Ploidacot/Tricot: Difference between revisions
Created page with "'''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. == Notation == While there is no agreed-upon notation system for tricot, the following is based on..." |
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'''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. | {{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=0|Cots=3|Pergen=[P8, P5/3]|Forms=5, 11, 16|Title=Tricot}}'''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. | ||
== Notation == | == Notation == | ||
While there is no agreed-upon notation system for tricot, the following is based on interpreting the generator as a supermajor second. ^^C and | While there is no agreed-upon notation system for tricot, the following is based on interpreting the generator as a supermajor second. ^^C and vDb are enharmonic. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Tricot intervals (assuming pure fifth and octave) | |+Tricot intervals (assuming pure fifth and octave) | ||
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==== 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. | ||
{{Todo| unify precision }} | |||
Latest revision as of 00:22, 2 September 2025
| Pergen | [P8, P5/3] |
| Numeral form | 3-cot |
| Pure generator size | 233.98 ¢ |
| Pure period size | 1200 ¢ |
| Forms | 5, 11, 16 |
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.
Notation
While there is no agreed-upon notation system for tricot, the following is based on interpreting the generator as a supermajor second. ^^C and vDb are enharmonic.
| # | 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 / perfect octave |
| 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 |
| 8 | 671.88 | vG | subfifth |
| 9 | 905.865 | A | major sixth |
A notable feature of tricot is the small diesis encountered after 5 steps. This makes tricot scales cluster around 5edo.
Temperament interpretations
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.
Mothra
Mothra is an extension to slendric which tempers out the syntonic comma, flattening the 3/2 further so that the major third is 5/4.
Rodan
Rodan is an extension to slendric which finds 5/4 at 17 generators up, or the submajor third in the notation provided.