7edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 545084694 - Original comment: ** |
Wikispaces>k9assassin **Imported revision 555718481 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:k9assassin|k9assassin]] and made on <tt>2015-07-24 19:43:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>555718481</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <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">[[toc|flat]] | ||
=" | ="Neutral diatonic"= | ||
7-edo divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. It is the fourth [[prime numbers|prime]] edo, after [[2edo]], [[3edo]] and [[5edo]]. | 7-edo divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. It is the fourth [[prime numbers|prime]] edo, after [[2edo]], [[3edo]] and [[5edo]]. | ||
Equal-heptatonic scales are used in non-western music in African cultures as well as an intregal part of early Thai and early Chinese music. It has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones). | |||
7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the comma (2^-2 3^-14 11^7). | 7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the comma (2^-2 3^-14 11^7). As a temperament, William Lynch gives it the name "Neutron[7]" just as the whole tone scale of 12 ET is known as "" | ||
Typically, 7-edo exists as the tuning for pentatonic scales in traditional thai music with the other two pitches acting as auxiliary tones. However, it can be used as an interesting diatonic scale choice as well in tunings such as 14 EDO or 21 EDO. | |||
The seventh of 7-edo is almost exactly the 29th harmonic ([[29_16|29/16]]), which can have a very agreeable sound with harmonic timbres. However it also finds itself nested between ratios such as 20/11 and 9/5, which gives it considerably higher [[harmonic entropy]] than [[harmonic seventh|7/4]], a much simpler overtone seventh. | The seventh of 7-edo is almost exactly the 29th harmonic ([[29_16|29/16]]), which can have a very agreeable sound with harmonic timbres. However it also finds itself nested between ratios such as 20/11 and 9/5, which gives it considerably higher [[harmonic entropy]] than [[harmonic seventh|7/4]], a much simpler overtone seventh. | ||
| Line 28: | Line 30: | ||
**interval name** || **The "neighborhood" of just intervals** || | **interval name** || **The "neighborhood" of just intervals** || | ||
|| 0 || 0.0 || unison / prime || exactly 1/1 || | || 0 || 0.0 || unison / prime || exactly 1/1 || | ||
|| 1 || 171.429, | || 1 || 171.429, | ||
51°25'43" || second || 6.424 c, 1°55'38" from Ptolemy (neutral) second 11/10 | 51°25'43" || second || 6.424 c, 1°55'38" from Ptolemy (neutral) second 11/10 | ||
3.215 c, 57'53" from second 54/49 | 3.215 c, 57'53" from second 54/49 | ||
-10.9<span style="line-height: 1.5;"> c, -3°17'33"76 from (Didymus) major second (small whole tone) 10/9</span> || | -10.9<span style="line-height: 1.5;"> c, -3°17'33"76 from (Didymus) major second (small whole tone) 10/9</span> || | ||
|| 2 || 342.857, | || 2 || 342.857, | ||
102°51'26" || third || -4.551 c, -1°21'55" from neutral third 11/9 || | 102°51'26" || third || -4.551 c, -1°21'55" from neutral third 11/9 || | ||
|| 3 || 514.286, | || 3 || 514.286, | ||
154°17'9" || fourth || 16.241 c, 4°52'20" from just fourth 4/3 (498.045 c) | 154°17'9" || fourth || 16.241 c, 4°52'20" from just fourth 4/3 (498.045 c) | ||
-5.265 c, -1°34'47" from wide fourth 27/20 || | -5.265 c, -1°34'47" from wide fourth 27/20 || | ||
| Line 55: | Line 57: | ||
=Related scales= | =Related scales= | ||
* Related in a lateral way to traditional Thai music. | * Related in a lateral way to traditional Thai music. Subset of 14 EDO and 21 EDO. | ||
==Notation== | ==Notation== | ||
* Notatable on a five-line staff without accidentals. | * Notatable on a five-line staff without accidentals. | ||
| Line 106: | Line 108: | ||
[[media type="custom" key="23473438"]]</pre></div> | [[media type="custom" key="23473438"]]</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>7edo</title></head><body><!-- ws:start:WikiTextTocRule:22:&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:22 --><!-- ws:start:WikiTextTocRule:23: --><a href="#x&quot; | <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>7edo</title></head><body><!-- ws:start:WikiTextTocRule:22:&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:22 --><!-- ws:start:WikiTextTocRule:23: --><a href="#x&quot;Neutral diatonic&quot;">&quot;Neutral diatonic&quot;</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Intervals in 7-edo">Intervals in 7-edo</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Related scales">Related scales</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | ||
