1540/1539: Difference between revisions

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'''1540/1539''', the '''kevolisma''', is a [[19-limit]] [[~~Superparticular ratio|~~superparticular comma]] of about 1.12 [[cent]]s. It is the amount by which a stack consisting of [[6/5]], [[9/7]], [[12/11]] and [[19/16]] ~~falls short of an~~ [[~~octave~~]]. By tempering it out is defined the '''kevolismic temperament''', which enables the [[kevolismic chords]].

'''1540/1539''', the '''kevolisma''', is an [[unnoticeable comma|unnoticeable]] [[19-limit]] (specifically 2.3.5.7.11.19-[[subgroup]]) [[superparticular]] [[comma]] of about 1.12 [[cent]]s. It is the amount by which [[140/81]], a stack consisting of [[10/9]] and [[14/9]], exceeds [[19/11]]. It is also the amount by which a stack consisting of [[10/9]] and [[11/9]] exceeds [[19/14]], and by which a stack consisting of [[14/9]] and [[11/9]] exceeds [[19/10]].

== Commatic relations ==

This comma is the difference between the following superparticular pairs:

* [[55/54]] and [[57/56]] *

* [[77/76]] and [[81/80]] *

* [[154/153]] and [[171/170]]

* [[210/209]] and [[243/242]] *

* [[286/285]] and [[351/350]]

* [[343/342]] and [[441/440]] *

* [[352/351]] and [[456/455]]

* [[385/384]] and [[513/512]] *

* [[400/399]] and [[540/539]] *

* [[495/494]] and [[729/728]]

* [[595/594]] and [[969/968]]

* [[1216/1215]] and [[5776/5775]] *

* [[1225/1224]] and [[5985/5984]]

* [[1331/1330]] and [[9801/9800]] *

* [[1445/1444]] and [[23409/23408]]

* [[1521/1520]] and [[123201/123200]]

Or as a relation in the four formal commas defined by [[Functional Just System]] and [[Helmholtz–Ellis notation]]:

* ([[33/32]]) / ((81/80)([[64/63]])(513/512)).

It factors into the following superparticular pairs:

* [[3025/3024]] and [[3136/3135]] *

* [[2926/2925]] and [[3250/3249]]

* [[2431/2430]] and [[4200/4199]]

* [[2376/2375]] and [[4375/4374]] *

* [[2080/2079]] and [[5929/5928]]

* [[1729/1728]] and [[14080/14079]]

<nowiki/>* relation within the 2.3.5.7.11.19 subgroup

== Temperaments ==

By tempering it out is defined the '''kevolismic temperament''', which enables the [[kevolismic chords]].

== Etymology ==

The name ''kevolisma'' was named by [[User:Xenllium|Xenllium]] in 2023. It refers to ~~[[Wikipedia:1540 Kevola~~|1540 Kevola]], the asteroid~~. Which~~ in turn was named after an observatory in Finland.

The name ''kevolisma'' was named by [[User:Xenllium|Xenllium]] in 2023. It refers to {{w|1540 Kevola}}, the asteroid, which in turn was named after an observatory in Finland.

== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

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-'''1540/1539''', the '''kevolisma''', is a [[19-limit]] [[Superparticular ratio|superparticular comma]] of about 1.12 [[cent]]s. It is the amount by which a stack consisting of [[6/5]], [[9/7]], [[12/11]] and [[19/16]] falls short of an [[octave]]. By tempering it out is defined the '''kevolismic temperament''', which enables the [[kevolismic chords]].
+'''1540/1539''', the '''kevolisma''', is an [[unnoticeable comma|unnoticeable]] [[19-limit]] (specifically 2.3.5.7.11.19-[[subgroup]]) [[superparticular]] [[comma]] of about 1.12 [[cent]]s. It is the amount by which [[140/81]], a stack consisting of [[10/9]] and [[14/9]], exceeds [[19/11]]. It is also the amount by which a stack consisting of [[10/9]] and [[11/9]] exceeds [[19/14]], and by which a stack consisting of [[14/9]] and [[11/9]] exceeds [[19/10]].
+== Commatic relations ==
+This comma is the difference between the following superparticular pairs:
+* [[55/54]] and [[57/56]] *
+* [[77/76]] and [[81/80]] *
+* [[154/153]] and [[171/170]]
+* [[210/209]] and [[243/242]] *
+* [[286/285]] and [[351/350]]
+* [[343/342]] and [[441/440]] *
+* [[352/351]] and [[456/455]]
+* [[385/384]] and [[513/512]] *
+* [[400/399]] and [[540/539]] *
+* [[495/494]] and [[729/728]]
+* [[595/594]] and [[969/968]]
+* [[1216/1215]] and [[5776/5775]] *
+* [[1225/1224]] and [[5985/5984]]
+* [[1331/1330]] and [[9801/9800]] *
+* [[1445/1444]] and [[23409/23408]]
+* [[1521/1520]] and [[123201/123200]]
+Or as a relation in the four formal commas defined by [[Functional Just System]] and [[Helmholtz–Ellis notation]]:
+* ([[33/32]]) / ((81/80)([[64/63]])(513/512)).
+It factors into the following superparticular pairs:
+* [[3025/3024]] and [[3136/3135]] *
+* [[2926/2925]] and [[3250/3249]]
+* [[2431/2430]] and [[4200/4199]]
+* [[2376/2375]] and [[4375/4374]] *
+* [[2080/2079]] and [[5929/5928]]
+* [[1729/1728]] and [[14080/14079]]
+<nowiki/>* relation within the 2.3.5.7.11.19 subgroup
+== Temperaments ==
+By tempering it out is defined the '''kevolismic temperament''', which enables the [[kevolismic chords]].
 == Etymology ==
-The name ''kevolisma'' was named by [[User:Xenllium|Xenllium]] in 2023. It refers to [[Wikipedia:1540 Kevola|1540 Kevola]], the asteroid. Which in turn was named after an observatory in Finland.
+The name ''kevolisma'' was named by [[User:Xenllium|Xenllium]] in 2023. It refers to {{w|1540 Kevola}}, the asteroid, which in turn was named after an observatory in Finland.
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]