14edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 601330454 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602052384 - 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:TallKite|TallKite]] and made on <tt>2016-12-13 06:51:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602052384</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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360° ||= 2/1 ||= 2/1 ||= 2 || Octave || | 360° ||= 2/1 ||= 2/1 ||= 2 || Octave || | ||
``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible. | ``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible. | ||
<span style="display: block; text-align: center;">``**``</span> | <span style="display: block; text-align: center;">``**``based on treating 14edo as an 11-limit temperament</span> | ||
=Chord Names= | |||
Ups and downs can be used to name 14edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. | |||
0-4-8 = C E G = C = C or C perfect | |||
0-3-8 = C Ev G = C(v3) = C down-three | |||
0-5-8 = C E^ G = C(^3) = C up-three | |||
0-4-7 = C E Gv = C(v5) = C down-five | |||
0-5-9 = C E^ G^ = C(^3,^5) = C up-three up-five | |||
0-4-8-12 = C E G B = C7 = C seven | |||
0-4-8-11 = C E G Bv = C(v7) = C down-seven | |||
0-3-8-12 = C Ev G B = C7(v3) = C seven down-three | |||
0-3-8-11 = C Ev G Bv = C.v7 = C dot down seven | |||
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | |||
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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>14edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/14%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | <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>14edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/14%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:27:&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:27 --><!-- ws:start:WikiTextTocRule:28: --><a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Chord Names">Chord Names</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Harmony">Harmony</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Notation">Notation</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#Images">Images</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Modes">Modes</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Books">Books</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 --><strong>Intervals</strong></h1> | ||
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<!-- ws:start:WikiTextRawRule:02:``*`` -->*<!-- ws:end:WikiTextRawRule:02 -->based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 <a class="wiki_link" href="/subgroup">subgroup</a>; other approaches are possible.<br /> | <!-- ws:start:WikiTextRawRule:02:``*`` -->*<!-- ws:end:WikiTextRawRule:02 -->based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 <a class="wiki_link" href="/subgroup">subgroup</a>; other approaches are possible.<br /> | ||
<span style="display: block; text-align: center;"><!-- ws:start:WikiTextRawRule:03:``**`` -->**<!-- ws:end:WikiTextRawRule:03 --></span><br /> | <span style="display: block; text-align: center;"><!-- ws:start:WikiTextRawRule:03:``**`` -->**<!-- ws:end:WikiTextRawRule:03 -->based on treating 14edo as an 11-limit temperament</span><br /> | ||
<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc1"><a name="Chord Names"></a><!-- ws:end:WikiTextHeadingRule:7 -->Chord Names</h1> | |||
<br /> | |||
Ups and downs can be used to name 14edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.<br /> | |||
<br /> | |||
0-4-8 = C E G = C = C or C perfect<br /> | |||
0-3-8 = C Ev G = C(v3) = C down-three<br /> | |||
0-5-8 = C E^ G = C(^3) = C up-three<br /> | |||
0-4-7 = C E Gv = C(v5) = C down-five<br /> | |||
0-5-9 = C E^ G^ = C(^3,^5) = C up-three up-five<br /> | |||
<br /> | |||
0-4-8-12 = C E G B = C7 = C seven<br /> | |||
0-4-8-11 = C E G Bv = C(v7) = C down-seven<br /> | |||
0-3-8-12 = C Ev G B = C7(v3) = C seven down-three<br /> | |||
0-3-8-11 = C Ev G Bv = C.v7 = C dot down seven<br /> | |||
<br /> | |||
For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc2"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:9 -->Rank two temperaments</h1> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2014edo%20rank%20two%20temperaments%20by%20badness">List of 14edo rank two temperaments by badness</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2014edo%20rank%20two%20temperaments%20by%20badness">List of 14edo rank two temperaments by badness</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc3"><a name="Harmony"></a><!-- ws:end:WikiTextHeadingRule:11 -->Harmony</h1> | ||
The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second &quot;Approximate Ratios&quot; column in the table above.<br /> | The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second &quot;Approximate Ratios&quot; column in the table above.<br /> | ||
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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.<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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h3&gt; --><h3 id="toc4"><a name="Harmony--Titanium[9]"></a><!-- ws:end:WikiTextHeadingRule:13 -->Titanium[9]</h3> | ||
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14edo is also the largest edo whose patent val supports <a class="wiki_link" href="/titanium">titanium</a> temperament, tempering out the chromatic semitone (21:20), and falling toward the &quot;brittle&quot; (fifths wider than in 9edo) end of that spectrum. Titanium is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres (&quot;bell-like&quot; or opaque-sounding ones probably work best). Titanium forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Titanium[9] has similarities to mavila, slendro, and pelog scales as well.<br /> | 14edo is also the largest edo whose patent val supports <a class="wiki_link" href="/titanium">titanium</a> temperament, tempering out the chromatic semitone (21:20), and falling toward the &quot;brittle&quot; (fifths wider than in 9edo) end of that spectrum. Titanium is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres (&quot;bell-like&quot; or opaque-sounding ones probably work best). Titanium forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Titanium[9] has similarities to mavila, slendro, and pelog scales as well.<br /> | ||
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14\14: The 10th<span style="vertical-align: sub;">9 </span>or &quot;enneatonic decave&quot;, (i. e., the octave, 2:1).<br /> | 14\14: The 10th<span style="vertical-align: sub;">9 </span>or &quot;enneatonic decave&quot;, (i. e., the octave, 2:1).<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc5"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:15 -->Notation</h1> | ||
<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 /> | <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 /> | ||
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The following chart (made by <a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a>) shows this recommendation as &quot;standard notation&quot; as well as a proposed alternative.<br /> | The following chart (made by <a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a>) shows this recommendation as &quot;standard notation&quot; as well as a proposed alternative.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:486:&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:486 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc6"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:17 -->Images</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc7"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:19 -->Commas</h1> | ||
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 52/1 |.)<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 52/1 |.)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc8"><a name="Modes"></a><!-- ws:end:WikiTextHeadingRule:21 --><strong><a class="wiki_link" href="/modes">Modes</a></strong></h1> | ||
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 /> | ||
5 4 5 - <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 4 5 - <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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:23:&lt;h1&gt; --><h1 id="toc9"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:23 -->Books</h1> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:488:&lt;img src=&quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" /><!-- ws:end:WikiTextLocalImageRule:488 --><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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:25:&lt;h1&gt; --><h1 id="toc10"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:25 --><strong>Compositions</strong></h1> | ||
<a class="wiki_link_ext" href="http://split-notes.com/004/" rel="nofollow">NANA WODORI</a> by knowsur<br /> | <a class="wiki_link_ext" href="http://split-notes.com/004/" rel="nofollow">NANA WODORI</a> by knowsur<br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3" rel="nofollow">Thereminnards</a> by Ralph Lewis<br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3" rel="nofollow">Thereminnards</a> by Ralph Lewis<br /> |