Introductory examples in Sagittal notation: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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=Equal temperaments (1): comparison of notation in different equal temperaments=

A special attraction of Sagittal notation is that it has been designed to notate both rational intervals (e.g. just intonation) and all kinds equal divisions of the octave. Basic guidelines for the latter, as defined in [[file:Sagittal.pdf|Sagittal.pdf]], are as follows:

# An interval in an equal temperament is to be notated in the same way as a just ratio for which the equal interval is the best approximation.

# Conventional staff notation (natural notes, sharps and flats) indicates tones in a series built on the equal division’s best approximation of a fifth.

There are a number of details to be observed here. First and most important point is that a notation defined this way is highly ambiguous. Every note of an equal-tempered system is best approximation for a whole range of just ratios - even an unlimited number of them, in fact. There are, in other words, extremely many [[https://en.wikipedia.org/wiki/Enharmonic|enharmonic equivalences]]. This is not necessarily a problem - enharmonic equivalences exist anyway, in conventional non-microtonal notation, too. Yet there are certain simplifications it make sense to define - certain commas, for example, vanish completely in some equal systems, as the syntonic comma in [[meantone]] systems.

[todo]

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<br />

With the Sagittal symbos for these three commas, a scale consisting of the overtones 4 to 11 can be written as follows:<br />

<img src="/file/view/SagittalOvertoneSeries.jpg/557089547/SagittalOvertoneSeries.jpg" alt="SagittalOvertoneSeries.jpg" title="SagittalOvertoneSeries.jpg" /><br />

<img src="/file/view/SagittalOvertoneSeries.jpg/557089547/SagittalOvertoneSeries.jpg" alt="SagittalOvertoneSeries.jpg" title="SagittalOvertoneSeries.jpg" /><br />

For a complete list of all comma symbols see <a class="wiki_link_ext" href="http://sagittal.org/" rel="nofollow">http://sagittal.org/</a> or <a href="http://xenharmonic.wikispaces.com/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/Sagittal.pdf/243193787/Sagittal.pdf');">sagittal.pdf</a>.<br />

<br />

<h1 id="toc1"><a name="Equal temperaments (1): comparison of notation in different equal temperaments"></a>Equal temperaments (1): comparison of notation in different equal temperaments</h1>

[todo]<br />

A special attraction of Sagittal notation is that it has been designed to notate both rational intervals (e.g. just intonation) and all kinds equal divisions of the octave. Basic guidelines for the latter, as defined in <a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');">Sagittal.pdf</a>, are as follows:<br />

<ol><li>An interval in an equal temperament is to be notated in the same way as a just ratio for which the equal interval is the best approximation.</li><li>Conventional staff notation (natural notes, sharps and flats) indicates tones in a series built on the equal division’s best approximation of a fifth.</li></ol><br />

There are a number of details to be observed here. First and most important point is that a notation defined this way is highly ambiguous. Every note of an equal-tempered system is best approximation for a whole range of just ratios - even an unlimited number of them, in fact. There are, in other words, extremely many <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Enharmonic" rel="nofollow">enharmonic equivalences</a>. This is not necessarily a problem - enharmonic equivalences exist anyway, in conventional non-microtonal notation, too. Yet there are certain simplifications it make sense to define - certain commas, for example, vanish completely in some equal systems, as the syntonic comma in <a class="wiki_link" href="/meantone">meantone</a> systems.<br />

<br />

[todo]<br />

<br />

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

[todo]</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>2015-08-21 06:13:47 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-21 08:45:59 UTC</tt>.<br>
-: The original revision id was <tt>557093495</tt>.<br>
+: The original revision id was <tt>557098125</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 20: / Line 20: @@
 =Equal temperaments (1): comparison of notation in different equal temperaments=
+A special attraction of Sagittal notation is that it has been designed to notate both rational intervals (e.g. just intonation) and all kinds equal divisions of the octave. Basic guidelines for the latter, as defined in [[file:Sagittal.pdf|Sagittal.pdf]], are as follows:
+# An interval in an equal temperament is to be notated in the same way as a just ratio for which the equal interval is the best approximation.
+# Conventional staff notation (natural notes, sharps and flats) indicates tones in a series built on the equal division’s best approximation of a fifth.
+There are a number of details to be observed here. First and most important point is that a notation defined this way is highly ambiguous. Every note of an equal-tempered system is best approximation for a whole range of just ratios - even an unlimited number of them, in fact. There are, in other words, extremely many [[https://en.wikipedia.org/wiki/Enharmonic|enharmonic equivalences]]. This is not necessarily a problem - enharmonic equivalences exist anyway, in conventional non-microtonal notation, too. Yet there are certain simplifications it make sense to define - certain commas, for example, vanish completely in some equal systems, as the syntonic comma in [[meantone]] systems.
 [todo]
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 &lt;br /&gt;
 With the Sagittal symbos for these three commas, a scale consisting of the overtones 4 to 11 can be written as follows:&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:6:&amp;lt;img src=&amp;quot;/file/view/SagittalOvertoneSeries.jpg/557089547/SagittalOvertoneSeries.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/SagittalOvertoneSeries.jpg/557089547/SagittalOvertoneSeries.jpg" alt="SagittalOvertoneSeries.jpg" title="SagittalOvertoneSeries.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:6 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:12:&amp;lt;img src=&amp;quot;/file/view/SagittalOvertoneSeries.jpg/557089547/SagittalOvertoneSeries.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/SagittalOvertoneSeries.jpg/557089547/SagittalOvertoneSeries.jpg" alt="SagittalOvertoneSeries.jpg" title="SagittalOvertoneSeries.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:12 --&gt;&lt;br /&gt;
 For a complete list of all comma symbols see &lt;a class="wiki_link_ext" href="http://sagittal.org/" rel="nofollow"&gt;http://sagittal.org/&lt;/a&gt; or &lt;a href="http://xenharmonic.wikispaces.com/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/Sagittal.pdf/243193787/Sagittal.pdf');"&gt;sagittal.pdf&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Equal temperaments (1): comparison of notation in different equal temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Equal temperaments (1): comparison of notation in different equal temperaments&lt;/h1&gt;
-  [todo]&lt;br /&gt;
+  A special attraction of Sagittal notation is that it has been designed to notate both rational intervals (e.g. just intonation) and all kinds equal divisions of the octave. Basic guidelines for the latter, as defined in &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;, are as follows:&lt;br /&gt;
+&lt;ol&gt;&lt;li&gt;An interval in an equal temperament is to be notated in the same way as a just ratio for which the equal interval is the best approximation.&lt;/li&gt;&lt;li&gt;Conventional staff notation (natural notes, sharps and flats) indicates tones in a series built on the equal division’s best approximation of a fifth.&lt;/li&gt;&lt;/ol&gt;&lt;br /&gt;
+There are a number of details to be observed here. First and most important point is that a notation defined this way is highly ambiguous. Every note of an equal-tempered system is best approximation for a whole range of just ratios - even an unlimited number of them, in fact. There are, in other words, extremely many &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Enharmonic" rel="nofollow"&gt;enharmonic equivalences&lt;/a&gt;. This is not necessarily a problem - enharmonic equivalences exist anyway, in conventional non-microtonal notation, too. Yet there are certain simplifications it make sense to define - certain commas, for example, vanish completely in some equal systems, as the syntonic comma in &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; systems.&lt;br /&gt;
+&lt;br /&gt;
+[todo]&lt;br /&gt;
 &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): an 11edo scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Equal temperaments (2): an 11edo scale&lt;/h1&gt;
   [todo]&lt;/body&gt;&lt;/html&gt;</pre></div>