Alphatricot family: Difference between revisions

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'''~~Tricot~~''' ~~is a~~ [[~~microtemperament~~]]~~, whose generator is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&70 temperament,~~ tempering out the [[~~tricot~~ comma]], {{monzo| 39 -29 3 }} ~~in the 5-limit~~.

The '''alphatricot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[alphatricot comma]] ({{monzo|legend=1| 39 -29 3 }}, [[ratio]]: 68 719 476 736 000 / 68 630 377 364 883).

There are some mappings for 7-limit extension of this temperament: trimot (53 & 70), trident (53 & 229) and trillium (53 & 441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to trimot, [[6144/6125|porwell comma]] (6144/6125) leads to trident, and [[4375/4374|ragisma]] (4375/4374) leads to trillium.

== ~~Tricot~~ ==

== Alphatricot ==

~~Tricot temperament can be described as 53&70 temperament~~, ~~tempering out~~ the [[~~tricot comma~~]], {{~~monzo~~| ~~39 -29~~ 3 }} in the ~~5-limit~~.

Alphatricot is a [[microtemperament]] whose generator is the real cube root of [[3/1|3rd]] [[harmonic]], 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Its [[ploidacot]] is alpha-tricot. It is a member of the [[schismic–Mercator equivalence continuum]] with {{nowrap|''n'' {{=}} 3 }}, so unless 53edo is used as a tuning, the schisma is always observed.

~~This~~ temperament was named by [[Paul Erlich]] in 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5041.html Yahoo! Tuning Group | ''Paul's new names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.

The temperament was named by [[Paul Erlich]] in 2002 as ''tricot''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5041.html Yahoo! Tuning Group | ''Paul's new names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>, but renamed in 2025 following the specifications of ploidacot.

[[Subgroup]]: 2.3.5

[[Comma list]]: {{monzo| 39 -29 3 }} ~~= 68719476736000/68630377364883~~

[[Comma list]]: {{monzo| 39 -29 3 }}

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=== 2.3.5.13 subgroup ===

''See also [[No-fives subgroup temperaments#Threedic~~]].''~~

Subgroup: 2.3.5.13

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* [[Tricot36]] – improper [[17L 19s]]

== ~~Trimot~~ ==

== Alphatrimot ==

~~Trimot~~, named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, can be described as the 53 & 70 temperament.

Alphatrimot, named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, can be described as the 53 & 70 temperament.

[[Subgroup]]: 2.3.5.7

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Badness: 0.032102

== ~~Trident~~ ==

== Alphatrident ==

~~Trident~~, named by [[Xenllium]] in 2021, can be described as the 53 & 229 temperament.

Alphatrident, named by [[Xenllium]] in 2021, can be described as the 53 & 229 temperament.

[[Subgroup]]: 2.3.5.7

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Badness: 0.046593

== ~~Trillium~~ ==

== Alphatrillium ==

~~Trillium~~, also named by [[Xenllium]] in 2021, can be described as the 53 & 441 temperament.

Alphatrillium, also named by [[Xenllium]] in 2021, can be described as the 53 & 441 temperament.

[[Subgroup]]: 2.3.5.7

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[[Category:Temperament families]]

[[Category:~~Tricot~~ family| ]]

[[Category:Alphatricot family| ]]

[[Category:~~Tricot~~| ]]

[[Category:Alphatricot| ]]

[[Category:Rank 2]]

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-'''Tricot''' is a [[microtemperament]], whose generator is the real cube root of third harmonic, 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Tricot temperament can be described as 53&amp;70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit.
+The '''alphatricot family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[alphatricot comma]] ({{monzo|legend=1| 39 -29 3 }}, [[ratio]]: 68 719 476 736 000 / 68 630 377 364 883).
 There are some mappings for 7-limit extension of this temperament: trimot (53 &amp; 70), trident (53 &amp; 229) and trillium (53 &amp; 441). Tempering out [[5120/5103|hemifamity comma]] (5120/5103) leads to trimot, [[6144/6125|porwell comma]] (6144/6125) leads to trident, and [[4375/4374|ragisma]] (4375/4374) leads to trillium.
-== Tricot ==
+== Alphatricot ==
-Tricot temperament can be described as 53&amp;70 temperament, tempering out the [[tricot comma]], {{monzo| 39 -29 3 }} in the 5-limit.
+Alphatricot is a [[microtemperament]] whose generator is the real cube root of [[3/1|3rd]] [[harmonic]], 3<sup>1/3</sup>, tuned between 63/44 and 13/9. Its [[ploidacot]] is alpha-tricot. It is a member of the [[schismic–Mercator equivalence continuum]] with {{nowrap|''n'' {{=}} 3 }}, so unless 53edo is used as a tuning, the schisma is always observed.
-This temperament was named by [[Paul Erlich]] in 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5041.html Yahoo! Tuning Group | ''Paul's new names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.
+The temperament was named by [[Paul Erlich]] in 2002 as ''tricot''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5041.html Yahoo! Tuning Group | ''Paul's new names'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>, but renamed in 2025 following the specifications of ploidacot.
 [[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| 39 -29 3 }} = 68719476736000/68630377364883
+[[Comma list]]: {{monzo| 39 -29 3 }}
 {{Mapping|legend=1| 1 0 -13 | 0 3 29 }}
@@ Line 25: / Line 25: @@
 === 2.3.5.13 subgroup ===
-''See also [[No-fives subgroup temperaments#Threedic]].''
+{{See also| No-fives subgroup temperaments #Threedic }}
 Subgroup: 2.3.5.13
@@ Line 48: / Line 48: @@
 * [[Tricot36]] – improper [[17L 19s]]
-== Trimot ==
+== Alphatrimot ==
-Trimot, named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, can be described as the 53 & 70 temperament.
+Alphatrimot, named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, can be described as the 53 & 70 temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 91: / Line 91: @@
 Badness: 0.032102
-== Trident ==
+== Alphatrident ==
-Trident, named by [[Xenllium]] in 2021, can be described as the 53 & 229 temperament.
+Alphatrident, named by [[Xenllium]] in 2021, can be described as the 53 & 229 temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 134: / Line 134: @@
 Badness: 0.046593
-== Trillium ==
+== Alphatrillium ==
-Trillium, also named by [[Xenllium]] in 2021, can be described as the 53 & 441 temperament.
+Alphatrillium, also named by [[Xenllium]] in 2021, can be described as the 53 & 441 temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 342: / Line 342: @@
 [[Category:Temperament families]]
-[[Category:Tricot family| ]] <!-- main article -->
+[[Category:Alphatricot family| ]] <!-- main article -->
-[[Category:Tricot| ]] <!-- key article -->
+[[Category:Alphatricot| ]] <!-- key article -->
 [[Category:Rank 2]]