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]] | ||
Revision as of 07:00, 13 March 2024
| Interval information |
superleap comma
Thozogu comma
reduced
The superparticular interval 91/90, the biome comma or superleap comma, is a small 13-limit comma of about 19 cents. 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 complements, 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 triangle superparticular, it factors neatly into (169/168)(196/195).
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.