513/512: Difference between revisions
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'''513/512''', the '''undevicesimal comma''', '''undevicesimal schisma''' or '''Boethius' comma''', is an [[Unnoticeable comma|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27|Pythagorean minor third (32/27)]] | '''513/512''', the '''undevicesimal comma''', '''undevicesimal schisma''' or '''Boethius' comma''', is an [[Unnoticeable comma|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27|Pythagorean minor third (32/27)]]. | ||
== Temperaments == | == Temperaments == | ||
: ''"Boethius" redirects here. For the medieval Roman platonist, see [[ | : ''"Boethius" redirects here. For the medieval Roman platonist, see [[Anicius Manlius Severinus Boethius]].'' | ||
By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. | By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enables the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]]. | ||
== Notation == | |||
This comma is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval. | |||
=== Sagittal notation === | |||
In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | )| }} and is called the '''19 schisma''', or '''19s''' for short, because the simplest interval it notates is 19/1 (equiv 19/16), as for example in D-F{{nbhsp}}{{sagittal | )| }}. The downward version is called '''1/19s''' or '''19s down''' and is represented by {{sagittal| )! }}. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Boethius]] | [[Category:Boethius]] | ||
[[Category:Commas named after their interval size]] | |||
[[Category:Commas named after polymaths]] | |||