Temperament families and clans: Difference between revisions

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{{Beginner|Subgroup temperament families, relationships, and genes}}

'''Temperament families''' and '''clans''' are ways to organize [[regular temperament]]s. Two temperaments are in the same ~~'''~~clan~~'''~~ if there is some [[subgroup]] in which both temperaments temper out the same single comma (which defines the clan). Each clan has a parent temperament, which is the temperament in the given subgroup in which precisely that comma is tempered out; this implies all temperaments in a clan must be of the same [[rank]] as each other and the parent temperament. (For example, the parent of the archytas clan is 2.3.7 archy, tempering out [[64/63]] in the [[2.3.7 subgroup]], and all rank-2 temperaments which temper out 64/63 in 2.3.7 are part of the archytas clan) A special case of clans are ~~'''~~families~~'''~~, where the common subgroup is a prime limit (2.3.5 for a rank-2 temperament, for example). ~~(Note that~~ a family is usually not called a clan.)

'''Temperament families''' and '''clans''' are ways to organize [[regular temperament]]s. Two temperaments are in the same clan if there is some [[subgroup]] in which both temperaments [[tempering out|temper out]] the same single [[comma]], which defines the clan. Each clan has a parent temperament, which is the temperament in the given subgroup in which precisely that comma is tempered out; this implies all temperaments in a clan must be of the same [[rank]] as each other and the parent temperament. (For example, the parent of the archytas clan is 2.3.7 archy, tempering out [[64/63]] in the [[2.3.7 subgroup]], and all rank-2 temperaments which temper out 64/63 in 2.3.7 are part of the archytas clan)

A special case of clans are families, where the common subgroup is a [[prime limit]] (2.3.5 for a rank-2 temperament, for example). However, a family is usually not called a clan.

Besides families and clans, there are pages that collect temperaments of a certain comma on this wiki. These pages are for temperaments one rank lower than its corresponding family, and are used because some temperaments are more closely associated with the comma than any other or otherwise do not belong to any notable family or clan.

For example, [[porky]] and [[porcupinefish]] are both in the [[porcupine family]], because they have a common 5-limit structure in which only the porcupine comma [[250/243]] is tempered out, which is equivalent to 5-limit [[porcupine]] temperament. In other words, they are both extensions of 2.3.5 porcupine (and in fact of 2.3.5.11 porkypine).

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== See also ==

* [[Tour of ~~Regular Temperaments~~]]

* [[Tour of regular temperaments]]

* [[:Category:Temperament families]]

* [[:Category: Temperament families]]

* [[:Category:Temperament clans]]

* [[:Category: Temperament clans]]

* [[:Category: Temperament collections]]

~~{{todo|inline=1|expand}}~~

[[Category:Regular temperament theory]]

[[Category:Temperament families| ]]

[[Category:Temperament clans| ]]

[[Category:Temperament collections| ]]

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 {{Beginner|Subgroup temperament families, relationships, and genes}}
-'''Temperament families''' and '''clans''' are ways to organize [[regular temperament]]s. Two temperaments are in the same '''clan''' if there is some [[subgroup]] in which both temperaments temper out the same single comma (which defines the clan). Each clan has a parent temperament, which is the temperament in the given subgroup in which precisely that comma is tempered out; this implies all temperaments in a clan must be of the same [[rank]] as each other and the parent temperament. (For example, the parent of the archytas clan is 2.3.7 archy, tempering out [[64/63]] in the [[2.3.7 subgroup]], and all rank-2 temperaments which temper out 64/63 in 2.3.7 are part of the archytas clan) A special case of clans are '''families''', where the common subgroup is a prime limit (2.3.5 for a rank-2 temperament, for example). (Note that a family is usually not called a clan.)
+'''Temperament families''' and '''clans''' are ways to organize [[regular temperament]]s. Two temperaments are in the same clan if there is some [[subgroup]] in which both temperaments [[tempering out|temper out]] the same single [[comma]], which defines the clan. Each clan has a parent temperament, which is the temperament in the given subgroup in which precisely that comma is tempered out; this implies all temperaments in a clan must be of the same [[rank]] as each other and the parent temperament. (For example, the parent of the archytas clan is 2.3.7 archy, tempering out [[64/63]] in the [[2.3.7 subgroup]], and all rank-2 temperaments which temper out 64/63 in 2.3.7 are part of the archytas clan)
+A special case of clans are families, where the common subgroup is a [[prime limit]] (2.3.5 for a rank-2 temperament, for example). However, a family is usually not called a clan.
+Besides families and clans, there are pages that collect temperaments of a certain comma on this wiki. These pages are for temperaments one rank lower than its corresponding family, and are used because some temperaments are more closely associated with the comma than any other or otherwise do not belong to any notable family or clan.
 For example, [[porky]] and [[porcupinefish]] are both in the [[porcupine family]], because they have a common 5-limit structure in which only the porcupine comma [[250/243]] is tempered out, which is equivalent to 5-limit [[porcupine]] temperament. In other words, they are both extensions of 2.3.5 porcupine (and in fact of 2.3.5.11 porkypine).
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 == See also ==
-* [[Tour of Regular Temperaments]]
+* [[Tour of regular temperaments]]
-* [[:Category:Temperament families]]
+* [[:Category: Temperament families]]
-* [[:Category:Temperament clans]]
+* [[:Category: Temperament clans]]
+* [[:Category: Temperament collections]]
-{{todo|inline=1|expand}}
 [[Category:Regular temperament theory]]
 [[Category:Temperament families| ]] <!-- Main article -->
 [[Category:Temperament clans| ]] <!-- Main article -->
+[[Category:Temperament collections| ]] <!-- Main article -->