, equated with [[45/26]]. This is | Here, the generator actually is 26/15, equated with [[45/26]]. This is an accurate temperament, tempering out the unnoticeable comma of [[676/675]], but it is defined in the awkward 2.3.13/5 subgroup. The semifourth here is [[15/13]][[~]][[52/45]]. | ||
As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth. | As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth. | ||
{{Todo| unify precision }} | {{Todo| unify precision }} | ||