Introductory examples in Sagittal notation: Difference between revisions
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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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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><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> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><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> | ||
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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> | ||