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="x&quot; | <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="x&quot;Neutral diatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:2 -->&quot;Neutral diatonic&quot;</h1> | ||
<br /> | <br /> | ||
7-edo divides the 1200-cent <a class="wiki_link" href="/octave">octave</a> into 7 equal parts, making its smallest interval <a class="wiki_link" href="/cent">171.428¢</a>, or the seventh root of 2. It is the fourth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, after <a class="wiki_link" href="/2edo">2edo</a>, <a class="wiki_link" href="/3edo">3edo</a> and <a class="wiki_link" href="/5edo">5edo</a>.<br /> | 7-edo divides the 1200-cent <a class="wiki_link" href="/octave">octave</a> into 7 equal parts, making its smallest interval <a class="wiki_link" href="/cent">171.428¢</a>, or the seventh root of 2. It is the fourth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, after <a class="wiki_link" href="/2edo">2edo</a>, <a class="wiki_link" href="/3edo">3edo</a> and <a class="wiki_link" href="/5edo">5edo</a>.<br /> | ||
<br /> | <br /> | ||
Equal-heptatonic scales are used in non-western music in African cultures as well as an intregal part of early Thai and early Chinese music. It has been speculated in &quot;Indian music:history and structure&quot;, that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).<br /> | |||
7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the comma (2^-2 3^-14 11^7).<br /> | 7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the comma (2^-2 3^-14 11^7). As a temperament, William Lynch gives it the name &quot;Neutron[7]&quot; just as the whole tone scale of 12 ET is known as &quot;&quot; <br /> | ||
<br /> | |||
Typically, 7-edo exists as the tuning for pentatonic scales in traditional thai music with the other two pitches acting as auxiliary tones. However, it can be used as an interesting diatonic scale choice as well in tunings such as 14 EDO or 21 EDO. <br /> | |||
<br /> | <br /> | ||
The seventh of 7-edo is almost exactly the 29th harmonic (<a class="wiki_link" href="/29_16">29/16</a>), which can have a very agreeable sound with harmonic timbres. However it also finds itself nested between ratios such as 20/11 and 9/5, which gives it considerably higher <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> than <a class="wiki_link" href="/harmonic%20seventh">7/4</a>, a much simpler overtone seventh.<br /> | The seventh of 7-edo is almost exactly the 29th harmonic (<a class="wiki_link" href="/29_16">29/16</a>), which can have a very agreeable sound with harmonic timbres. However it also finds itself nested between ratios such as 20/11 and 9/5, which gives it considerably higher <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> than <a class="wiki_link" href="/harmonic%20seventh">7/4</a>, a much simpler overtone seventh.<br /> | ||
| Line 152: | Line 156: | ||
<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>171.429, <br /> | <td>171.429,<br /> | ||
51°25'43&quot;<br /> | 51°25'43&quot;<br /> | ||
</td> | </td> | ||
| Line 165: | Line 169: | ||
<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>342.857, <br /> | <td>342.857,<br /> | ||
102°51'26&quot;<br /> | 102°51'26&quot;<br /> | ||
</td> | </td> | ||
| Line 176: | Line 180: | ||
<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>514.286, <br /> | <td>514.286,<br /> | ||
154°17'9&quot;<br /> | 154°17'9&quot;<br /> | ||
</td> | </td> | ||
| Line 241: | Line 245: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="Related scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Related scales</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="Related scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Related scales</h1> | ||
<ul><li>Related in a lateral way to traditional Thai music.</li></ul><!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="Related scales-Notation"></a><!-- ws:end:WikiTextHeadingRule:8 -->Notation</h2> | <ul><li>Related in a lateral way to traditional Thai music. Subset of 14 EDO and 21 EDO.</li></ul><!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="Related scales-Notation"></a><!-- ws:end:WikiTextHeadingRule:8 -->Notation</h2> | ||
<ul><li>Notatable on a five-line staff without accidentals.</li></ul><!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc4"><a name="Related scales-Harmony"></a><!-- ws:end:WikiTextHeadingRule:10 -->Harmony</h2> | <ul><li>Notatable on a five-line staff without accidentals.</li></ul><!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc4"><a name="Related scales-Harmony"></a><!-- ws:end:WikiTextHeadingRule:10 -->Harmony</h2> | ||
There is no distinction between Major or Minor; each pitch class is unique.<br /> | There is no distinction between Major or Minor; each pitch class is unique.<br /> | ||