Ploidacot/Alpha-dicot: Difference between revisions
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{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=1|Cots=2|Pergen=[P8, P4/2]|Forms=5, 9, 14, 19|Title=Alpha | {{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=1|Cots=2|Pergen=[P8, P4/2]|Forms=5, 9, 14, 19|Title=Alpha-dicot|Wedgie=2}}'''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''' would mean the same thing. However, the preferred term is alpha-dicot. | ||
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. | ||
== Intervals and notation == | == Intervals and notation == | ||
Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[ | Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]). | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 30: | Line 30: | ||
|- | |- | ||
| −6 | | −6 | ||
| 294. | | 294.13 | ||
| Eb | | Eb | ||
| minor third | | minor third | ||
| Line 50: | Line 50: | ||
|- | |- | ||
| −2 | | −2 | ||
| 498. | | 498.04 | ||
| F | | F | ||
| perfect fourth | | perfect fourth | ||
| Line 105: | Line 105: | ||
|- | |- | ||
| 9 | | 9 | ||
| 158. | | 158.80 | ||
| | | | ||
| | | | ||
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=== Bug === | === Bug === | ||
[[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the | [[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the simplest (arguably) reasonable 5-limit interpretation of this ploidacot. | ||
The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]]. | The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]]. | ||
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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. | ||
[[Category:Ploidacots|Alpha-dicot]] | |||