15edo: Difference between revisions
Wikispaces>k9assassin **Imported revision 604190146 - Original comment: ** |
Wikispaces>k9assassin **Imported revision 604275784 - Original comment: ** |
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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:k9assassin|k9assassin]] and made on <tt>2017-01- | : This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2017-01-16 22:40:05 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>604275784</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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==Summary== | ==Summary== | ||
15 Equal or 15 EDO is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5-EDO which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15 EDO returns to the octave if stacked five times which is radically different than a meantone system. | 15 Equal or 15 EDO is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5-EDO which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15 EDO returns to the octave if stacked five times which is radically different than a meantone system. | ||
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||= Degree ||= Cents ||= Solfege | ||= Degree ||= Cents ||= Solfege | ||
(porcupine-based) ||= Porcupine[8] | (porcupine-based) ||= Porcupine[8] | ||
(Greek) ||= Blackwood | |||
"guitar notation" ||= Porcupine[7] | "guitar notation" ||= Porcupine[7] | ||
(traditional) ||= Blackwood | (traditional) ||= Blackwood | ||
Decimal ||= Approximate Ratios* || | Decimal ||= Approximate Ratios* || | ||
||= 0 ||= 0 ||= do ||= | ||= 0 ||= 0 ||= do ||= α ||= E ||= G ||= 1 ||= 1/1 || | ||
||= 1 ||= 80 ||= di ||= | ||= 1 ||= 80 ||= di ||= α/ β\ ||= E# ||= G# / Abb ||= 1# / 2b ||= 25/24, 21/20, 16/15 || | ||
||= 2 ||= 160 ||= ru ||= | ||= 2 ||= 160 ||= ru ||= β ||= Gb ||= Gx / Ab ||= 2 ||= 11/10, 12/11, 10/9 || | ||
||= 3 ||= 240 ||= re ||= | ||= 3 ||= 240 ||= re ||= β/ χ\ ||= G ||= A ||= 3 ||= 8/7, 7/6, 9/8 || | ||
||= 4 ||= 320 ||= me ||= | ||= 4 ||= 320 ||= me ||= χ ||= G# ||= A# / Bb ||= 3# / 4b ||= 6/5, 11/9 || | ||
||= 5 ||= 400 ||= mi ||= | ||= 5 ||= 400 ||= mi ||= χ/ δ\ ||= Ab ||= B ||= 4 ||= 5/4, 14/11 || | ||
||= 6 ||= 480 ||= fa ||= ð | ||= 6 ||= 480 ||= fa ||= ð ||= A ||= B# / Cb ||= 5 ||= 4/3, 9/7, 21/16 || | ||
||= 7 ||= 560 ||= fu ||= | ||= 7 ||= 560 ||= fu ||= δ/ ε\ ||= A# ||= C ||= 5# / 6b ||= 11/8, 7/5 || | ||
||= 8 ||= 640 ||= su ||= | ||= 8 ||= 640 ||= su ||= ε ||= Bb ||= C# / Db ||= 6 ||= 16/11, 10/7 || | ||
||= 9 ||= 720 ||= sol ||= | ||= 9 ||= 720 ||= sol ||= ε/ φ\ ||= B ||= D ||= 7 ||= 3/2, 14/9, 32/21 || | ||
||= 10 ||= 800 ||= le ||= | ||= 10 ||= 800 ||= le ||= φ ||= B# ||= D# / Eb ||= 7# / 8b ||= 8/5, 11/7 || | ||
||= 11 ||= 880 ||= la ||= | ||= 11 ||= 880 ||= la ||= φ/ γ\ ||= Db ||= E ||= 8 ||= 5/3, 18/11 || | ||
||= 12 ||= 960 ||= ta ||= | ||= 12 ||= 960 ||= ta ||= γ ||= D ||= E# / Fb ||= 9 ||= 7/4, 12/7, 16/9 || | ||
||= 13 ||= 1040 ||= tu ||= | ||= 13 ||= 1040 ||= tu ||= γ/ η\ ||= D# ||= F ||= 9# / 0b ||= 20/11, 11/6, 9/5 || | ||
||= 14 ||= 1120 ||= ti ||= | ||= 14 ||= 1120 ||= ti ||= η ||= Eb ||= F# /Gb ||= 0 ||= 48/25, 40/21, 15/8 || | ||
||= 15 ||= 1200 ||= do ||= | ||= 15 ||= 1200 ||= do ||= α ||= E ||= G ||= 1 ||= 2/1 || | ||
*based on treating 15-EDO as an 11-limit temperament; other approaches are possible | *based on treating 15-EDO as an 11-limit temperament; other approaches are possible | ||
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||= [[16_13|16/13]], [[13_8|13/8]] ||= 39.472 || | ||= [[16_13|16/13]], [[13_8|13/8]] ||= 39.472 || | ||
= | =Notation= | ||
There are a variety of other ways to notate 15-edo, and the choice of notation depends heavily which rank-2 temperament or MOS scale one wishes to treat as being the "main focus" of 15-edo composition. | There are a variety of other ways to notate 15-edo, and the choice of notation depends heavily which rank-2 temperament or MOS scale one wishes to treat as being the "main focus" of 15-edo composition. | ||
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==Porcupine Notation== | ==Porcupine Notation== | ||
* See the main [[Porcupine Notation|porcupine notation]] page. | * See the main [[Porcupine Notation|porcupine notation]] page. | ||
Porcupine notation bases porcupine[8] LLLLLLLs scale using eight nominals α β χ δ ε φ γ η. Others have proposed ABCDEFGHA but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in place with a close resemblance to the spelling of ABCDEFGHA. | |||
==Interval names for Porcupine[8]:== | ==Interval names for Porcupine[8]:== | ||
|| Cents || Interval Name || Note names || | || Cents || Interval Name || Note names || | ||
|| 80 || Half Quill || | || 80 || Half Quill || α - β\ || | ||
|| 160 || Quill || | || 160 || Quill || α - β || | ||
|| 240 || Small Diquill || | || 240 || Small Diquill || α - χ\ || | ||
|| 320 || Large Diquill || | || 320 || Large Diquill || α - χ || | ||
|| 400 || Small Triquill || | || 400 || Small Triquill || α - δ\ || | ||
|| 480 || Large Triquill || | || 480 || Large Triquill || α - δ || | ||
