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>2015-08-21 06:13: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-21 06:13:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>557093495</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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As the introduction [[file:Sagittal.pdf|Sagittal.pdf]] says, Sagittal notation uses a conventional staff on which the natural notes are in a single series of fifths, i.e, in the case of just intonation, in [[3-limit|Pythagorean tuning]]. The meaning of conventional sharps and flats is Pythagorean as well, i.e. they stand for raising the corresponding note by a [[2187_2048|Pythagorean chromatic semitone (apotome)]], a "large" semitone 113.7 cents in size. | As the introduction [[file:Sagittal.pdf|Sagittal.pdf]] says, Sagittal notation uses a conventional staff on which the natural notes are in a single series of fifths, i.e, in the case of just intonation, in [[3-limit|Pythagorean tuning]]. The meaning of conventional sharps and flats is Pythagorean as well, i.e. they stand for raising the corresponding note by a [[2187_2048|Pythagorean chromatic semitone (apotome)]], a "large" semitone 113.7 cents in size. | ||
For the notation of notes in higher [[Harmonic Limit|limits]], additional symbols are introduced. The intervals these symbols | For the notation of notes in higher [[Harmonic Limit|limits]], additional symbols are introduced. The intervals these symbols stand for are mostly [[Comma|commas]] - the maybe most elementary example is the [[81_80|syntonic comma]] (ratio 81/80, 21.506 cents), the difference between a pythagorean and a just major third, necessary for just intonation in [[5-limit]]. Other elementary commas appearing along the overtone series are: in [[7-limit]] the [[64_63|septimal comma or Architas' comma]] (64/63, 27.264 Cents), the difference between a minor and a harmonic seventh, and, in [[11-limit]], the [[33_32|undecimal comma or al-Farabi quarter-tone]] (33/32, 53.2729 cents), the difference between an undecimal semi-augmented and a perfect fourth. | ||
With the Sagittal symbos for these three commas, a scale consisting of the overtones 4 to 11 can be written as follows: | With the Sagittal symbos for these three commas, a scale consisting of the overtones 4 to 11 can be written as follows: | ||
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=Equal temperaments (1): comparison of notation in different equal temperaments= | =Equal temperaments (1): comparison of notation in different equal temperaments= | ||
[todo] | [todo] | ||
=Equal temperaments (2): an 11edo scale= | =Equal temperaments (2): an 11edo scale= | ||
[todo]</pre></div> | [todo]</pre></div> | ||
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As the introduction <a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');">Sagittal.pdf</a> says, Sagittal notation uses a conventional staff on which the natural notes are in a single series of fifths, i.e, in the case of just intonation, in <a class="wiki_link" href="/3-limit">Pythagorean tuning</a>. The meaning of conventional sharps and flats is Pythagorean as well, i.e. they stand for raising the corresponding note by a <a class="wiki_link" href="/2187_2048">Pythagorean chromatic semitone (apotome)</a>, a &quot;large&quot; semitone 113.7 cents in size.<br /> | As the introduction <a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');">Sagittal.pdf</a> says, Sagittal notation uses a conventional staff on which the natural notes are in a single series of fifths, i.e, in the case of just intonation, in <a class="wiki_link" href="/3-limit">Pythagorean tuning</a>. The meaning of conventional sharps and flats is Pythagorean as well, i.e. they stand for raising the corresponding note by a <a class="wiki_link" href="/2187_2048">Pythagorean chromatic semitone (apotome)</a>, a &quot;large&quot; semitone 113.7 cents in size.<br /> | ||
<br /> | <br /> | ||
For the notation of notes in higher <a class="wiki_link" href="/Harmonic%20Limit">limits</a>, additional symbols are introduced. The intervals these symbols | For the notation of notes in higher <a class="wiki_link" href="/Harmonic%20Limit">limits</a>, additional symbols are introduced. The intervals these symbols stand for are mostly <a class="wiki_link" href="/Comma">commas</a> - the maybe most elementary example is the <a class="wiki_link" href="/81_80">syntonic comma</a> (ratio 81/80, 21.506 cents), the difference between a pythagorean and a just major third, necessary for just intonation in <a class="wiki_link" href="/5-limit">5-limit</a>. Other elementary commas appearing along the overtone series are: in <a class="wiki_link" href="/7-limit">7-limit</a> the <a class="wiki_link" href="/64_63">septimal comma or Architas' comma</a> (64/63, 27.264 Cents), the difference between a minor and a harmonic seventh, and, in <a class="wiki_link" href="/11-limit">11-limit</a>, the <a class="wiki_link" href="/33_32">undecimal comma or al-Farabi quarter-tone</a> (33/32, 53.2729 cents), the difference between an undecimal semi-augmented and a perfect fourth.<br /> | ||
<br /> | <br /> | ||
