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 | ! Cents | ||
!Name | ! Notation | ||
! Name | |||
|- | |- | ||
| | | −9 | ||
|294.135 | | 294.135 | ||
|Eb | | Eb | ||
|minor third | | minor third | ||
|- | |- | ||
| | | −8 | ||
|528.12 | | 528.12 | ||
|^F | | ^F | ||
|superfourth | | superfourth | ||
|- | |- | ||
| | | −7 | ||
|762.105 | | 762.105 | ||
|vAb | | vAb | ||
|subminor sixth | | subminor sixth | ||
|- | |- | ||
| | | −6 | ||
|996.09 | | 996.09 | ||
|Bb | | Bb | ||
|minor seventh | | minor seventh | ||
|- | |- | ||
| | | −5 | ||
|30.075 | | 30.075 | ||
|^C | | ^C | ||
|superunison | | superunison | ||
|- | |- | ||
| | | −4 | ||
|264.06 | | 264.06 | ||
|vEb | | vEb | ||
|subminor third | | subminor third | ||
|- | |- | ||
| | | −3 | ||
|498.045 | | 498.045 | ||
|F | | F | ||
|perfect fourth | | perfect fourth | ||
|- | |- | ||
| | | −2 | ||
|732.03 | | 732.03 | ||
|^G | | ^G | ||
|superfifth | | superfifth | ||
|- | |- | ||
| | | −1 | ||
|966.015 | | 966.015 | ||
|vBb | | vBb | ||
|subminor seventh | | subminor seventh | ||
|- | |- | ||
|0 | | 0 | ||
|0 | | 0 | ||
|C | | C | ||
|perfect unison | | perfect unison | ||
|- | |- | ||
|1 | | 1 | ||
|233.985 | | 233.985 | ||
|^D | | ^D | ||
|supermajor second | | supermajor second | ||
|- | |- | ||
|2 | | 2 | ||
|467.97 | | 467.97 | ||
|vF | | vF | ||
|subfourth | | subfourth | ||
|- | |- | ||
|3 | | 3 | ||
|701.955 | | 701.955 | ||
|G | | G | ||
|perfect fifth | | perfect fifth | ||
|- | |- | ||
|4 | | 4 | ||
|935.94 | | 935.94 | ||
|^A | | ^A | ||
|supermajor sixth | | supermajor sixth | ||
|- | |- | ||
|5 | | 5 | ||
|1169.925 | | 1169.925 | ||
|vC | | vC | ||
|suboctave | | suboctave | ||
|- | |- | ||
|6 | | 6 | ||
|203.91 | | 203.91 | ||
|D | | D | ||
|major second | | major second | ||
|- | |- | ||
|7 | | 7 | ||
|437.895 | | 437.895 | ||
|^E | | ^E | ||
|supermajor third | | supermajor third | ||
|- | |- | ||
|8 | | 8 | ||
|671.88 | | 671.88 | ||
|vG | | vG | ||
|subfifth | | subfifth | ||
|- | |- | ||
|9 | | 9 | ||
|905.865 | | 905.865 | ||
|A | | A | ||
|major sixth | | 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. | ||
==== Mothra ==== | ==== Mothra ==== | ||
Mothra is an extension to slendric which tempers out the syntonic comma, flattening the | [[Mothra]] is an extension to slendric which tempers out [[81/80|the syntonic comma]], flattening the 3/2 further so that the major third is [[5/4]]. | ||
==== Rodan ==== | ==== Rodan ==== | ||
Rodan is an extension to slendric which finds 5/4 at 17 generators up, or the submajor third in the notation provided. | [[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]]. | |||