|| 560 || Small Fourquill || | || 560 || Small Fourquill || α - ε\ || | ||
|| 640 || Large Fourquill || | || 640 || Large Fourquill || α - ε || | ||
|| 720 || Small Fivequill || | || 720 || Small Fivequill || α - φ\ || | ||
|| 800 || Large Fivequill || | || 800 || Large Fivequill || α - φ || | ||
|| 880 || Small Sixquill || | || 880 || Small Sixquill || α - γ\ || | ||
|| 960 || Large Sixquill || | || 960 || Large Sixquill || α - γ || | ||
|| 1040 || Small Sevenquill || | || 1040 || Small Sevenquill || α - η\ || | ||
|| 1120 || Large Sevenquill || | || 1120 || Large Sevenquill || α - η || | ||
|| 1200 || Octoquill || | || 1200 || Octoquill || α - α || | ||
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[[media type="custom" key="23473468"]]</pre></div> | [[media type="custom" key="23473468"]]</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"><html><head><title>15edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>15edo</title></head><body><!-- ws:start:WikiTextTocRule:30:&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:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 1em;"><a href="#x15-Tone Equal Temperament (15-EDO)">15-Tone Equal Temperament (15-EDO)</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#x15-Tone Equal Temperament (15-EDO)-Summary">Summary</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#Images">Images</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 2em;"><a href="#Intervals-Selected just intervals by error">Selected just intervals by error</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 2em;"><a href="#Notation-Blackwood Notation">Blackwood Notation</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#Notation-Porcupine Notation">Porcupine Notation</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#Notation-Interval names for Porcupine[8]:">Interval names for Porcupine[8]:</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 1em;"><a href="#Rank two temperaments">Rank two temperaments</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 1em;"><a href="#Commas">Commas</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 1em;"><a href="#Theory">Theory</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 1em;"><a href="#Practical Theory / Books">Practical Theory / Books</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 1em;"><a href="#Compositions">Compositions</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --></div> | ||
<!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="x15-Tone Equal Temperament (15-EDO)"></a><!-- ws:end:WikiTextHeadingRule:2 -->15-Tone Equal Temperament (15-EDO)</h1> | |||
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<!-- ws:start:WikiTextLocalImageRule: | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="x15-Tone Equal Temperament (15-EDO)-Summary"></a><!-- ws:end:WikiTextHeadingRule:4 -->Summary</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="x15-Tone Equal Temperament (15-EDO)-Summary"></a><!-- ws:end:WikiTextHeadingRule:4 -->Summary</h2> | ||
15 Equal or 15 EDO is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5-EDO which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15 EDO returns to the octave if stacked five times which is radically different than a meantone system.<br /> | 15 Equal or 15 EDO is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5-EDO which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15 EDO returns to the octave if stacked five times which is radically different than a meantone system.<br /> | ||
<br /> | <br /> | ||
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A recommended method to the notation of 15-edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the &quot;quill&quot; is the name given to the two step interval (160c) of 15-edo while the &quot;small quill&quot; (80c) is the chroma of 15-edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15-edo into a seven nominal based framework.<br /> | A recommended method to the notation of 15-edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the &quot;quill&quot; is the name given to the two step interval (160c) of 15-edo while the &quot;small quill&quot; (80c) is the chroma of 15-edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15-edo into a seven nominal based framework.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:6 -->Images</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1351:&lt;img src=&quot;/file/view/15edo%20wheel.png/516943384/225x225/15edo%20wheel.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 225px; width: 225px;&quot; /&gt; --><img src="/file/view/15edo%20wheel.png/516943384/225x225/15edo%20wheel.png" alt="15edo wheel.png" title="15edo wheel.png" style="height: 225px; width: 225px;" /><!-- ws:end:WikiTextLocalImageRule:1351 --><!-- ws:start:WikiTextLocalImageRule:1352:&lt;img src=&quot;/file/view/15edo%20wheel%2002.png/516943402/250x250/15edo%20wheel%2002.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 250px; width: 250px;&quot; /&gt; --><img src="/file/view/15edo%20wheel%2002.png/516943402/250x250/15edo%20wheel%2002.png" alt="15edo wheel 02.png" title="15edo wheel 02.png" style="height: 250px; width: 250px;" /><!-- ws:end:WikiTextLocalImageRule:1352 --><!-- ws:start:WikiTextLocalImageRule:1353:&lt;img src=&quot;/file/view/15edo%20wheel%2003.png/516943418/220x220/15edo%20wheel%2003.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 220px; width: 220px;&quot; /&gt; --><img src="/file/view/15edo%20wheel%2003.png/516943418/220x220/15edo%20wheel%2003.png" alt="15edo wheel 03.png" title="15edo wheel 03.png" style="height: 220px; width: 220px;" /><!-- ws:end:WikiTextLocalImageRule:1353 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals</h1> | ||
