441/440: Difference between revisions

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{{Infobox Interval

| ~~Icon~~ =

| Name = werckisma

| ~~Ratio~~ = ~~441/440~~

| Color name = 1uzzg2, luzozogu 2nd,<br>Luzozogu comma

~~| Monzo = -3 2 -1 2 -1~~

| Comma = yes

~~| Cents = 3.93016~~

~~| Name = Werckmeister's undecimal septenarian schisma~~, <br> ~~werckisma~~

~~| Color name =~~ Luzozogu

| ~~FJS name =~~

~~| Sound~~ =

}}

'''441/440''', also known as '''Werckmeister's undecimal septenarian schisma''', or more simply, the '''werckisma''', is a [[small comma|small]] [[superparticular]] [[11-limit]] comma with a size of roughly 3.93 [[cent]]s. It is the difference between [[21/20]] and [[22/21]], and between [[80/63]] ( = ([[10/9]])([[8/7]])) and [[14/11]], as well as the amount by which a stack of two [[21/16]] septimal subfourths exceeds a single [[55/32]] supermajor sixth. It also arises as the following comma differences: ([[49/48]])/([[55/54]]), ([[56/55]])([[64/63]]), ([[81/80]])/([[99/98]]), ([[126/125]])/([[176/175]]), and ([[243/242]])/([[540/539]]).

~~'''441/440''', also known as '''Werckmeister's undecimal septenarian schisma''', or, more simply, the '''werckisma''', is a [[small comma|small]] [[superparticular]]~~ [[11~~-limit~~]] ~~comma with a size of roughly 3.93 [[cents]]. It forms the difference between a stack of~~ two [[21/16~~]] septimal subfourths and a single~~ [[55/32]] ~~supermajor sixth~~, and~~, in addition to equating these two intervals, tempering out the werckisma also~~ makes [[werckismic chords]] possible.

== Temperaments ==

Tempering it out splits [[11/10]] into two even halves, equates 21/16 with [[55/42]] to create some interesting-sounding triads, and makes [[werckismic chords]] possible. See [[Rank-4 temperament #Werckismic (441/440)]] for some technical data. See [[Werckismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.

== See also ==

* [[Werckismic chords]]

* [[Werckismic temperaments]]

* [[Small comma]]

* [[List of superparticular intervals]]

[[Category:~~11-limit~~]]

[[Category:Werckismic]]

[[Category:~~Small comma~~]]

[[Category:Commas named after composers]]

[[Category:~~Superparticular~~]]

[[Category:Commas named after music theorists]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = werckisma
-| Ratio = 441/440
+| Color name = 1uzzg2, luzozogu 2nd,<br>Luzozogu comma
-| Monzo = -3 2 -1 2 -1
+| Comma = yes
-| Cents = 3.93016
-| Name = Werckmeister's undecimal septenarian schisma, <br> werckisma
-| Color name = Luzozogu
-| FJS name =
-| Sound =
 }}
+'''441/440''', also known as '''Werckmeister's undecimal septenarian schisma''', or more simply, the '''werckisma''', is a [[small comma|small]] [[superparticular]] [[11-limit]] comma with a size of roughly 3.93 [[cent]]s. It is the difference between [[21/20]] and [[22/21]], and between [[80/63]] ( = ([[10/9]])([[8/7]])) and [[14/11]], as well as the amount by which a stack of two [[21/16]] septimal subfourths exceeds a single [[55/32]] supermajor sixth. It also arises as the following comma differences: ([[49/48]])/([[55/54]]), ([[56/55]])([[64/63]]), ([[81/80]])/([[99/98]]), ([[126/125]])/([[176/175]]), and ([[243/242]])/([[540/539]]).
-'''441/440''', also known as '''Werckmeister's undecimal septenarian schisma''', or, more simply, the '''werckisma''', is a [[small comma|small]] [[superparticular]] [[11-limit]] comma with a size of roughly 3.93 [[cents]].  It forms the difference between a stack of two [[21/16]] septimal subfourths and a single [[55/32]] supermajor sixth, and, in addition to equating these two intervals, tempering out the werckisma also makes [[werckismic chords]] possible.
+== Temperaments ==
+Tempering it out splits [[11/10]] into two even halves, equates 21/16 with [[55/42]] to create some interesting-sounding triads, and makes [[werckismic chords]] possible. See [[Rank-4 temperament #Werckismic (441/440)]] for some technical data. See [[Werckismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.
 == See also ==
-* [[Werckismic chords]]
-* [[Werckismic temperaments]]
-* [[Small comma]]
 * [[List of superparticular intervals]]
-[[Category:11-limit]]
+[[Category:Werckismic]]
-[[Category:Small comma]]
+[[Category:Commas named after composers]]
-[[Category:Superparticular]]
+[[Category:Commas named after music theorists]]