14edo: Difference between revisions
Wikispaces>vaisvil **Imported revision 241874603 - Original comment: ** |
Wikispaces>igliashon **Imported revision 241875649 - 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:igliashon|igliashon]] and made on <tt>2011-07-18 22:49:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>241875649</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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==**14-EDO intervals:**== | ==**14-EDO intervals:**== | ||
|| **DEGREE** || **NOTE** || **CENTS** || **Nearest | || **DEGREE** || **NOTE** || **CENTS** || **Nearest** | ||
|| 0 || **C** || 0 || **1/1** || 0 || **None** || | **Ratio** || **Cents** || **Error** ||= **Approximate** | ||
|| 1 || C* || 85.714 || 21/20 || 84.467 || +1.247 || | **Just Interval** ||= **Nearest** | ||
|| 2 || D || 171.429 || 32/29 || 170.423 || +1.006 || | **Harmonic** || | ||
|| **3·** || **D*** || **257.143** || **36/31** || **258.874** || **-1.731** || | || 0 || **C** || 0 || **1/1** || 0 || **None** ||= 1/1 ||= 1 || | ||
|| 4 || E || 342.857 || 39/32 || 342.483 || +0.374 || | || 1 || C* || 85.714 || 21/20 || 84.467 || +1.247 ||= ||= 67 || | ||
|| **5·** || **E*** || **428.571** || **32/25** || **427.373** || **+1.198** || | || 2 || D || 171.429 || 32/29 || 170.423 || +1.006 ||= 11/10, 10/9 ||= 71 || | ||
|| 6 || F || 514.286 || 39/29 || 512.905 || +1.381 || | || **3·** || **D*** || **257.143** || **36/31** || **258.874** || **-1.731** ||= 7/6, 8/7 ||= 37 || | ||
|| **7·** || **F*** || **600** || **99/70** || **600.088** || **-0.088** || | || 4 || E || 342.857 || 39/32 || 342.483 || +0.374 ||= 11/9 ||= 39 || | ||
|| 8 || G || 685.714 || 58/39 || 687.095 || -1.381 || | || **5·** || **E*** || **428.571** || **32/25** || **427.373** || **+1.198** ||= 9/7 ||= 41 || | ||
|| **9·** || **G*** || **771.429** || **25/16** || **772.627** || **-1.198** || | || 6 || F || 514.286 || 39/29 || 512.905 || +1.381 ||= 4/3 ||= 43 || | ||
|| 10 || A || 857.143 || 64/39 || 857.517 || -0.374 || | || **7·** || **F*** || **600** || **99/70** || **600.088** || **-0.088** ||= 7/5, 10/7 ||= 91 || | ||
|| **11·** || **A*** || **942.857** || **31/18** || **941.126** || **+1.731** || | || 8 || G || 685.714 || 58/39 || 687.095 || -1.381 ||= 3/2 ||= 95 || | ||
|| 12 || B || 1028.571 || 29/16 || 1029.577 || -1.006 || | || **9·** || **G*** || **771.429** || **25/16** || **772.627** || **-1.198** ||= 14/9 ||= 25 || | ||
|| 13 || B* || 1114.286 || 40/21 || 1115.533 || -1.247 || | || 10 || A || 857.143 || 64/39 || 857.517 || -0.374 ||= 18/11 ||= 105 || | ||
|| **14··(or 0)** || **C** || **1200** || **2/1** || **1200** || **None** || | || **11·** || **A*** || **942.857** || **31/18** || **941.126** || **+1.731** ||= 12/7, 7/4 ||= 55 || | ||
|| 12 || B || 1028.571 || 29/16 || 1029.577 || -1.006 ||= 20/11, 9/5 ||= 29 || | |||
|| 13 || B* || 1114.286 || 40/21 || 1115.533 || -1.247 ||= ||= 61 || | |||
|| **14··(or 0)** || **C** || **1200** || **2/1** || **1200** || **None** ||= 2/1 ||= 2 || | |||
==Harmony== | |||
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, and in 28-EDO we can bump that up to 4:5:7:9:11, perhaps even 4:5:6:7:9:11 if we are feeling charitable). 6:7:9 appears to be better-approximated than it actually sounds, though it is still reasonably consonant. | |||
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. | |||
[[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"]] | ||
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<td><strong>CENTS</strong><br /> | <td><strong>CENTS</strong><br /> | ||
</td> | </td> | ||
<td><strong>Nearest | <td><strong>Nearest</strong><br /> | ||
<strong>Ratio</strong><br /> | |||
</td> | </td> | ||
<td><strong>Cents</strong><br /> | <td><strong>Cents</strong><br /> | ||
</td> | </td> | ||
<td><strong>Error</strong><br /> | <td><strong>Error</strong><br /> | ||
</td> | |||
<td style="text-align: center;"><strong>Approximate</strong><br /> | |||
<strong>Just Interval</strong><br /> | |||
</td> | |||
<td style="text-align: center;"><strong>Nearest</strong><br /> | |||
<strong>Harmonic</strong><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td><strong>None</strong><br /> | <td><strong>None</strong><br /> | ||
</td> | |||
<td style="text-align: center;">1/1<br /> | |||
</td> | |||
<td style="text-align: center;">1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>+1.247<br /> | <td>+1.247<br /> | ||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">67<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>+1.006<br /> | <td>+1.006<br /> | ||
</td> | |||
<td style="text-align: center;">11/10, 10/9<br /> | |||
</td> | |||