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</td> | </td> | ||
<td style="text-align: center;">Porcupine[8]<br /> | <td style="text-align: center;">Porcupine[8]<br /> | ||
(Greek)<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">Blackwood<br /> | <td style="text-align: center;">Blackwood<br /> | ||
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<td style="text-align: center;">do<br /> | <td style="text-align: center;">do<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">α<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
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<td style="text-align: center;">di<br /> | <td style="text-align: center;">di<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">α/ β\<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E#<br /> | <td style="text-align: center;">E#<br /> | ||
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<td style="text-align: center;">ru<br /> | <td style="text-align: center;">ru<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">β<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Gb<br /> | <td style="text-align: center;">Gb<br /> | ||
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<td style="text-align: center;">re<br /> | <td style="text-align: center;">re<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">β/ χ\<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
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<td style="text-align: center;">me<br /> | <td style="text-align: center;">me<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">χ<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G#<br /> | <td style="text-align: center;">G#<br /> | ||
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<td style="text-align: center;">mi<br /> | <td style="text-align: center;">mi<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">χ/ δ\<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Ab<br /> | <td style="text-align: center;">Ab<br /> | ||
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<td style="text-align: center;">fa<br /> | <td style="text-align: center;">fa<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">ð | <td style="text-align: center;">ð<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
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<td style="text-align: center;">fu<br /> | <td style="text-align: center;">fu<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">δ/ ε\<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A#<br /> | <td style="text-align: center;">A#<br /> | ||
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<td style="text-align: center;">su<br /> | <td style="text-align: center;">su<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">ε<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Bb<br /> | <td style="text-align: center;">Bb<br /> | ||
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<td style="text-align: center;">sol<br /> | <td style="text-align: center;">sol<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">ε/ φ\<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">B<br /> | ||
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<td style="text-align: center;">le<br /> | <td style="text-align: center;">le<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">φ<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B#<br /> | <td style="text-align: center;">B#<br /> | ||
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<td style="text-align: center;">la<br /> | <td style="text-align: center;">la<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">φ/ γ\<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Db<br /> | <td style="text-align: center;">Db<br /> | ||
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<td style="text-align: center;">ta<br /> | <td style="text-align: center;">ta<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">γ<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
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<td style="text-align: center;">tu<br /> | <td style="text-align: center;">tu<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">γ/ η\<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D#<br /> | <td style="text-align: center;">D#<br /> | ||
