14edo: Difference between revisions
Wikispaces>guest **Imported revision 242215355 - Original comment: ** |
Wikispaces>xenjacob **Imported revision 247223555 - 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:xenjacob|xenjacob]] and made on <tt>2011-08-20 15:06:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>247223555</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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<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">=<span style="color: #790025; font-family: 'Times New Roman',Times,serif; font-size: 109%;">[[media type="custom" key="10021329"]]14 tone equal temperament</span>= | <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">=<span style="color: #790025; font-family: 'Times New Roman',Times,serif; font-size: 109%;">[[media type="custom" key="10021329"]]14 tone equal temperament</span>= | ||
==**14-EDO | ==**14-EDO interval analysis**== | ||
|| **DEGREE** || **NOTE** || **CENTS** ||= **Approximate** | || **DEGREE** || **NOTE** | ||
**Ratios*** ||= **Nearest** | **NAME** || **CENTS** ||= **Approximate** | ||
**Ratios**** ||= **Nearest** | |||
**Harmonic** || **Interval Type** || | **Harmonic** || **Interval Type** || | ||
|| 0 || C || 0 ||= 1/1 ||= 1 || Unison || | || 0 || C || 0 ||= 1/1 ||= 1 || Unison || | ||
|| 1 || C* || 85.714 ||= 81/77, 126/121 ||= 67 || Narrow Minor 2nd || | || 1 || C* || 85.714 ||= 81/77, 126/121 ||= 67 || Narrow Minor 2nd || | ||
|| 2 || D || 171.429 ||= 11/10, 10/9 ||= 71 || Neutral 2nd, or | || 2 || D || 171.429 ||= 11/10, 10/9 ||= 71 || Neutral 2nd, or | ||
Narrow Major 2nd || | Narrow Major 2nd || | ||
|| 3· || D* || 257.143 ||= 81/70, 90/77 ||= 37 || Subminor 3rd || | || 3· || D* || 257.143 ||= 81/70, 90/77 ||= 37 || Subminor 3rd || | ||
| Line 29: | Line 30: | ||
|| 13 || B* || 1114.286 ||= 154/81, 121/63 ||= 61 || Wide Major 7th || | || 13 || B* || 1114.286 ||= 154/81, 121/63 ||= 61 || Wide Major 7th || | ||
|| 14··(or 0) || C || 1200 ||= 2/1 ||= 2 || Octave || | || 14··(or 0) || C || 1200 ||= 2/1 ||= 2 || Octave || | ||
*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible. | **based on treating 14-EDO as a 2.11/5.11/7.11/9 [[subgroup]]; other approaches are possible. | ||
== == | |||
==Harmony== | ==Harmony== | ||
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14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad. | 14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad. | ||
==Notation== | |||
[[Ivor Darreg]] wrote in [[http://sonic-arts.org/darreg/dar15.htm|this article]]: | |||
//The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.// | |||
The following chart (made by who?) shows this recommendation as "standard notation" as well as a proposed alternative. | |||
[[image:Ciclo_Tetradecafonía.png width="456" height="468" caption="Intervallic Cycle of 14 steps Equal per Octave"]] | [[image:Ciclo_Tetradecafonía.png width="456" height="468" caption="Intervallic Cycle of 14 steps Equal per Octave"]] | ||
== | ==Commas:== | ||
14 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 14 22 33 39 48 52 |.) | 14 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 14 22 33 39 48 52 |.) | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 || | ||
| Line 93: | Line 101: | ||
[[media type="custom" key="9748118"]] | [[media type="custom" key="9748118"]] | ||
Thereminnards by Ralph Lewis | |||
Pendula for amplified trombone by Philip Scheussler | |||
<span class="ymp-btn-page-play ymp-media-4c2dab90062954a92dc59831018d92d9">[[http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3|Riding the L]]</span> by [[@http://chrisvaisvil.com/?p=943|Chris Vaisvil]] | <span class="ymp-btn-page-play ymp-media-4c2dab90062954a92dc59831018d92d9">[[http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3|Riding the L]]</span> by [[@http://chrisvaisvil.com/?p=943|Chris Vaisvil]] | ||
<span class="ymp-btn-page-play ymp-media-579db51554bd270599a9397e8446cdb9">[[http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3|Thorium Road]]</span> by [[Jon Lyle Smith]] | <span class="ymp-btn-page-play ymp-media-579db51554bd270599a9397e8446cdb9">[[http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3|Thorium Road]]</span> by [[Jon Lyle Smith]] | ||
| Line 104: | Line 114: | ||
</script><!-- ws:end:WikiTextMediaRule:0 -->14 tone equal temperament</span></h1> | </script><!-- ws:end:WikiTextMediaRule:0 -->14 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="x14 tone equal temperament-14-EDO | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="x14 tone equal temperament-14-EDO interval analysis"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>14-EDO interval analysis</strong></h2> | ||
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</td> | </td> | ||
<td><strong>NOTE</strong><br /> | <td><strong>NOTE</strong><br /> | ||
<strong>NAME</strong><br /> | |||
</td> | </td> | ||
<td><strong>CENTS</strong><br /> | <td><strong>CENTS</strong><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><strong>Approximate</strong><br /> | <td style="text-align: center;"><strong>Approximate</strong><br /> | ||
<strong>Ratios</strong> | <strong>Ratios</strong><strong><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><strong>Nearest< | <td style="text-align: center;"></strong>Nearest<strong><br /> | ||
<strong>Harmonic< | </strong>Harmonic<strong><br /> | ||
</td> | </td> | ||
<td><strong>Interval Type< | <td></strong>Interval Type<strong><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 163: | Line 174: | ||
<td style="text-align: center;">71<br /> | <td style="text-align: center;">71<br /> | ||
</td> | </td> | ||
<td>Neutral 2nd, or <br /> | <td>Neutral 2nd, or<br /> | ||
Narrow Major 2nd<br /> | Narrow Major 2nd<br /> | ||
</td> | </td> | ||
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</table> | </table> | ||
</strong>based on treating 14-EDO as a 2.11/5.11/7.11/9 <a class="wiki_link" href="/subgroup">subgroup</a>; other approaches are possible.<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc2"><a name="x14 tone equal temperament-Harmony"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc2"><!-- ws:end:WikiTextHeadingRule:6 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="x14 tone equal temperament-Harmony"></a><!-- ws:end:WikiTextHeadingRule:8 -->Harmony</h2> | |||