<td style="text-align: center;">71<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td><strong>-1.731</strong><br /> | <td><strong>-1.731</strong><br /> | ||
</td> | |||
<td style="text-align: center;">7/6, 8/7<br /> | |||
</td> | |||
<td style="text-align: center;">37<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>+0.374<br /> | <td>+0.374<br /> | ||
</td> | |||
<td style="text-align: center;">11/9<br /> | |||
</td> | |||
<td style="text-align: center;">39<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td><strong>+1.198</strong><br /> | <td><strong>+1.198</strong><br /> | ||
</td> | |||
<td style="text-align: center;">9/7<br /> | |||
</td> | |||
<td style="text-align: center;">41<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>+1.381<br /> | <td>+1.381<br /> | ||
</td> | |||
<td style="text-align: center;">4/3<br /> | |||
</td> | |||
<td style="text-align: center;">43<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td><strong>-0.088</strong><br /> | <td><strong>-0.088</strong><br /> | ||
</td> | |||
<td style="text-align: center;">7/5, 10/7<br /> | |||
</td> | |||
<td style="text-align: center;">91<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>-1.381<br /> | <td>-1.381<br /> | ||
</td> | |||
<td style="text-align: center;">3/2<br /> | |||
</td> | |||
<td style="text-align: center;">95<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td><strong>-1.198</strong><br /> | <td><strong>-1.198</strong><br /> | ||
</td> | |||
<td style="text-align: center;">14/9<br /> | |||
</td> | |||
<td style="text-align: center;">25<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>-0.374<br /> | <td>-0.374<br /> | ||
</td> | |||
<td style="text-align: center;">18/11<br /> | |||
</td> | |||
<td style="text-align: center;">105<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td><strong>+1.731</strong><br /> | <td><strong>+1.731</strong><br /> | ||
</td> | |||
<td style="text-align: center;">12/7, 7/4<br /> | |||
</td> | |||
<td style="text-align: center;">55<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>-1.006<br /> | <td>-1.006<br /> | ||
</td> | |||
<td style="text-align: center;">20/11, 9/5<br /> | |||
</td> | |||
<td style="text-align: center;">29<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>-1.247<br /> | <td>-1.247<br /> | ||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">61<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td><strong>None</strong><br /> | <td><strong>None</strong><br /> | ||
</td> | |||
<td style="text-align: center;">2/1<br /> | |||
</td> | |||
<td style="text-align: center;">2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc2"><a name="x14 tone equal temperament-Harmony"></a><!-- ws:end:WikiTextHeadingRule:6 -->Harmony</h2> | ||
<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, and in 28-EDO we can bump that up to 4:5:7:9:11, perhaps even 4:5:6:7:9:11 if we are feeling charitable). 6:7:9 appears to be better-approximated than it actually sounds, though it is still reasonably consonant.<br /> | |||
<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:WikiTextLocalImageRule:466:&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:466 --><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="x14 tone equal temperament-Commas:"></a><!-- ws:end:WikiTextHeadingRule:8 --><span style="font-size: 1.3em;">Commas:</span></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 /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc4"><a name="x14 tone equal temperament-14 tone equal modes:"></a><!-- ws:end:WikiTextHeadingRule:10 --><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 /> | ||
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<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:12:&lt;h2&gt; --><h2 id="toc5"><a name="x14 tone equal temperament-Instruments:"></a><!-- ws:end:WikiTextHeadingRule:12 -->Instruments:</h2> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:468:&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:468 --><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:14:&lt;h2&gt; --><h2 id="toc6"><a name="x14 tone equal temperament-Books:"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong>Books:</strong></h2> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:467:&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:467 --><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:16:&lt;h2&gt; --><h2 id="toc7"><a name="x14 tone equal temperament-Compositions:"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>Compositions:</strong></h2> | ||
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</script><!-- ws:end:WikiTextMediaRule:1 --><br /> | </script><!-- ws:end:WikiTextMediaRule:1 --><br /> | ||