Ploidacot/Alpha-tricot: Difference between revisions
Created page with "'''Alpha-tricot''' is a temperament archetype where the generator is a wide tritone of about 625-640 cents, three of which stack to form a perfect twelfth of 3/1, and the period is a 2/1 octave. Alpha-tricot temperaments generate the 2L 5s, 2L 7s, and 2L 9s MOS structures. Alpha-tricot temperaments split the diatonic whole tone into three equal parts, producing both supermajor/subminor and supraminor/submajor intervals. == Intervals and notation == T..." |
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'''Alpha-tricot''' is a temperament archetype where the generator is a wide tritone of about 625-640 cents, three of which stack to form a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Alpha-tricot temperaments generate the [[2L 5s]], [[2L 7s]], and [[2L 9s]] MOS structures. Alpha-tricot temperaments split the diatonic whole tone into three equal parts, producing both supermajor/subminor and supraminor/submajor intervals. | {{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=1|Cots=3|Pergen=[P8, P11/3]|Forms=5, 7, 12|Title=Alpha-tricot}}'''Alpha-tricot''' is a temperament archetype where the generator is a wide tritone of about 625-640 cents, three of which stack to form a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Alpha-tricot temperaments generate the [[2L 5s]], [[2L 7s]], and [[2L 9s]] MOS structures. Alpha-tricot temperaments split the diatonic whole tone into three equal parts, producing both supermajor/subminor and supraminor/submajor intervals. | ||
== Intervals and notation == | == Intervals and notation == | ||
| Line 13: | Line 13: | ||
|- | |- | ||
| -9 | | -9 | ||
|294. | |294.14 | ||
|Eb | |Eb | ||
|minor third | |minor third | ||
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|- | |- | ||
| -7 | | -7 | ||
|362. | |362.11 | ||
|vE | |vE | ||
|submajor third | |submajor third | ||
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|- | |- | ||
| -5 | | -5 | ||
|430. | |430.08 | ||
|^Fb | |^Fb | ||
|supradiminished fourth | |supradiminished fourth | ||
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|- | |- | ||
| -3 | | -3 | ||
|498. | |498.05 | ||
|F | |F | ||
|perfect fourth | |perfect fourth | ||
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|- | |- | ||
| -1 | | -1 | ||
|566. | |566.02 | ||
|vF# | |vF# | ||
|subaugmented fourth | |subaugmented fourth | ||
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|- | |- | ||
|1 | |1 | ||
|633. | |633.99 | ||
|^Gb | |^Gb | ||
|supradiminished fifth | |supradiminished fifth | ||
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|- | |- | ||
|3 | |3 | ||
|701. | |701.96 | ||
|G | |G | ||
|perfect fifth | |perfect fifth | ||
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|- | |- | ||
|5 | |5 | ||
|769. | |769.93 | ||
|vG# | |vG# | ||
|subaugmented fifth | |subaugmented fifth | ||
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|- | |- | ||
|7 | |7 | ||
|837. | |837.9 | ||
|^Ab | |^Ab | ||
|supraminor sixth | |supraminor sixth | ||
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|- | |- | ||
|9 | |9 | ||
|905. | |905.87 | ||
|A | |A | ||
|major sixth | |major sixth | ||
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Any valid alpha-tricot temperament assigns a just interpretation to the individual generator. | Any valid alpha-tricot temperament assigns a just interpretation to the individual generator. | ||
=== Alphatricot === | === [[Alphatricot]] === | ||
Formerly inaccurately just called "tricot", this is a 5-limit microtemperament with the alpha-tricot structure (hence its name). In the 2.3.5.13 interpretation, the generator is 13/9, and 5/4 is found at ''29'' generators up, the submajor third in the "superaugmented fourth" notation. As a microtemperament, it is tuned best when the fifth is around just. | Formerly inaccurately just called "tricot", this is a 5-limit microtemperament with the alpha-tricot structure (hence its name). In the 2.3.5.13 interpretation, the generator is 13/9, and 5/4 is found at ''29'' generators up, the submajor third in the "superaugmented fourth" notation. As a microtemperament, it is tuned best when the fifth is around just. | ||
=== Liese === | === Liese === | ||
Liese identifies the generator with 10/7. To extend to the full 7-limit, the meantone mapping of 5 is used (12 generators or 4 fifths up), which has the benefit of flattening the fifth to make the 10/7 more accurate. | [[Liese]] identifies the generator with 10/7. To extend to the full 7-limit, the meantone mapping of 5 is used (12 generators or 4 fifths up), which has the benefit of flattening the fifth to make the 10/7 more accurate. | ||
=== 12288/12167 === | === 12288/12167 === | ||
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=== Paralimmal === | === Paralimmal === | ||
Paralimmal maps the generator to 16/11, meaning it is best tuned with a sharpened fifth (around 715-720 cents or so). | [[Paralimmal]] maps the generator to 16/11, meaning it is best tuned with a sharpened fifth (around 715-720 cents or so). | ||
{{Todo| unify precision }} | |||