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<td style="text-align: center;">ti<br /> | <td style="text-align: center;">ti<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">η<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Eb<br /> | <td style="text-align: center;">Eb<br /> | ||
| Line 609: | Line 582: | ||
<td style="text-align: center;">do<br /> | <td style="text-align: center;">do<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">α<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
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<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802896?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24802896&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/15ed2-001.svg">alt : Your browser has no SVG support.</object><!-- ws:end:WikiTextMediaRule:0 --><br /> | <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802896?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24802896&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/15ed2-001.svg">alt : Your browser has no SVG support.</object><!-- ws:end:WikiTextMediaRule:0 --><br /> | ||
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<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:1354:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/15ed2-001.svg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@15ed2-001.svg&quot; title=&quot;File: 15ed2-001.svg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/15ed2-001.svg/480716490/15ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/15ed2-001.svg/480716490/15ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="15ed2-001.svg" /></a><div><a href="/file/view/15ed2-001.svg/480716490/15ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/15ed2-001.svg/480716490/15ed2-001.svg');" class="filename" title="15ed2-001.svg">15ed2-001.svg</a><br /><ul><li><a href="/file/detail/15ed2-001.svg">Details</a></li><li><a href="/file/view/15ed2-001.svg/480716490/15ed2-001.svg">Download</a></li><li style="color: #666">16 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:1354 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc4"><a name="Intervals-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:10 -->Selected just intervals by error</h2> | ||
The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 15edo (ordered by absolute error).<br /> | The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 15edo (ordered by absolute error).<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc5"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:12 -->Notation</h1> | ||
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There are a variety of other ways to notate 15-edo, and the choice of notation depends heavily which rank-2 temperament or MOS scale one wishes to treat as being the &quot;main focus&quot; of 15-edo composition.<br /> | There are a variety of other ways to notate 15-edo, and the choice of notation depends heavily which rank-2 temperament or MOS scale one wishes to treat as being the &quot;main focus&quot; of 15-edo composition.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Notation-Blackwood Notation"></a><!-- ws:end:WikiTextHeadingRule:14 -->Blackwood Notation</h2> | ||
<ul><li><strong>Decimal Version:</strong> Using the nominals 1-0 (with 0 representing &quot;10&quot;), one of the three chains of 5-edo is represented by the odd numbers, the second by the even numbers, and the third by numbers with accidentals (either odd numbers with sharps, or even numbers with flats).</li><li><strong>Guitar Version:</strong> On a 15-edo guitar, because the &quot;perfect fourth&quot; comes from 5-edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the circle of fourths on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15-edo, it is necessary to use accidentals to notate intervals on the other two chains of 5-edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15-edo on the guitar, since 5-edo provides a useful set of 3-limit landmarks (or &quot;perfect fourths&quot; and &quot;perfect fifths&quot;) that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.</li></ul><br /> | <ul><li><strong>Decimal Version:</strong> Using the nominals 1-0 (with 0 representing &quot;10&quot;), one of the three chains of 5-edo is represented by the odd numbers, the second by the even numbers, and the third by numbers with accidentals (either odd numbers with sharps, or even numbers with flats).</li><li><strong>Guitar Version:</strong> On a 15-edo guitar, because the &quot;perfect fourth&quot; comes from 5-edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the circle of fourths on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15-edo, it is necessary to use accidentals to notate intervals on the other two chains of 5-edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15-edo on the guitar, since 5-edo provides a useful set of 3-limit landmarks (or &quot;perfect fourths&quot; and &quot;perfect fifths&quot;) that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.</li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="Notation-Porcupine Notation"></a><!-- ws:end:WikiTextHeadingRule:16 -->Porcupine Notation</h2> | ||
