Ploidacot/Tricot: Difference between revisions
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{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=0|Cots=3|Pergen=[P8, P5/3]|Forms= | {{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=0|Cots=3|Pergen=[P8, P5/3]|Forms=11, 16, 21, 26|Title=Tricot|Wedgie=3}}'''Tricot''' is a temperament archetype where the generator is a supermajor second, three of which stack to form a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Tricot temperaments usually generate the [[5L 1s]] and [[5L 6s]] MOS structures. Tricot temperaments produce "supermajor" and "subminor" intervals, splitting the diatonic semitone into three parts. | ||
== Intervals and notation == | |||
While there is no agreed-upon notation system for tricot, the following is based on interpreting the generator as a supermajor second, allowing for an ^ or v to stand for 1/3 of a diatonic semitone, so ^^C and vDb are enharmonic. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+Tricot intervals (assuming pure fifth and octave) | |+ style="font-size: 105%;" | Tricot intervals (assuming pure fifth and octave) | ||
|- | |- | ||
! # | |||
! Cents | |||
! Notation | |||
! Name | |||
|- | |- | ||
| | | −9 | ||
| | | 294.135 | ||
| | | Eb | ||
| | | minor third | ||
|- | |- | ||
| | | −8 | ||
| | | 528.12 | ||
| | | ^F | ||
| | | superfourth | ||
|- | |- | ||
| | | −7 | ||
| | | 762.105 | ||
| | | vAb | ||
| | | subminor sixth | ||
|- | |- | ||
| | | −6 | ||
| | | 996.09 | ||
| | | Bb | ||
| | | minor seventh | ||
|- | |- | ||
| | | −5 | ||
| | | 30.075 | ||
| | | ^C | ||
| | | superunison | ||
|- | |- | ||
| | | −4 | ||
| | | 264.06 | ||
| | | vEb | ||
| | | subminor third | ||
|- | |- | ||
| | | −3 | ||
| | | 498.045 | ||
| | | F | ||
| | | perfect fourth | ||
|- | |- | ||
| | | −2 | ||
| | | 732.03 | ||
| | | ^G | ||
| | | superfifth | ||
|- | |- | ||
| | | −1 | ||
| | | 966.015 | ||
| | | vBb | ||
| | | subminor seventh | ||
|- | |- | ||
| | | 0 | ||
| | | 0 | ||
| | | C | ||
| | | perfect unison | ||
|- | |- | ||
| | | 1 | ||
| | | 233.985 | ||
| | | ^D | ||
| | | supermajor second | ||
|- | |- | ||
| | | 2 | ||
| | | 467.97 | ||
| | | vF | ||
| | | subfourth | ||
|- | |- | ||
| | | 3 | ||
| | | 701.955 | ||
| | | G | ||
| | | perfect fifth | ||
|- | |- | ||
| | | 4 | ||
| | | 935.94 | ||
| | | ^A | ||
| | | supermajor sixth | ||
|- | |- | ||
| | | 5 | ||
| | | 1169.925 | ||
| | | vC | ||
| | | suboctave | ||
|- | |- | ||
| | | 6 | ||
| | | 203.91 | ||
| | | D | ||
| | | major second | ||
|- | |- | ||
| | | 7 | ||
| | | 437.895 | ||
| | | ^E | ||
| | | supermajor third | ||
|- | |- | ||
|9 | | 8 | ||
|905.865 | | 671.88 | ||
|A | | vG | ||
|major sixth | | subfifth | ||
|- | |||
| 9 | |||
| 905.865 | |||
| A | |||
| major sixth | |||
|} | |} | ||
A notable feature of tricot is the small diesis, known as the [[quark]], encountered after 5 steps, which represents one-third of a [[diatonic semitone]]. This makes tricot scales cluster around [[5edo]]. | A notable feature of tricot is the small diesis, known as the [[quark]], encountered after 5 steps, which represents one-third of a [[diatonic semitone]]. This makes tricot scales cluster around [[5edo]]. | ||
== Temperament interpretations == | == Temperament interpretations == | ||
=== Slendric === | === Slendric === | ||
[[Slendric]] is the most obvious [[7-limit]] interpretation of tricot, where the generator is [[8/7]] and three of them stack to make [[3/2]]. It is best tuned with a slightly flattened 3/2, or equivalently a slightly sharpened 8/7, but the just tuning of either works. | [[Slendric]] is the most obvious [[7-limit]] interpretation of tricot, where the generator is [[8/7]] and three of them stack to make [[3/2]]. It is best tuned with a slightly flattened 3/2, or equivalently a slightly sharpened 8/7, but the just tuning of either works. | ||
| Line 118: | Line 120: | ||
[[Rodan]] is an extension to slendric which finds 5/4 at 17 generators up, or the submajor third in the notation provided, and is tuned with a slightly sharpened fifth. | [[Rodan]] is an extension to slendric which finds 5/4 at 17 generators up, or the submajor third in the notation provided, and is tuned with a slightly sharpened fifth. | ||
==== Guiron ==== | |||
[[Guiron]] is an extension to slendric which finds 5/4 at 24 generators down (diminished fourth), tempering out the [[schisma]]. | |||
[[Category:Ploidacots|Tricot]] | |||