105/104: Difference between revisions

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'''105/104''', the '''animist comma''', is a [[13-limit]] [[small comma]]. It arises in several places in 13-limit just intonation, most notably as the difference between [[15/8]] and [[13/7]], between [[8/5]] and [[21/13]], between [[8/7]] and [[15/13]], and between [[21/16]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[16/15]] and [[14/13]], between [[5/4]] and [[26/21]], between [[7/4]] and [[26/15]], and between [[32/21]] and [[20/13]]).

Being a [[square superparticular|triangle superparticular]], it factors neatly into ([[196/195]])([[225/224]]).

== Temperaments ==

Tempering out this comma leads to a form of '''animist temperament'''. An obvious further temperament is to temper out [[196/195]] and/or [[~~225~~/~~224~~]]~~, which~~ in the 2.3.5.7.13 [[subgroup]] is an [[extension]] of [[marvel]] and a [[restriction]] of [[tripod]].

Tempering out this comma leads to a form of '''animist temperament'''. An obvious further temperament is to temper out 196/195 and/or 225/224, equating [[15/14]] with 14/13~16/15. This in the 2.3.5.7.13 [[subgroup]] is an [[extension]] of [[marvel]] and a [[restriction]] of [[tripod]].

== See also ==

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 '''105/104''', the '''animist comma''', is a [[13-limit]] [[small comma]]. It arises in several places in 13-limit just intonation, most notably as the difference between [[15/8]] and [[13/7]], between [[8/5]] and [[21/13]], between [[8/7]] and [[15/13]], and between [[21/16]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[16/15]] and [[14/13]], between [[5/4]] and [[26/21]], between [[7/4]] and [[26/15]], and between [[32/21]] and [[20/13]]).
+Being a [[square superparticular|triangle superparticular]], it factors neatly into ([[196/195]])([[225/224]]).
 == Temperaments ==
-Tempering out this comma leads to a form of '''animist temperament'''. An obvious further temperament is to temper out [[196/195]] and/or [[225/224]], which in the 2.3.5.7.13 [[subgroup]] is an [[extension]] of [[marvel]] and a [[restriction]] of [[tripod]].
+Tempering out this comma leads to a form of '''animist temperament'''. An obvious further temperament is to temper out 196/195 and/or 225/224, equating [[15/14]] with 14/13~16/15. This in the 2.3.5.7.13 [[subgroup]] is an [[extension]] of [[marvel]] and a [[restriction]] of [[tripod]].
 == See also ==