Just intonation subgroup: Difference between revisions

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A prime subgroup that does not omit any primes < ''p'' (e.g. 2.3.5, 2.3.5.7, 2.3.5.7.11, etc. but not 2.3.7 or 3.5.7) is simply called [[Harmonic limit|''p''-limit JI]]. It is customary of just intonation subgroups to refer only to prime subgroups that do omit such primes, as well as the other two categories.

The following terminology has been proposed for streamlining pedagogy: Given a subgroup written as generated by a fixed (non-redundant) set: ''a''.''b''.''c''.[…].''d'', call any member of this set a '''basis element''', '''structural prime''', or '''formal prime'''.<ref>The meaning of "formal" this term is using is "of external form or structure, rather than nature or content", which is to say that a formal prime is not necessarily ''actually'' a prime, but we treat them as if they were. The original coiner of this term, [[Inthar]], has recommended its disuse, in favor of the mathematically accurate and generic "basis element", or possibly something else which indicates the co-uniqueness of the elements.</ref> For example, if the group is written 2.5/3.7/3, the basis elements are 2, 5/3 and 7/3.

The following terminology has been proposed for streamlining pedagogy: Given a subgroup written as generated by a fixed (non-redundant) set: ''a''.''b''.''c''.[…].''d'', call any member of this set a '''basis element''', '''structural prime''', or "'''formal prime'''".<ref>The meaning of "formal" this term is using is "of external form or structure, rather than nature or content", which is to say that a formal prime is not necessarily ''actually'' a prime, but we treat them as if they were. The original coiner of this term, [[Inthar]], has recommended its disuse, in favor of the mathematically accurate and generic "basis element", or possibly something else which indicates the co-uniqueness of the elements.</ref> For example, if the group is written 2.5/3.7/3, the basis elements are 2, 5/3 and 7/3.

== Normalization ==

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 A prime subgroup that does not omit any primes < ''p'' (e.g. 2.3.5, 2.3.5.7, 2.3.5.7.11, etc. but not 2.3.7 or 3.5.7) is simply called [[Harmonic limit|''p''-limit JI]]. It is customary of just intonation subgroups to refer only to prime subgroups that do omit such primes, as well as the other two categories.
-The following terminology has been proposed for streamlining pedagogy: Given a subgroup written as generated by a fixed (non-redundant) set: ''a''.''b''.''c''.[…].''d'', call any member of this set a '''basis element''', '''structural prime''', or '''formal prime'''.<ref>The meaning of "formal" this term is using is "of external form or structure, rather than nature or content", which is to say that a formal prime is not necessarily ''actually'' a prime, but we treat them as if they were. The original coiner of this term, [[Inthar]], has recommended its disuse, in favor of the mathematically accurate and generic "basis element", or possibly something else which indicates the co-uniqueness of the elements.</ref> For example, if the group is written 2.5/3.7/3, the basis elements are 2, 5/3 and 7/3.
+The following terminology has been proposed for streamlining pedagogy: Given a subgroup written as generated by a fixed (non-redundant) set: ''a''.''b''.''c''.[…].''d'', call any member of this set a '''basis element''', '''structural prime''', or "'''formal prime'''".<ref>The meaning of "formal" this term is using is "of external form or structure, rather than nature or content", which is to say that a formal prime is not necessarily ''actually'' a prime, but we treat them as if they were. The original coiner of this term, [[Inthar]], has recommended its disuse, in favor of the mathematically accurate and generic "basis element", or possibly something else which indicates the co-uniqueness of the elements.</ref> For example, if the group is written 2.5/3.7/3, the basis elements are 2, 5/3 and 7/3.
 == Normalization ==