Ploidacot/Triploid monocot: Difference between revisions
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{{Breadcrumb}}{{Infobox ploidacot|Ploids=3|Shears=0|Cots=1|Pergen=[P8/3, P5]|Forms=9, 12, 15, 27|Title=Triploid monocot|Wedgie=3}} | {{Breadcrumb}}{{Infobox ploidacot|Ploids=3|Shears=0|Cots=1|Pergen=[P8/3, P5]|Forms=9, 12, 15, 27|Title=Triploid monocot|Wedgie=3}} | ||
'''Triploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is 1/3 of a [[2/1]] octave, or 400{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{2\sqrt[3]{4}}{3}</math>. Triploid monocot temperaments usually generate the [[3L 6s]] MOS structure and either [[3L 9s]] (and thus [[12L 3s]]) or [[9L 3s]] as children. | '''Triploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is 1/3 of a [[2/1]] octave, or 400{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{2\sqrt[3]{4}}{3}</math>. Triploid monocot temperaments usually generate the [[3L 6s]] MOS structure and either [[3L 9s]] (and thus [[12L 3s]]) or [[9L 3s]] (when the fifth is flatter than [[12edo|7\12]]) as children. | ||
== Intervals and notation == | == Intervals and notation == | ||
While there is no agreed-upon notation system for triploid monocot, the following is based on interpreting the generator as a semitone (1/3 of a minor third), allowing for an ^ or v to stand for 1/3 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]), so vvC# and ^Db are enharmonic. | While there is no agreed-upon notation system for triploid monocot, the following is based on interpreting the generator as a semitone (1/3 of a minor third), allowing for an ^ or v to stand for 1/3 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]), so vvC# and ^Db are enharmonic. | ||
{| class="wikitable" | {| class="wikitable center-1 right-2 right-5 right-8" | ||
|+ style="font-size: 105%;" | Triploid monocot intervals (assuming pure fifth and octave) | |+ style="font-size: 105%;" | Triploid monocot intervals (assuming pure fifth and octave) | ||
|- | |- | ||
| Line 90: | Line 90: | ||
|- | |- | ||
| 0 | | 0 | ||
| 0 | | 0.00 | ||
| C | | C | ||
| unison | | unison | ||
| 400 | | 400.00 | ||
| vE | | vE | ||
| — | | — | ||
| 800 | | 800.00 | ||
| ^Ab | | ^Ab | ||
| — | | — | ||
| Line 174: | Line 174: | ||
=== Augmented === | === Augmented === | ||
[[Augmented family|Augmented]] sets [[5/4]] as a period, and uses a fifth as a free generator. There are some extensions for 7-limit: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9). In the 11-limit, these extensions equate 5/4 and [[14/11]] as a period. | [[Augmented family|Augmented]] sets [[5/4]] as a period, and uses a fifth as a free generator. There are some extensions for 7-limit: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9). In the 11-limit, these extensions equate 5/4 and [[14/11]] as a period. | ||