Schisma: Difference between revisions

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The '''schisma''', '''32805/32768''', is the difference between the [[Pythagorean comma]] and the [[syntonic comma]]. It is equal to ([[9/8]])4/([[8/5]]) and to ([[135/128]])/([[256/243]]) and also to ([[9/8]])3/([[64/45]]).

The '''schisma''', '''32805/32768''', is a small interval about 2 [[cent]]s. It arises as the difference between the [[Pythagorean comma]] and the [[syntonic comma]]. It is equal to ([[9/8]])4/([[8/5]]) and to ([[135/128]])/([[256/243]]) and also to ([[9/8]])3/([[64/45]]).

== History and etymology ==

''Schisma'' is a borrowing of Ancient Greek, meaning "split". The term was first used by [[Boethius]] (6th century), in his ''De institutione musica'', using it to refer to half of the [[Pythagorean comma]]. The modern sense was introduced by [[Helmholtz]]' ''On the Sensations of Tone'', in particular the translation by [[Alexander Ellis]], where it is spelled ''skhisma''. Since it is extremely close to the [[superparticular]] ratio [[887/886]] {{nowrap|(2-1 443-1 887)}}, it is used interchangably with this interval in some of Helmholtz' writing.

== Temperaments ==

Tempering out this comma gives a [[5-limit]] microtemperament called [[schismic|schismatic, schismic or helmholtz]], which if extended to larger [[subgroup]]s leads to the [[schismatic family]] of temperaments.

== Other intervals ==

Commas arising from the difference between a stack of Pythagorean intervals and other primes may also be called schismas. The difference between the [[Pythagorean comma]] and [[septimal comma]] is called the [[septimal schisma]]. Other examples are [[undevicesimal schisma]] and [[Alpharabian schisma]].

== Trivia ==

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== See also ==

* [[Pythagorean tuning]]

* [[Unnoticeable comma]]

[[Category:Schismatic]]

[[Category:Commas named for their regular temperament properties]]

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 {{Wikipedia| Schisma }}
-The '''schisma''', '''32805/32768''', is the difference between the [[Pythagorean comma]] and the [[syntonic comma]]. It is equal to ([[9/8]])<sup>4</sup>/([[8/5]]) and to ([[135/128]])/([[256/243]]) and also to ([[9/8]])<sup>3</sup>/([[64/45]]).
+The '''schisma''', '''32805/32768''', is a small interval about 2 [[cent]]s. It arises as the difference between the [[Pythagorean comma]] and the [[syntonic comma]]. It is equal to ([[9/8]])<sup>4</sup>/([[8/5]]) and to ([[135/128]])/([[256/243]]) and also to ([[9/8]])<sup>3</sup>/([[64/45]]).
+== History and etymology ==
+''Schisma'' is a borrowing of Ancient Greek, meaning "split". The term was first used by [[Boethius]] (6th century), in his ''De institutione musica'', using it to refer to half of the [[Pythagorean comma]]. The modern sense was introduced by [[Helmholtz]]' ''On the Sensations of Tone'', in particular the translation by [[Alexander Ellis]], where it is spelled ''skhisma''. Since it is extremely close to the [[superparticular]] ratio [[887/886]] {{nowrap|(2<sup>-1</sup> 443<sup>-1</sup> 887)}}, it is used interchangably with this interval in some of Helmholtz' writing.
 == Temperaments ==
-{{main|schismatic family}}
+{{main|Schismatic family}}
 Tempering out this comma gives a [[5-limit]] microtemperament called [[schismic|schismatic, schismic or helmholtz]], which if extended to larger [[subgroup]]s leads to the [[schismatic family]] of temperaments.
+== Other intervals ==
+Commas arising from the difference between a stack of Pythagorean intervals and other primes may also be called schismas. The difference between the [[Pythagorean comma]] and [[septimal comma]] is called the [[septimal schisma]]. Other examples are [[undevicesimal schisma]] and [[Alpharabian schisma]].
 == Trivia ==
@@ Line 23: / Line 30: @@
 == See also ==
+* [[Pythagorean tuning]]
 * [[Unnoticeable comma]]
 [[Category:Schismatic]]
 [[Category:Commas named for their regular temperament properties]]