16edo: Difference between revisions
Wikispaces>guest **Imported revision 156700977 - Original comment: ** |
Wikispaces>tetraF **Imported revision 161052841 - 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: | : This revision was by author [[User:tetraF|tetraF]] and made on <tt>2010-09-08 04:27:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>161052841</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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16-EDO notation can be easy utilizing Goldsmith's Circle of keys, Nominals, and respective Notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon | 16-EDO notation can be easy utilizing Goldsmith's Circle of keys, Nominals, and respective Notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon | ||
additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO. | additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO. | ||
=**Armodue theory**= | |||
//(summary translation from the italian site)// | |||
Not only referring to the 16-edo equal temperament, but also to half-equal and Lou Harrison's Just intonation 16 note scale, natural octave division of <span style="-webkit-border-horizontal-spacing: 1px; -webkit-border-vertical-spacing: 1px; font-family: Verdana; font-size: small; line-height: normal;">Andrián Pertout, </span> | |||
<span style="-webkit-border-horizontal-spacing: 1px; -webkit-border-vertical-spacing: 1px; font-family: Verdana; font-size: small; line-height: normal;">and 16-to-31 overtone scale, </span>Armodue is proposed as __totally new notation and theory system__. | |||
Attempting of making much easy as possible the approach to Armodue, but conscious they had to give new names to the notes that constitutes the system, the italian creators of <span style="background-attachment: initial; background-clip: initial; background-color: initial; url(http: //www.wikispaces.com/i/a.gif); background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;">[[@http://armodue.com|Armodue]]</span> system called them numbering from 1 to 9: | |||
1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9 | |||
Consequently, the interval between a note at frequency n and other at frequency 2n is called **tenth**. | |||
For composing in Armodue it's useful using a **tetragram** (staff with 4 lines) | |||
[[image:http://www.armodue.com/TETR-[1].jpg caption="copyright Armodue, used with permission"]] | |||
In a musical piece, for which esecution, if we need to write on two o more tetragrams, the notes will be written in the same way for every tetragram. | |||
In other words, the "1" note will be written immediately under the first line __in every tenth__. | |||
In Armodue we have only a numeric clef, that show us the tenth: | |||
[[image:http://www.armodue.com/Chiave.gif caption="copyright Armodue, used with permission"]] | |||
The clefs 1,2,3... refers to the tenths: first, second, third... | |||
So, in the illustrated example above, first tetragram (from top) refers to the 3rd tenth (central tenth, corresponding at equivalent octave C3-C4), | |||
the second tetragram to the 5th tenth and the third to the 2nd. If we need to write simultaneously on several staves, we will draws normal braces. | |||
The keyboard conceived by Armodue authors has the same disposition of the Goldsmith's one (except the curvature): | |||
[[image:http://www.armodue.com/Tastiera.jpg caption="copyright Armodue, used by permission"]] | |||
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[[@http://www.ronsword.com/sounds/ronsword_miracle528_part3.mp3|16-tet Magic Drone]] by Ron Sword</pre></div> | [[@http://www.ronsword.com/sounds/ronsword_miracle528_part3.mp3|16-tet Magic Drone]] by Ron Sword</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>16edo</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>16edo</title></head><body><!-- ws:start:WikiTextTocRule:12:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Hexadecaphonic Octave Theory">Hexadecaphonic Octave Theory</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#toc1"> </a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Hexadecaphonic Notation:">Hexadecaphonic Notation:</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Armodue theory">Armodue theory</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#External theory links">External theory links</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextRemoteImageRule:21:&lt;img src=&quot;http://ronsword.com/DSgoldsmith_piece.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 380px; width: 1120px;&quot; /&gt; --><img src="http://ronsword.com/DSgoldsmith_piece.jpg" alt="external image DSgoldsmith_piece.jpg" title="external image DSgoldsmith_piece.jpg" style="height: 380px; width: 1120px;" /><!-- ws:end:WikiTextRemoteImageRule:21 --><br /> | ||
<hr /> | <hr /> | ||
<br /> | <br /> | ||
16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.<br /> | 16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextUserlinkRule:00:[[user:Andrew_Heathwaite|1281203319]] --><span class="membersnap">- <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"><img src="http://www.wikispaces.com/user/pic/Andrew_Heathwaite-lg.jpg" width="16" height="16" alt="Andrew_Heathwaite" class="userPicture" /></a> <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;">Andrew_Heathwaite</a> <small>Aug 7, 2010</small></span><!-- ws:end:WikiTextUserlinkRule:00 --> adds: If we take the 300-cent minor third as an approximation of the harmonic 19th (19/16, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad. The interval between the 28th &amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's &quot;narrow fifth&quot;. example on Goldsmith board: <!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextUserlinkRule:00:[[user:Andrew_Heathwaite|1281203319]] --><span class="membersnap">- <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"><img src="http://www.wikispaces.com/user/pic/Andrew_Heathwaite-lg.jpg" width="16" height="16" alt="Andrew_Heathwaite" class="userPicture" /></a> <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;">Andrew_Heathwaite</a> <small>Aug 7, 2010</small></span><!-- ws:end:WikiTextUserlinkRule:00 --> adds: If we take the 300-cent minor third as an approximation of the harmonic 19th (19/16, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad. The interval between the 28th &amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's &quot;narrow fifth&quot;. example on Goldsmith board: <!-- ws:start:WikiTextRemoteImageRule:22:&lt;img src=&quot;http://www.ronsword.com/161928%20copy.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 92px; width: 158px;&quot; /&gt; --><img src="http://www.ronsword.com/161928%20copy.jpg" alt="external image 161928%20copy.jpg" title="external image 161928%20copy.jpg" style="height: 92px; width: 158px;" /><!-- ws:end:WikiTextRemoteImageRule:22 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Hexadecaphonic Octave Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Hexadecaphonic Octave Theory</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Hexadecaphonic Octave Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Hexadecaphonic Octave Theory</h1> | ||
