Introductory examples in Sagittal notation: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-23 11:51:02 UTC</tt>.<br>

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-23 12:01:49 UTC</tt>.<br>

: The original revision id was <tt>~~557205421~~</tt>.<br>

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

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

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=Equal temperaments (2): 11edo scale=

As second example, an [[11edo]] scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols for [[22edo]] are used. ~~Analogously~~, the recommended symbols for [[16edo]] are those of [[48edo]].

As second example, an [[11edo]] scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols for [[22edo]] are used. For the same reason, the recommended symbols for [[16edo]] are those of [[48edo]].

[[image:xenharmonie/Sagittal11EDO.jpg caption="Sagittal11EDO.jpg"]]

[[image:xenharmonie/Sagittal11EDO.jpg width="496" height="283" caption="Sagittal11EDO.jpg"]]

<span style="background-color: #ffffff;">(Rendering Juhani Nuorvala)</span>

~~[todo]~~</pre></div>

Observe that both lines show the same scale! The different appearance is caused by enharmonic equivalence effects. The upper line uses only conventional symbols, which is valid but gives the wrong impression of an up and down movement - it is in fact a simple ascending scale made of 11edo steps. The second line requires additional symbols but has a more intuitive appearance.</pre></div>

<h4>Original HTML content:</h4>

<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>Introductory examples in Sagittal notation</title></head><body><div id="toc"><h1 class="nopad">Table of Contents</h1><div style="margin-left: 1em;"><a href="#Just intonation: notating an overtone scale">Just intonation: notating an overtone scale</a></div>

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<br />

<h1 id="toc2"><a name="Equal temperaments (2): 11edo scale"></a>Equal temperaments (2): 11edo scale</h1>

As second example, an <a class="wiki_link" href="/11edo">11edo</a> scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols for <a class="wiki_link" href="/22edo">22edo</a> are used. ~~Analogously~~, the recommended symbols for <a class="wiki_link" href="/16edo">16edo</a> are those of <a class="wiki_link" href="/48edo">48edo</a>.<br />

As second example, an <a class="wiki_link" href="/11edo">11edo</a> scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols for <a class="wiki_link" href="/22edo">22edo</a> are used. For the same reason, the recommended symbols for <a class="wiki_link" href="/16edo">16edo</a> are those of <a class="wiki_link" href="/48edo">48edo</a>.<br />

<table class="captionBox"><tr><td class="captionedImage"><img src="http://xenharmonie.wikispaces.com/file/view/Sagittal11EDO.jpg/556903777/Sagittal11EDO.jpg" alt="Sagittal11EDO.jpg" title="Sagittal11EDO.jpg" /></td></tr><tr><td class="imageCaption">Sagittal11EDO.jpg</td></tr></table><br />

<table class="captionBox"><tr><td class="captionedImage"><img src="http://xenharmonie.wikispaces.com/file/view/Sagittal11EDO.jpg/556903777/496x283/Sagittal11EDO.jpg" alt="Sagittal11EDO.jpg" title="Sagittal11EDO.jpg" style="height: 283px; width: 496px;" /></td></tr><tr><td class="imageCaption">Sagittal11EDO.jpg</td></tr></table><br />

<span style="background-color: #ffffff;">(Rendering Juhani Nuorvala)</span><br />

<br />

~~[todo]~~</body></html></pre></div>

Observe that both lines show the same scale! The different appearance is caused by enharmonic equivalence effects. The upper line uses only conventional symbols, which is valid but gives the wrong impression of an up and down movement - it is in fact a simple ascending scale made of 11edo steps. The second line requires additional symbols but has a more intuitive appearance.</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-23 11:51:02 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-23 12:01:49 UTC</tt>.<br>
-: The original revision id was <tt>557205421</tt>.<br>
+: The original revision id was <tt>557205817</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 40: / Line 40: @@
 =Equal temperaments (2): 11edo scale=
-As second example, an [[11edo]] scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols for [[22edo]] are used. Analogously, the recommended symbols for [[16edo]] are those of [[48edo]].
+As second example, an [[11edo]] scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols for [[22edo]] are used. For the same reason, the recommended symbols for [[16edo]] are those of [[48edo]].
-[[image:xenharmonie/Sagittal11EDO.jpg caption="Sagittal11EDO.jpg"]]
+[[image:xenharmonie/Sagittal11EDO.jpg width="496" height="283" caption="Sagittal11EDO.jpg"]]
 &lt;span style="background-color: #ffffff;"&gt;(Rendering Juhani Nuorvala)&lt;/span&gt;
-[todo]</pre></div>
+Observe that both lines show the same scale! The different appearance is caused by enharmonic equivalence effects. The upper line uses only conventional symbols, which is valid but gives the wrong impression of an up and down movement - it is in fact a simple ascending scale made of 11edo steps. The second line requires additional symbols but has a more intuitive appearance.</pre></div>
 <h4>Original HTML content:</h4>
 <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;Introductory examples in Sagittal notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Just intonation: notating an overtone scale"&gt;Just intonation: notating an overtone scale&lt;/a&gt;&lt;/div&gt;
@@ Line 81: / Line 81: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Equal temperaments (2): 11edo scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Equal temperaments (2): 11edo scale&lt;/h1&gt;
-  As second example, an &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt; scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols for &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; are used. Analogously, the recommended symbols for &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; are those of &lt;a class="wiki_link" href="/48edo"&gt;48edo&lt;/a&gt;.&lt;br /&gt;
+  As second example, an &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt; scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols for &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; are used. For the same reason, the recommended symbols for &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; are those of &lt;a class="wiki_link" href="/48edo"&gt;48edo&lt;/a&gt;.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:19:&amp;lt;img src=&amp;quot;http://xenharmonie.wikispaces.com/file/view/Sagittal11EDO.jpg/556903777/Sagittal11EDO.jpg&amp;quot; alt=&amp;quot;Sagittal11EDO.jpg&amp;quot; title=&amp;quot;Sagittal11EDO.jpg&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://xenharmonie.wikispaces.com/file/view/Sagittal11EDO.jpg/556903777/Sagittal11EDO.jpg" alt="Sagittal11EDO.jpg" title="Sagittal11EDO.jpg" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Sagittal11EDO.jpg&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:19 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:19:&amp;lt;img src=&amp;quot;http://xenharmonie.wikispaces.com/file/view/Sagittal11EDO.jpg/556903777/496x283/Sagittal11EDO.jpg&amp;quot; alt=&amp;quot;Sagittal11EDO.jpg&amp;quot; title=&amp;quot;Sagittal11EDO.jpg&amp;quot; style=&amp;quot;height: 283px; width: 496px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://xenharmonie.wikispaces.com/file/view/Sagittal11EDO.jpg/556903777/496x283/Sagittal11EDO.jpg" alt="Sagittal11EDO.jpg" title="Sagittal11EDO.jpg" style="height: 283px; width: 496px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Sagittal11EDO.jpg&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:19 --&gt;&lt;br /&gt;
 &lt;span style="background-color: #ffffff;"&gt;(Rendering Juhani Nuorvala)&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-[todo]&lt;/body&gt;&lt;/html&gt;</pre></div>
+Observe that both lines show the same scale! The different appearance is caused by enharmonic equivalence effects. The upper line uses only conventional symbols, which is valid but gives the wrong impression of an up and down movement - it is in fact a simple ascending scale made of 11edo steps. The second line requires additional symbols but has a more intuitive appearance.&lt;/body&gt;&lt;/html&gt;</pre></div>