<ul><li>See the main <a class="wiki_link" href="/Porcupine%20Notation">porcupine notation</a> page.</li></ul> | <ul><li>See the main <a class="wiki_link" href="/Porcupine%20Notation">porcupine notation</a> page.</li></ul>Porcupine notation bases porcupine[8] LLLLLLLs scale using eight nominals α β χ δ ε φ γ η. Others have proposed ABCDEFGHA but conflicts with european notation have caused many to reject this approach. Thus greek letters can be used in place with a close resemblance to the spelling of ABCDEFGHA. <br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="Notation-Interval names for Porcupine[8]:"></a><!-- ws:end:WikiTextHeadingRule:18 -->Interval names for Porcupine[8]:</h2> | ||
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<td>Half Quill<br /> | <td>Half Quill<br /> | ||
</td> | </td> | ||
<td> | <td>α - β\<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,125: | Line 1,090: | ||
<td>Quill<br /> | <td>Quill<br /> | ||
</td> | </td> | ||
<td> | <td>α - β<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,133: | Line 1,098: | ||
<td>Small Diquill<br /> | <td>Small Diquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - χ\<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,141: | Line 1,106: | ||
<td>Large Diquill<br /> | <td>Large Diquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - χ<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,149: | Line 1,114: | ||
<td>Small Triquill<br /> | <td>Small Triquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - δ\<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Large Triquill<br /> | <td>Large Triquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - δ<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Small Fourquill<br /> | <td>Small Fourquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - ε\<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Large Fourquill<br /> | <td>Large Fourquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - ε<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Small Fivequill<br /> | <td>Small Fivequill<br /> | ||
</td> | </td> | ||
<td> | <td>α - φ\<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Large Fivequill<br /> | <td>Large Fivequill<br /> | ||
</td> | </td> | ||
<td> | <td>α - φ<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Small Sixquill<br /> | <td>Small Sixquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - γ\<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Large Sixquill<br /> | <td>Large Sixquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - γ<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Small Sevenquill<br /> | <td>Small Sevenquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - η\<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Large Sevenquill<br /> | <td>Large Sevenquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - η<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Octoquill<br /> | <td>Octoquill<br /> | ||
</td> | </td> | ||
<td> | <td>α - α<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc9"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:20 -->Rank two temperaments</h1> | ||
<a class="wiki_link" href="/List%20of%2015et%20rank%20two%20temperaments%20by%20badness">List of 15et rank two temperaments by badness</a><br /> | <a class="wiki_link" href="/List%20of%2015et%20rank%20two%20temperaments%20by%20badness">List of 15et rank two temperaments by badness</a><br /> | ||
<a class="wiki_link" href="/List%20of%20edo-distinct%2015et%20rank%20two%20temperaments">List of edo-distinct 15et rank two temperaments</a><br /> | <a class="wiki_link" href="/List%20of%20edo-distinct%2015et%20rank%20two%20temperaments">List of edo-distinct 15et rank two temperaments</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc10"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:22 -->Commas</h1> | ||
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15 EDO <a class="wiki_link" href="/tempering%20out">tempers</a> out the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 15 24 35 42 52 56 |.)<br /> | 15 EDO <a class="wiki_link" href="/tempering%20out">tempers</a> out the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 15 24 35 42 52 56 |.)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc11"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:24 -->Theory</h1> | ||
<a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar35.htm" rel="nofollow">The 15-Tone Scale System</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xZyzKBEW" rel="nofollow">Permalink</a><br /> | <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar35.htm" rel="nofollow">The 15-Tone Scale System</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xZyzKBEW" rel="nofollow">Permalink</a><br /> | ||
<a class="wiki_link_ext" href="http://www.inteas.com/Penta01.htm" rel="nofollow">The Pentadecaphonic System</a><br /> | <a class="wiki_link_ext" href="http://www.inteas.com/Penta01.htm" rel="nofollow">The Pentadecaphonic System</a><br /> | ||
