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. A temperament family ~~starts with~~ a ~~full~~ [[~~Harmonic limit|prime~~-limit]] ~~temperament~~ which [[~~Tempering out|tempers out~~]] ~~only one~~ [[~~comma~~]], and ~~includes~~ [[~~extension~~]]~~s of it~~. ~~A temperament clan is similar~~ to ~~a temperament family but it starts with a~~ [[~~subgroup~~]] ~~temperament instead~~.

'''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. (For example, the parent of the archytas clan is 2.3.7 archy, tempering out 64/63 in the 2.3.7 subgroup.) 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.)

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).

[[Ultrapyth]] and superpyth are both in the [[archytas clan]], because they have a common 2.3.7 structure equivalent to [[archy]], as they both temper out 64/63 in the 2.3.7 subgroup. In other words, they are both extensions of 2.3.7 archy.

== See also ==

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 {{Beginner|Subgroup temperament families, relationships, and genes}}
-'''Temperament families''' and '''clans''' are ways to organize [[regular temperament]]s. A temperament family starts with a full [[Harmonic limit|prime-limit]] temperament which [[Tempering out|tempers out]] only one [[comma]], and includes [[extension]]s of it. A temperament clan is similar to a temperament family but it starts with a [[subgroup]] temperament instead.
+'''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. (For example, the parent of the archytas clan is 2.3.7 archy, tempering out 64/63 in the 2.3.7 subgroup.) 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.)
+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).
+[[Ultrapyth]] and superpyth are both in the [[archytas clan]], because they have a common 2.3.7 structure equivalent to [[archy]], as they both temper out 64/63 in the 2.3.7 subgroup. In other words, they are both extensions of 2.3.7 archy.
 == See also ==