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 how [[no-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. ~~[[7edf]] (nearly [[12edo]], allowing it to be played concurrently with normal music),~~ [[11edf]] and [[12edf]] are the smallest [[EDF]]s which offer a plausible rendition of 3/2.5/2.7/2 subgroup. Notable commas that could be tempered 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, the Sirius comma [[3125/3087]], [[20480/19683]], and [[99/98]].

There are rank-1 and rank-2 [[regular temperament]]s that can be built on this system. [[11edf]] and [[12edf]] are the smallest [[EDF]]s which offer a plausible rendition of 3/2.5/2.7/2 subgroup. Notable commas that could be tempered 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, the Sirius comma [[3125/3087]], [[20480/19683]], and [[99/98]].

== 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 how [[no-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. [[7edf]] (nearly [[12edo]], allowing it to be played concurrently with normal music), [[11edf]] and [[12edf]] are the smallest [[EDF]]s which offer a plausible rendition of 3/2.5/2.7/2 subgroup.  Notable commas that could be tempered 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, the Sirius comma [[3125/3087]], [[20480/19683]], and [[99/98]].
+There are rank-1 and rank-2 [[regular temperament]]s that can be built on this system. [[11edf]] and [[12edf]] are the smallest [[EDF]]s which offer a plausible rendition of 3/2.5/2.7/2 subgroup.  Notable commas that could be tempered 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, the Sirius comma [[3125/3087]], [[20480/19683]], and [[99/98]].
 == Intervals and chords ==