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Introductory examples in Sagittal notation: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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 11:32:16 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-23 11:51:02 UTC</tt>.<br>
: The original revision id was <tt>557204745</tt>.<br>
: The original revision id was <tt>557205421</tt>.<br>
: The revision comment was: <tt></tt><br>
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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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Finally, [[31edo]] (last example) is like 12edo a meantone system and thus tempers out the syntonic comma - but not the septimal comma, exactly opposite to 22edo in this aspect. The septimal comma, in turn coincides with the undecimal comma here - both are approximated by one 31edo step. The recommended standard symbol for this interval in 31edo is the symbol for the undecimal comma (quartertone), so the tetrad in question could be notated with a quartertone symbol at the Bb. In our example, the enharmonic equivalent A# is used instead, which is possible because 31edo is a [[Meantone family#Septimal%20meantone|septimal meantone]] system.
Finally, [[31edo]] (last example) is like 12edo a meantone system and thus tempers out the syntonic comma - but not the septimal comma, exactly opposite to 22edo in this aspect. The septimal comma, in turn coincides with the undecimal comma here - both are approximated by one 31edo step. The recommended standard symbol for this interval in 31edo is the symbol for the undecimal comma (quartertone), so the tetrad in question could be notated with a quartertone symbol at the Bb. In our example, the enharmonic equivalent A# is used instead, which is possible because 31edo is a [[Meantone family#Septimal%20meantone|septimal meantone]] system.


=Equal temperaments (2): an 11edo scale=  
=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]].
[[image:xenharmonie/Sagittal11EDO.jpg caption="Sagittal11EDO.jpg"]]
&lt;span style="background-color: #ffffff;"&gt;(Rendering Juhani Nuorvala)&lt;/span&gt;
 
[todo]</pre></div>
[todo]</pre></div>
<h4>Original HTML content:</h4>
<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;
<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;
&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Equal temperaments (1): comparison of notation in different equal temperaments"&gt;Equal temperaments (1): comparison of notation in different equal temperaments&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Equal temperaments (1): comparison of notation in different equal temperaments"&gt;Equal temperaments (1): comparison of notation in different equal temperaments&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Equal temperaments (2): an 11edo scale"&gt;Equal temperaments (2): an 11edo scale&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Equal temperaments (2): 11edo scale"&gt;Equal temperaments (2): 11edo scale&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;This page lists a few elementary examples that hopefully shed some light on the philosophy (and the pitfalls!) of &lt;a class="wiki_link" href="/Sagittal%20notation"&gt;Sagittal notation&lt;/a&gt;. For a detailed introduction into Sagittal notation the document &lt;a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');"&gt;Sagittal.pdf&lt;/a&gt; is the reference.&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;This page lists a few elementary examples that hopefully shed some light on the philosophy (and the pitfalls!) of &lt;a class="wiki_link" href="/Sagittal%20notation"&gt;Sagittal notation&lt;/a&gt;. For a detailed introduction into Sagittal notation the document &lt;a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');"&gt;Sagittal.pdf&lt;/a&gt; is the reference.&lt;br /&gt;
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Finally, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; (last example) is like 12edo a meantone system and thus tempers out the syntonic comma - but not the septimal comma, exactly opposite to 22edo in this aspect. The septimal comma, in turn coincides with the undecimal comma here - both are approximated by one 31edo step. The recommended standard symbol for this interval in 31edo is the symbol for the undecimal comma (quartertone), so the tetrad in question could be notated with a quartertone symbol at the Bb. In our example, the enharmonic equivalent A# is used instead, which is possible because 31edo is a &lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone"&gt;septimal meantone&lt;/a&gt; system.&lt;br /&gt;
Finally, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; (last example) is like 12edo a meantone system and thus tempers out the syntonic comma - but not the septimal comma, exactly opposite to 22edo in this aspect. The septimal comma, in turn coincides with the undecimal comma here - both are approximated by one 31edo step. The recommended standard symbol for this interval in 31edo is the symbol for the undecimal comma (quartertone), so the tetrad in question could be notated with a quartertone symbol at the Bb. In our example, the enharmonic equivalent A# is used instead, which is possible because 31edo is a &lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone"&gt;septimal meantone&lt;/a&gt; system.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Equal temperaments (2): an 11edo scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Equal temperaments (2): an 11edo scale&lt;/h1&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;
  [todo]&lt;/body&gt;&lt;/html&gt;</pre></div>
  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;
&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;
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[todo]&lt;/body&gt;&lt;/html&gt;</pre></div>
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