Half-prime subgroup: Difference between revisions
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They correspond to [[EDF]]s if used as a rank-1 tempered systems. | They correspond to [[EDF]]s if used as a rank-1 tempered systems. | ||
== Generalizations == | == Generalizations == | ||
Half-prime subgroups can be generalized for other denominators, such as to third-prime subgroups (5/3.7/3.11/3.13/3..., which are suitable for [[5/3]] as the equave), or "quarter-prime subgroups" (5/4.7/4.11/4.13/4..., which are suitable for [[5/4]] as the equave). They can also be restricted to remove 3/2 for usage in [[Ed5/2]] systems. | Half-prime subgroups can be generalized for other denominators, such as to third-prime subgroups (5/3.7/3.11/3.13/3..., which are suitable for [[5/3]] as the equave), or "quarter-prime subgroups" (5/4.7/4.11/4.13/4..., which are suitable for [[5/4]] as the equave). They can also be restricted to remove 3/2 for usage in [[Ed5/2]] systems. | ||
If numerators are allowed to be composite numbers as well as primes in a subgroup, then it could be called half-basis subgroups{{idiosyncratic}}, third basis subgroups{{idiosyncratic}}, quarter basis subgroups{{idiosyncratic}}, etc. Because "[[basis element]]s" is the generalized form of "primes" in a subgroup. | |||
== Harmony == | == Harmony == | ||
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* [[Subgroup temperament]] | * [[Subgroup temperament]] | ||
* [[Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma]] | * [[Carlos Alpha]], [[Carlos Beta]], [[Carlos Gamma]] | ||
* [[Basal subgroup]] | |||
[[Category:Subgroup]] | [[Category:Subgroup]] | ||
[[Category:Just intonation]] | [[Category:Just intonation]] | ||