Half-prime subgroup: Difference between revisions

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'''Half-prime subgroups''' are a family of [[nonoctave]] [[just intonation subgroup]]s where the basis elements are the halves of primes (3/2, 5/2, 7/2, 11/2 and etc.), rather than the primes themselves. Similar to hown[[o-twos subgroup]]s are usually considered with a period of [[3/1]], half-prime subgroups can be considered with a period of [[3/2]] or more complexly [[5/2]], so present a possible JI interpretation of [[EDF]]s and [[Ed5/2]]s. They were first considered by [[User:CompactStar|CompactStar]] in 2023.

'''Half-prime subgroups''' are a family of [[nonoctave]] [[just intonation subgroup]]s where the basis elements are the halves of primes ([[3/2]], [[5/2]], [[7/2]], [[11/2]] and etc.), rather than the primes themselves. Similar to hown[[o-twos subgroup]]s are usually considered with a period of [[3/1]], half-prime subgroups can be considered with a period of [[3/2]] or more complexly [[5/2]], so present a possible JI interpretation of [[EDF]]s and [[Ed5/2]]s. They were first considered by [[User:CompactStar|CompactStar]] in 2023.

There are rank-1 and rank-2 [[regular temperament]]s that can be built on this system. [[11edf]] and [[12edf]] (which have Ed5/2 counterparts as [[25ed5/2]] and [[27ed5/2]]) are the smallest ~~EDFs~~ which offer a plausible rendition of 3/2.5/2.7/2 subgroup. Notable commas are the [[hemimage comma]], which if tempered results in a chain of [[28/27]]s that is similar to the previously-mentioned 11edf and 12edf,

There are rank-1 and rank-2 [[regular temperament]]s that can be built on this system. [[11edf]] and [[12edf]] (which have [[Ed5/2]] counterparts as [[25ed5/2]] and [[27ed5/2]]) are the smallest [[EDF]]s which offer a plausible rendition of 3/2.5/2.7/2 subgroup. Notable commas are the [[hemimage comma]], which if tempered results in a chain of [[28/27]]s that is similar to the previously-mentioned 11edf and 12edf,

== Intervals and chords ==

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-'''Half-prime subgroups''' are a family of [[nonoctave]] [[just intonation subgroup]]s where the basis elements are the halves of primes (3/2, 5/2, 7/2, 11/2 and etc.), rather than the primes themselves. Similar to hown[[o-twos subgroup]]s are usually considered with a period of [[3/1]], half-prime subgroups can be considered with a period of [[3/2]] or more complexly [[5/2]], so present a possible JI interpretation of [[EDF]]s and [[Ed5/2]]s. They were first considered by [[User:CompactStar|CompactStar]] in 2023.
+'''Half-prime subgroups''' are a family of [[nonoctave]] [[just intonation subgroup]]s where the basis elements are the halves of primes ([[3/2]], [[5/2]], [[7/2]], [[11/2]] and etc.), rather than the primes themselves. Similar to hown[[o-twos subgroup]]s are usually considered with a period of [[3/1]], half-prime subgroups can be considered with a period of [[3/2]] or more complexly [[5/2]], so present a possible JI interpretation of [[EDF]]s and [[Ed5/2]]s. They were first considered by [[User:CompactStar|CompactStar]] in 2023.
-There are rank-1 and rank-2 [[regular temperament]]s that can be built on this system. [[11edf]] and [[12edf]] (which have Ed5/2 counterparts as [[25ed5/2]] and [[27ed5/2]]) are the smallest EDFs which offer a plausible rendition of 3/2.5/2.7/2 subgroup. Notable commas are the [[hemimage comma]], which if tempered results in a chain of [[28/27]]s that is similar to the previously-mentioned 11edf and 12edf,
+There are rank-1 and rank-2 [[regular temperament]]s that can be built on this system. [[11edf]] and [[12edf]] (which have [[Ed5/2]] counterparts as [[25ed5/2]] and [[27ed5/2]]) are the smallest [[EDF]]s which offer a plausible rendition of 3/2.5/2.7/2 subgroup. Notable commas are the [[hemimage comma]], which if tempered results in a chain of [[28/27]]s that is similar to the previously-mentioned 11edf and 12edf,
 == Intervals and chords ==