Schisma: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES<~~/~~h2>~~

{{interwiki

~~This~~ is ~~an imported revision from Wikispaces~~. ~~The revision metadata~~ is ~~included below for reference:~~<br>

| de = 32805/32768

~~: This revision was by author~~ [[~~User:genewardsmith|genewardsmith~~]] and ~~made on~~ <tt>~~2011-08-08 15:40:51 UTC~~</tt>.~~<br>~~

| en = 32805/32768

: The ~~original revision id~~ was ~~<tt>244889805</tt>~~.~~<br>~~

| es =

: The ~~revision comment~~ was~~: <tt></tt><br>~~

| ja =

~~The revision contents are below~~, ~~presented both~~ in the ~~original Wikispaces Wikitext format~~, ~~and in HTML exactly as Wikispaces rendered~~ it.<br>

}}

<h4>~~Original Wikitext content:~~</h4>

{{Infobox Interval

~~<div style~~=~~"width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style~~=~~"margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class~~=~~"old~~-~~revision-html">~~[[~~http://en~~.~~wikipedia~~.~~org/wiki/Schisma~~]]<~~/pre~~></~~div~~>

| Ratio = 32805/32768

<h4>~~Original HTML content:~~</h4>

| Name = schisma

<~~div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"~~><~~pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"~~>~~<html><head><title>32805_32768<~~/~~title><~~/~~head><body><a class~~=~~"wiki_link_ext" href~~=~~"http~~:~~//en.wikipedia.org/wiki/Schisma" rel="nofollow">http~~:~~//en.wikipedia.org/wiki/Schisma</a></body></html></pre></div>~~

| Color name = Ly-2, Layo comma

| Comma = yes

}}

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 ==

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 ==

The schisma explains how the greatly composite numbers 1048576 (2<sup>20</sup>) and 104976 (18<sup>4</sup>) look alike in decimal. The largest common power of two between these numbers is 2<sup>5</sup>, (when 1049760 is written to equalize) and when reduced by that, 1049760/1048576 becomes 32805/32768.

== See also ==

* [[Pythagorean tuning]]

* [[Unnoticeable comma]]

[[Category:Schismatic]]

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

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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{interwiki
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| de = 32805/32768
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-08 15:40:51 UTC</tt>.<br>
+| en = 32805/32768
-: The original revision id was <tt>244889805</tt>.<br>
+| es =
-: The revision comment was: <tt></tt><br>
+| ja =
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+}}
-<h4>Original Wikitext content:</h4>
+{{Infobox Interval
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[http://en.wikipedia.org/wiki/Schisma]]</pre></div>
+| Ratio = 32805/32768
-<h4>Original HTML content:</h4>
+| Name = schisma
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;32805_32768&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schisma" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Schisma&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+| Color name = Ly-2, Layo comma
+| Comma = yes
+}}
+{{Wikipedia| Schisma }}
+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 ==
+The schisma explains how the greatly composite numbers 1048576 (2<sup>20</sup>) and 104976 (18<sup>4</sup>) look alike in decimal. The largest common power of two between these numbers is 2<sup>5</sup>, (when 1049760 is written to equalize) and when reduced by that, 1049760/1048576 becomes 32805/32768.
+== See also ==
+* [[Pythagorean tuning]]
+* [[Unnoticeable comma]]
+[[Category:Schismatic]]
+[[Category:Commas named for their regular temperament properties]]