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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[todo]<br /> | [todo]<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Equal temperaments (2): an 11edo scale"></a><!-- ws:end:WikiTextHeadingRule:4 -->Equal temperaments (2): an 11edo scale</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Equal temperaments (2): an 11edo scale"></a><!-- ws:end:WikiTextHeadingRule:4 -->Equal temperaments (2): an 11edo scale</h1> | ||
[todo]</body></html></pre></div> | [todo]</body></html></pre></div> | ||
Revision as of 06:13, 21 August 2015
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
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Original Wikitext content:
[[Sagittal notation|Overview Sagittal notation]] 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= As the introduction [[file:Sagittal.pdf|Sagittal.pdf]] says, Sagittal notation uses a conventional staff on which the natural notes are in a single series of fifths, i.e, in the case of just intonation, in [[3-limit|Pythagorean tuning]]. The meaning of conventional sharps and flats is Pythagorean as well, i.e. they stand for raising the corresponding note by a [[2187_2048|Pythagorean chromatic semitone (apotome)]], a "large" semitone 113.7 cents in size. For the notation of notes in higher [[Harmonic Limit|limits]], additional symbols are introduced. The intervals these symbols stand for are mostly [[Comma|commas]] - the maybe most elementary example is the [[81_80|syntonic comma]] (ratio 81/80, 21.506 cents), the difference between a pythagorean and a just major third, necessary for just intonation in [[5-limit]]. Other elementary commas appearing along the overtone series are: in [[7-limit]] the [[64_63|septimal comma or Architas' comma]] (64/63, 27.264 Cents), the difference between a minor and a harmonic seventh, and, in [[11-limit]], the [[33_32|undecimal comma or al-Farabi quarter-tone]] (33/32, 53.2729 cents), the difference between an undecimal semi-augmented and a perfect fourth. With the Sagittal symbos for these three commas, a scale consisting of the overtones 4 to 11 can be written as follows: [[image:SagittalOvertoneSeries.jpg]] For a complete list of all comma symbols see [[http://sagittal.org/]] or [[file:xenharmonic/Sagittal.pdf|sagittal.pdf]]. =Equal temperaments (1): comparison of notation in different equal temperaments= [todo] =Equal temperaments (2): an 11edo scale= [todo]
Original HTML content:
<html><head><title>Introductory examples in Sagittal notation</title></head><body><a class="wiki_link" href="/Sagittal%20notation">Overview Sagittal notation</a><br />
<br />
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 />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Just intonation: notating an overtone scale"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just intonation: notating an overtone scale</h1>
As the introduction <a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');">Sagittal.pdf</a> says, Sagittal notation uses a conventional staff on which the natural notes are in a single series of fifths, i.e, in the case of just intonation, in <a class="wiki_link" href="/3-limit">Pythagorean tuning</a>. The meaning of conventional sharps and flats is Pythagorean as well, i.e. they stand for raising the corresponding note by a <a class="wiki_link" href="/2187_2048">Pythagorean chromatic semitone (apotome)</a>, a "large" semitone 113.7 cents in size.<br />
<br />
For the notation of notes in higher <a class="wiki_link" href="/Harmonic%20Limit">limits</a>, additional symbols are introduced. The intervals these symbols stand for are mostly <a class="wiki_link" href="/Comma">commas</a> - the maybe most elementary example is the <a class="wiki_link" href="/81_80">syntonic comma</a> (ratio 81/80, 21.506 cents), the difference between a pythagorean and a just major third, necessary for just intonation in <a class="wiki_link" href="/5-limit">5-limit</a>. Other elementary commas appearing along the overtone series are: in <a class="wiki_link" href="/7-limit">7-limit</a> the <a class="wiki_link" href="/64_63">septimal comma or Architas' comma</a> (64/63, 27.264 Cents), the difference between a minor and a harmonic seventh, and, in <a class="wiki_link" href="/11-limit">11-limit</a>, the <a class="wiki_link" href="/33_32">undecimal comma or al-Farabi quarter-tone</a> (33/32, 53.2729 cents), the difference between an undecimal semi-augmented and a perfect fourth.<br />
<br />
With the Sagittal symbos for these three commas, a scale consisting of the overtones 4 to 11 can be written as follows:<br />
<!-- ws:start:WikiTextLocalImageRule:6:<img src="/file/view/SagittalOvertoneSeries.jpg/557089547/SagittalOvertoneSeries.jpg" alt="" title="" /> --><img src="/file/view/SagittalOvertoneSeries.jpg/557089547/SagittalOvertoneSeries.jpg" alt="SagittalOvertoneSeries.jpg" title="SagittalOvertoneSeries.jpg" /><!-- ws:end:WikiTextLocalImageRule:6 --><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 />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Equal temperaments (1): comparison of notation in different equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Equal temperaments (1): comparison of notation in different equal temperaments</h1>
[todo]<br />
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<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Equal temperaments (2): an 11edo scale"></a><!-- ws:end:WikiTextHeadingRule:4 -->Equal temperaments (2): an 11edo scale</h1>
[todo]</body></html>