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16-EDO notation can be easy utilizing Goldsmith's Circle of keys, Nominals, and respective Notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon <br /> | 16-EDO notation can be easy utilizing Goldsmith's Circle of keys, Nominals, and respective Notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon <br /> | ||
additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO. <br /> | additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO. <br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Armodue theory"></a><!-- ws:end:WikiTextHeadingRule:6 --><strong>Armodue theory</strong></h1> | |||
<em>(summary translation from the italian site)</em><br /> | |||
<br /> | |||
Not only referring to the 16-edo equal temperament, but also to half-equal and Lou Harrison's Just intonation 16 note scale, natural octave division of <span style="-webkit-border-horizontal-spacing: 1px; -webkit-border-vertical-spacing: 1px; font-family: Verdana; font-size: small; line-height: normal;">Andrián Pertout, </span><br /> | |||
<span style="-webkit-border-horizontal-spacing: 1px; -webkit-border-vertical-spacing: 1px; font-family: Verdana; font-size: small; line-height: normal;">and 16-to-31 overtone scale, </span>Armodue is proposed as <u>totally new notation and theory system</u>.<br /> | |||
<br /> | |||
Attempting of making much easy as possible the approach to Armodue, but conscious they had to give new names to the notes that constitutes the system, the italian creators of <span style="background-attachment: initial; background-clip: initial; background-color: initial; url(http: //www.wikispaces.com/i/a.gif); background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"><a class="wiki_link_ext" href="http://armodue.com" rel="nofollow" target="_blank">Armodue</a></span> system called them numbering from 1 to 9:<br /> | |||
<br /> | |||
1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9<br /> | |||
<br /> | |||
Consequently, the interval between a note at frequency n and other at frequency 2n is called <strong>tenth</strong>.<br /> | |||
<br /> | |||
<br /> | |||
<br /> | |||
For composing in Armodue it's useful using a <strong>tetragram</strong> (staff with 4 lines)<br /> | |||
<br /> | |||
[[image:<!-- ws:start:WikiTextUrlRule:152:http://www.armodue.com/TETR- --><a class="wiki_link_ext" href="http://www.armodue.com/TETR-" rel="nofollow">http://www.armodue.com/TETR-</a><!-- ws:end:WikiTextUrlRule:152 -->[1].jpg caption=&quot;copyright Armodue, used with permission&quot;]]<br /> | |||
<br /> | |||
In a musical piece, for which esecution, if we need to write on two o more tetragrams, the notes will be written in the same way for every tetragram.<br /> | |||
In other words, the &quot;1&quot; note will be written immediately under the first line <u>in every tenth</u>.<br /> | |||
<br /> | |||
In Armodue we have only a numeric clef, that show us the tenth:<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:23:&lt;img src=&quot;http://www.armodue.com/Chiave.gif&quot; alt=&quot;copyright Armodue, used with permission&quot; title=&quot;copyright Armodue, used with permission&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="http://www.armodue.com/Chiave.gif" alt="copyright Armodue, used with permission" title="copyright Armodue, used with permission" /></td></tr><tr><td class="imageCaption">copyright Armodue, used with permission</td></tr></table><!-- ws:end:WikiTextRemoteImageRule:23 --><br /> | |||
<br /> | |||
<br /> | |||
<br /> | |||
The clefs 1,2,3... refers to the tenths: first, second, third...<br /> | |||
So, in the illustrated example above, first tetragram (from top) refers to the 3rd tenth (central tenth, corresponding at equivalent octave C3-C4), <br /> | |||
the second tetragram to the 5th tenth and the third to the 2nd. If we need to write simultaneously on several staves, we will draws normal braces.<br /> | |||
<br /> | |||
The keyboard conceived by Armodue authors has the same disposition of the Goldsmith's one (except the curvature):<br /> | |||
<!-- ws:start:WikiTextRemoteImageRule:24:&lt;img src=&quot;http://www.armodue.com/Tastiera.jpg&quot; alt=&quot;copyright Armodue, used by permission&quot; title=&quot;copyright Armodue, used by permission&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="http://www.armodue.com/Tastiera.jpg" alt="copyright Armodue, used by permission" title="copyright Armodue, used by permission" /></td></tr><tr><td class="imageCaption">copyright Armodue, used by permission</td></tr></table><!-- ws:end:WikiTextRemoteImageRule:24 --><br /> | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="External theory links"></a><!-- ws:end:WikiTextHeadingRule:8 -->External theory links</h1> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow">Armodue</a>: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions - translation, anyone?<br /> | <a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow">Armodue</a>: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions - translation, anyone?<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:25:&lt;img src=&quot;http://ronsword.com/images/ESG_sm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 161px; width: 120px;&quot; /&gt; --><img src="http://ronsword.com/images/ESG_sm.jpg" alt="external image ESG_sm.jpg" title="external image ESG_sm.jpg" style="height: 161px; width: 120px;" /><!-- ws:end:WikiTextRemoteImageRule:25 --><br /> | ||
Sword, Ronald. &quot;Hexadecaphonic Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).<br /> | Sword, Ronald. &quot;Hexadecaphonic Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).<br /> | ||
Sword, Ronald. &quot;Esadekaphonic Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning)<br /> | Sword, Ronald. &quot;Esadekaphonic Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Compositions</h1> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/16tet.mid" rel="nofollow">Etude in 16-tone equal tuning</a> by Herman Miller<br /> | <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/16tet.mid" rel="nofollow">Etude in 16-tone equal tuning</a> by Herman Miller<br /> | ||