<a class="wiki_link_ext" href="http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html" rel="nofollow">15-EDO Tutorial</a> by <a class="wiki_link" href="/Brent%20Carson">Brent Carson</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeJYBsDg" rel="nofollow">Permalink</a><br /> | <a class="wiki_link_ext" href="http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html" rel="nofollow">15-EDO Tutorial</a> by <a class="wiki_link" href="/Brent%20Carson">Brent Carson</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeJYBsDg" rel="nofollow">Permalink</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc12"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:26 -->Practical Theory / Books</h1> | ||
<a class="wiki_link_ext" href="http://www.swordguitars.com" rel="nofollow">Sword, Ronald. &quot;Pendecaphonic Scales for Guitar&quot; IAAA Press, UK-USA. First Ed: June 2009.</a> - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions.<br /> | <a class="wiki_link_ext" href="http://www.swordguitars.com" rel="nofollow">Sword, Ronald. &quot;Pendecaphonic Scales for Guitar&quot; IAAA Press, UK-USA. First Ed: June 2009.</a> - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc13"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:28 -->Compositions</h1> | ||
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<strong><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/" rel="nofollow" target="_blank">XA 15-ET Directory</a></strong><br /> | <strong><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/" rel="nofollow" target="_blank">XA 15-ET Directory</a></strong><br /> | ||
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<a class="wiki_link_ext" href="http://youtu.be/6TyQ9kDm2fk" rel="nofollow">Ode For Ada</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/5f07ebbdf8b4ba8ef067ed3d00a38357-158.html" rel="nofollow">blog entry</a>)<br /> | <a class="wiki_link_ext" href="http://youtu.be/6TyQ9kDm2fk" rel="nofollow">Ode For Ada</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/5f07ebbdf8b4ba8ef067ed3d00a38357-158.html" rel="nofollow">blog entry</a>)<br /> | ||
Suite in 15-Note Equal Tuning, opus 33 by Easley Blackwood (as well as one of the Twelve Microtonal Etudes, opus 28)<br /> | Suite in 15-Note Equal Tuning, opus 33 by Easley Blackwood (as well as one of the Twelve Microtonal Etudes, opus 28)<br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:1355:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/15edo-Chords.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@15edo-Chords.ogg&quot; title=&quot;File: 15edo-Chords.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg" onclick="ws.common.trackFileLink('/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="15edo-Chords.ogg" /></a><div><a href="/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg" onclick="ws.common.trackFileLink('/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg');" class="filename" title="15edo-Chords.ogg">15edo-Chords.ogg</a><br /><ul><li><a href="/file/detail/15edo-Chords.ogg">Details</a></li><li><a href="/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg">Download</a></li><li style="color: #666">2 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:1355 --> Some nice sounds I found in 15 EDO<br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:1356:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/happenstance15.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@happenstance15.ogg&quot; title=&quot;File: happenstance15.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/happenstance15.ogg/257380320/happenstance15.ogg" onclick="ws.common.trackFileLink('/file/view/happenstance15.ogg/257380320/happenstance15.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="happenstance15.ogg" /></a><div><a href="/file/view/happenstance15.ogg/257380320/happenstance15.ogg" onclick="ws.common.trackFileLink('/file/view/happenstance15.ogg/257380320/happenstance15.ogg');" class="filename" title="happenstance15.ogg">happenstance15.ogg</a><br /><ul><li><a href="/file/detail/happenstance15.ogg">Details</a></li><li><a href="/file/view/happenstance15.ogg/257380320/happenstance15.ogg">Download</a></li><li style="color: #666">6 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:1356 -->Sonic experiment in 15. Somewhat familiar tonality.<br /> | ||
<span class="long-title"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=kQECU5ecCd4" rel="nofollow" target="_blank">Portrait of insects with 15-tone equal tempered guitar music </a></span><br /> | <span class="long-title"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=kQECU5ecCd4" rel="nofollow" target="_blank">Portrait of insects with 15-tone equal tempered guitar music </a></span><br /> | ||
<a class="wiki_link_ext" href="http://www.reverbnation.com/ffffiale/song/3073160-pentadecafonicoda-15et" rel="nofollow">PentadecafoniCoda (15et)</a> by <span class="wiki_link_ext">F.F.F. Fiale</span><br /> | <a class="wiki_link_ext" href="http://www.reverbnation.com/ffffiale/song/3073160-pentadecafonicoda-15et" rel="nofollow">PentadecafoniCoda (15et)</a> by <span class="wiki_link_ext">F.F.F. Fiale</span><br /> | ||