91/90: Difference between revisions
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The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma|small]] [[13-limit]] [[comma]] of about 19 [[cent]]s. It arises in several places in 13-limit just intonation, most notably as the difference between [[13/12]] and [[15/14]], between [[13/9]] and [[7/5]], between [[7/6]] and [[15/13]], and between [[9/7]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[24/13]] and [[28/15]], between [[18/13]] and [[10/7]], between [[12/7]] and [[26/15]], and between [[14/9]] and [[20/13]]). | The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma|small]] [[13-limit]] [[comma]] of about 19 [[cent]]s. It arises in several places in 13-limit just intonation, most notably as the difference between [[13/12]] and [[15/14]], between [[13/9]] and [[7/5]], between [[7/6]] and [[15/13]], and between [[9/7]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[24/13]] and [[28/15]], between [[18/13]] and [[10/7]], between [[12/7]] and [[26/15]], and between [[14/9]] and [[20/13]]). | ||
Being a [[square superparticular|triangle superparticular]], it factors neatly into ([[169/168]])([[196/195]]). | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma in the full 13-limit results in the rank-5 '''biosphere temperament'''. See [[The Biosphere]]. An obvious further temperament is to temper out 169/168 and/or 196/195, equating [[14/13]] with 13/12~15/14. This in the 2.3.5.7.13 [[subgroup]] results in the [[sengic]] temperament. | |||
== Etymology == | |||
Observably, ''superleap'' is a contraction of ''superpyth'' and ''leapday'', referring to the two rank-2 temperaments that temper out this comma. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||