<br /> | <br /> | ||
The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).<br /> | The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).<br /> | ||
| Line 345: | Line 357: | ||
14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.<br /> | 14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc4"><a name="x14 tone equal temperament-Notation"></a><!-- ws:end:WikiTextHeadingRule:10 -->Notation</h2> | |||
<a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> wrote in <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar15.htm" rel="nofollow">this article</a>: <br /> | |||
<br /> | |||
<em>The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.</em><br /> | |||
<br /> | |||
The following chart (made by who?) shows this recommendation as &quot;standard notation&quot; as well as a proposed alternative.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:406:&lt;img src=&quot;/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png&quot; alt=&quot;Intervallic Cycle of 14 steps Equal per Octave&quot; title=&quot;Intervallic Cycle of 14 steps Equal per Octave&quot; style=&quot;height: 468px; width: 456px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 14 steps Equal per Octave</td></tr></table><!-- ws:end:WikiTextLocalImageRule:406 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc5"><a name="x14 tone equal temperament-Commas:"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas:</h2> | ||
14 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 14 22 33 39 48 52 |.)<br /> | 14 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 14 22 33 39 48 52 |.)<br /> | ||
| Line 512: | Line 530: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="x14 tone equal temperament-14 tone equal modes:"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong>14 tone equal <a class="wiki_link" href="/modes">modes</a>:</strong></h2> | ||
6 6 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of <a class="wiki_link" href="/2L1s">2L1s</a><br /> | 6 6 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of <a class="wiki_link" href="/2L1s">2L1s</a><br /> | ||
5 5 4 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/2L1s">2L1s</a></span><br /> | 5 5 4 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/2L1s">2L1s</a></span><br /> | ||
| Line 539: | Line 557: | ||
<strong>1 1 2 1 1 1 2 1 1 1 2</strong> - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/3L8s">3L8s</a></span><br /> | <strong>1 1 2 1 1 1 2 1 1 1 2</strong> - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/3L8s">3L8s</a></span><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="x14 tone equal temperament-Instruments:"></a><!-- ws:end:WikiTextHeadingRule:16 -->Instruments:</h2> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:408:&lt;img src=&quot;http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 256px; width: 750px;&quot; /&gt; --><img src="http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg" alt="external image 14edo+guitar+%282%29.jpg" title="external image 14edo+guitar+%282%29.jpg" style="height: 256px; width: 750px;" /><!-- ws:end:WikiTextRemoteImageRule:408 --><br /> | ||
<em>A Tetradecaphonic Guitar. 14-EDO Guitar by Ron Sword.</em><br /> | <em>A Tetradecaphonic Guitar. 14-EDO Guitar by Ron Sword.</em><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="x14 tone equal temperament-Books:"></a><!-- ws:end:WikiTextHeadingRule:18 --><strong>Books:</strong></h2> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:407:&lt;img src=&quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 431px; width: 360px;&quot; /&gt; --><img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" style="height: 431px; width: 360px;" /><!-- ws:end:WikiTextLocalImageRule:407 --><br /> | ||
<em>Sword, Ron. &quot;Tetradecaphonic Scales for Guitar&quot; IAAA Press. First Ed: June 2009.</em><br /> | <em>Sword, Ron. &quot;Tetradecaphonic Scales for Guitar&quot; IAAA Press. First Ed: June 2009.</em><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc9"><a name="x14 tone equal temperament-Compositions:"></a><!-- ws:end:WikiTextHeadingRule:20 --><strong>Compositions:</strong></h2> | ||
<!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/9748118?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;9748118&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"> | <!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/9748118?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;9748118&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"> | ||
</script><!-- ws:end:WikiTextMediaRule:1 --><br /> | </script><!-- ws:end:WikiTextMediaRule:1 --><br /> | ||
<br /> | <br /> | ||
Thereminnards by Ralph Lewis<br /> | |||
Pendula for amplified trombone by Philip Scheussler<br /> | |||
<span class="ymp-btn-page-play ymp-media-4c2dab90062954a92dc59831018d92d9"><a class="wiki_link_ext" href="http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3" rel="nofollow">Riding the L</a></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=943" rel="nofollow" target="_blank">Chris Vaisvil</a><br /> | <span class="ymp-btn-page-play ymp-media-4c2dab90062954a92dc59831018d92d9"><a class="wiki_link_ext" href="http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3" rel="nofollow">Riding the L</a></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=943" rel="nofollow" target="_blank">Chris Vaisvil</a><br /> | ||
<span class="ymp-btn-page-play ymp-media-579db51554bd270599a9397e8446cdb9"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3" rel="nofollow">Thorium Road</a></span> by <a class="wiki_link" href="/Jon%20Lyle%20Smith">Jon Lyle Smith</a><br /> | <span class="ymp-btn-page-play ymp-media-579db51554bd270599a9397e8446cdb9"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3" rel="nofollow">Thorium Road</a></span> by <a class="wiki_link" href="/Jon%20Lyle%20Smith">Jon Lyle Smith</a><br /> | ||