Introductory examples in Sagittal notation: Difference between revisions
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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>2015-08-22 10: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-22 10:39:31 UTC</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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<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">[[ | <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">[[toc]] | ||
This page lists a few elementary examples that hopefully shed some light on the philosophy (and the pitfalls!) of Sagittal notation. For a detailed introduction into Sagittal notation the document [[file:Sagittal.pdf|Sagittal.pdf]] is the reference. | This page lists a few elementary examples that hopefully shed some light on the philosophy (and the pitfalls!) of [[Sagittal notation]]. For a detailed introduction into Sagittal notation the document [[file:Sagittal.pdf|Sagittal.pdf]] is the reference. | ||
=Just intonation: notating an overtone scale= | =Just intonation: notating an overtone scale= | ||
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The second example shows the best approximation for the same chord in [[12edo]]. Here, both the syntonic as the septimal comma are tempered out, so none of the additional symbols is necessary. The best approximation of the otonal tetrad is the same as the best approximation for a Pythagorean dominant seventh chord and can be written the same way. We see that Sagittal notation, when used for the western standard tuning, is identical to conventioal notation. | The second example shows the best approximation for the same chord in [[12edo]]. Here, both the syntonic as the septimal comma are tempered out, so none of the additional symbols is necessary. The best approximation of the otonal tetrad is the same as the best approximation for a Pythagorean dominant seventh chord and can be written the same way. We see that Sagittal notation, when used for the western standard tuning, is identical to conventioal notation. | ||
In [[22edo]] (third example), however, the septimal comma is tempered out, but not the syntonic comma. Therefore the symbol at the Bb note can be omitted, but the symbol at the E note must stay. | |||
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<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 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><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><div style="margin-left: 1em;"><a href="#Just intonation: notating an overtone scale">Just intonation: notating an overtone scale</a></div> | ||
<br /> | <!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --><div style="margin-left: 1em;"><a href="#Equal temperaments (1): comparison of notation in different equal temperaments">Equal temperaments (1): comparison of notation in different equal temperaments</a></div> | ||
This page lists a few elementary examples that hopefully shed some light on the philosophy (and the pitfalls!) of Sagittal notation. For a detailed introduction into Sagittal notation the document <a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');">Sagittal.pdf</a> is the reference.<br /> | <!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><div style="margin-left: 1em;"><a href="#Equal temperaments (2): an 11edo scale">Equal temperaments (2): an 11edo scale</a></div> | ||
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This page lists a few elementary examples that hopefully shed some light on the philosophy (and the pitfalls!) of <a class="wiki_link" href="/Sagittal%20notation">Sagittal notation</a>. For a detailed introduction into Sagittal notation the document <a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');">Sagittal.pdf</a> is the reference.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Just intonation: notating an overtone scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just intonation: notating an overtone scale</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Just intonation: notating an overtone scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just intonation: notating an overtone scale</h1> | ||
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With the Sagittal symbos for these three commas, a scale consisting of the overtones 4 to 11 can be written as follows:<br /> | With the Sagittal symbos for these three commas, a scale consisting of the overtones 4 to 11 can be written as follows:<br /> | ||
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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 /> | 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 /> | ||
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Below is an example how the standard notation systems for some equal termperaments differ.<br /> | Below is an example how the standard notation systems for some equal termperaments differ.<br /> | ||
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What is displayed is the tetrad consisting of the overtones 4 to 7 (respectively, in equal temperaments, of their approximations), a chord resembling a dominant seventh chord. First appears in mixed Sagittal notation for just intonation, with the syntonic comma symbol at the E note and the septimal vomma symbol at the Bb note.<br /> | What is displayed is the tetrad consisting of the overtones 4 to 7 (respectively, in equal temperaments, of their approximations), a chord resembling a dominant seventh chord. First appears in mixed Sagittal notation for just intonation, with the syntonic comma symbol at the E note and the septimal vomma symbol at the Bb note.<br /> | ||
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The second example shows the best approximation for the same chord in <a class="wiki_link" href="/12edo">12edo</a>. Here, both the syntonic as the septimal comma are tempered out, so none of the additional symbols is necessary. The best approximation of the otonal tetrad is the same as the best approximation for a Pythagorean dominant seventh chord and can be written the same way. We see that Sagittal notation, when used for the western standard tuning, is identical to conventioal notation.<br /> | The second example shows the best approximation for the same chord in <a class="wiki_link" href="/12edo">12edo</a>. Here, both the syntonic as the septimal comma are tempered out, so none of the additional symbols is necessary. The best approximation of the otonal tetrad is the same as the best approximation for a Pythagorean dominant seventh chord and can be written the same way. We see that Sagittal notation, when used for the western standard tuning, is identical to conventioal notation.<br /> | ||
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In <a class="wiki_link" href="/22edo">22edo</a> (third example), however, the septimal comma is tempered out, but not the syntonic comma. Therefore the symbol at the Bb note can be omitted, but the symbol at the E note must stay.<br /> | |||
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[todo]<br /> | [todo]<br /> | ||