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]]). | '''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 == | == Temperaments == | ||
Tempering out this comma leads to a form of '''animist temperament'''. An obvious further temperament is to temper out | 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 == | == See also == | ||
Revision as of 06:50, 13 March 2024
| Interval information |
small tridecimal comma
Thuzoyo comma
reduced
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 complements, 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 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, 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.