Schisma: Difference between revisions

(22 intermediate revisions by 9 users not shown)

Line 6:

}}

{{Infobox Interval

~~| JI glyph =~~

| Ratio = 32805/32768

~~| Monzo = -15 8 1~~

~~| Cents = 1.9537~~

| Name = schisma

| Color name =

| Color name = Ly-2, Layo comma

~~| FJS name = d~~-2~~5~~

| Comma = yes

| ~~Sound~~ =

}}

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]]). Tempering it out gives a [[5-limit]] microtemperament called [[~~Schismatic family#Schismatic aka Helmholtz~~|schismatic, schismic or ~~Helmholtz~~]], which if extended to larger ~~subgroups~~ leads to the [[schismatic family]] of temperaments.

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 ==

Line 23:

Line 30:

== See also ==

* [[Pythagorean tuning]]

* [[Unnoticeable comma]]

~~[[Category:5-limit]]~~

~~[[Category:Unnoticeable comma]]~~

[[Category:Schismatic]]

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

@@ Line 6: / Line 6: @@
 }}
 {{Infobox Interval
-| JI glyph =
 | Ratio = 32805/32768
-| Monzo = -15 8 1
-| Cents = 1.9537
 | Name = schisma
-| Color name =
+| Color name = Ly-2, Layo comma
-| FJS name = d-2<sup>5</sup>
+| Comma = yes
-| Sound =
 }}
 {{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]]). Tempering it out gives a [[5-limit]] microtemperament called [[Schismatic family#Schismatic aka Helmholtz|schismatic, schismic or Helmholtz]], which if extended to larger subgroups leads to the [[schismatic family]] of temperaments.
+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}}
+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:5-limit]]
-[[Category:Unnoticeable comma]]
 [[Category:Schismatic]]
+[[Category:Commas named for their regular temperament properties]]