21/16: Difference between revisions
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Wikispaces>Andrew_Heathwaite **Imported revision 254177102 - Original comment: ** |
Wikispaces>spt3125 **Imported revision 513256280 - 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:spt3125|spt3125]] and made on <tt>2014-06-08 15:48:04 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>513256280</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">21/16 | <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">**21/16** | ||
|-4 1 0 1> | |||
470.7809 cents | |||
[[media type="file" key="jid_21_16_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_21_16_pluck_adu_dr220.mp3|sound sample]] | |||
21/16 is [[21_20|21/20]] away from 5/4. This is an interval of about 84.5¢, a small semitone. This introduces the possibility of treating 21/16 as a dissonance to resolve down to 5/4. It can just as easily step up to 3/2 by [[8_7|8/7]], the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an [[11-limit]] system, [[11_8|11/8]] is also nearby, so that 21/16 can step up by the small semitone of [[22_21|22/21]] (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible. | 21/16, the septimal sub-fourth, is an interval of the [[7-limit|7 prime-limit]] measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of [[4_3|4/3]] by [[64_63|64/63]], a microtone of approximately 27.3¢. It can be treated as the 21st overtone, octave reduced. Since 21 is 3*7, 21 can be also treated as the 3rd harmonic above the 7th or the 7th harmonic above the 3rd, or both. This identity can be made clear in a chord such as 8:12:14:21, which has a just perfect fifth of [[3_2|3/2]] between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths ([[7_4|7/4]]) in this chord, between 8 and 14 and between 12 and 21. The voicing of this chord is significant, as 3/2 sounds more consonant than its inversion 4/3 and 21/8 (an octave above 21/16) sounds more consonant than 21/16. | ||
21/16 is [[21_20|21/20]] away from [[5_4|5/4]]. This is an interval of about 84.5¢, a small semitone. This introduces the possibility of treating 21/16 as a dissonance to resolve down to 5/4. It can just as easily step up to 3/2 by [[8_7|8/7]], the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an [[11-limit]] system, [[11_8|11/8]] is also nearby, so that 21/16 can step up by the small semitone of [[22_21|22/21]] (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible. | |||
The 7-limit is known for its subminor and supermajor 2nds, 3rds, 6ths and 7ths. 21/16 is also an essential interval of the 7-limit and worth distinguishing. | The 7-limit is known for its subminor and supermajor 2nds, 3rds, 6ths and 7ths. 21/16 is also an essential interval of the 7-limit and worth distinguishing. | ||
| Line 14: | Line 19: | ||
See: [[Gallery of Just Intervals]]</pre></div> | See: [[Gallery of Just Intervals]]</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>21_16</title></head><body>21/16, the septimal sub-fourth, is an interval of the <a class="wiki_link" href="/7-limit">7 prime-limit</a> measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of <a class="wiki_link" href="/4_3">4/3</a> by <a class="wiki_link" href="/64_63">64/63</a>, a microtone of approximately 27.3¢. It can be treated as the 21st overtone, octave reduced. Since 21 is 3*7, 21 can be also treated as the 3rd harmonic above the 7th or the 7th harmonic above the 3rd, or both. This identity can be made clear in a chord such as 8:12:14:21, which has a just perfect fifth of <a class="wiki_link" href="/3_2">3/2</a> between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths (<a class="wiki_link" href="/7_4">7/4</a>) in this chord, between 8 and 14 and between 12 and 21. The voicing of this chord is significant, as 3/2 sounds more consonant than its inversion 4/3 and 21/8 (an octave above 21/16) sounds more consonant than 21/16.<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>21_16</title></head><body><strong>21/16</strong><br /> | ||
|-4 1 0 1&gt;<br /> | |||
470.7809 cents<br /> | |||
<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_21_16_pluck_adu_dr220.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;jid_21_16_pluck_adu_dr220.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_21_16_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --> <a href="http://xenharmonic.wikispaces.com/file/view/jid_21_16_pluck_adu_dr220.mp3/513250062/jid_21_16_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_21_16_pluck_adu_dr220.mp3/513250062/jid_21_16_pluck_adu_dr220.mp3');">sound sample</a><br /> | |||
<br /> | |||
21/16, the septimal sub-fourth, is an interval of the <a class="wiki_link" href="/7-limit">7 prime-limit</a> measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of <a class="wiki_link" href="/4_3">4/3</a> by <a class="wiki_link" href="/64_63">64/63</a>, a microtone of approximately 27.3¢. It can be treated as the 21st overtone, octave reduced. Since 21 is 3*7, 21 can be also treated as the 3rd harmonic above the 7th or the 7th harmonic above the 3rd, or both. This identity can be made clear in a chord such as 8:12:14:21, which has a just perfect fifth of <a class="wiki_link" href="/3_2">3/2</a> between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths (<a class="wiki_link" href="/7_4">7/4</a>) in this chord, between 8 and 14 and between 12 and 21. The voicing of this chord is significant, as 3/2 sounds more consonant than its inversion 4/3 and 21/8 (an octave above 21/16) sounds more consonant than 21/16.<br /> | |||
<br /> | <br /> | ||
21/16 is <a class="wiki_link" href="/21_20">21/20</a> away from 5/4. This is an interval of about 84.5¢, a small semitone. This introduces the possibility of treating 21/16 as a dissonance to resolve down to 5/4. It can just as easily step up to 3/2 by <a class="wiki_link" href="/8_7">8/7</a>, the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an <a class="wiki_link" href="/11-limit">11-limit</a> system, <a class="wiki_link" href="/11_8">11/8</a> is also nearby, so that 21/16 can step up by the small semitone of <a class="wiki_link" href="/22_21">22/21</a> (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible.<br /> | 21/16 is <a class="wiki_link" href="/21_20">21/20</a> away from <a class="wiki_link" href="/5_4">5/4</a>. This is an interval of about 84.5¢, a small semitone. This introduces the possibility of treating 21/16 as a dissonance to resolve down to 5/4. It can just as easily step up to 3/2 by <a class="wiki_link" href="/8_7">8/7</a>, the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an <a class="wiki_link" href="/11-limit">11-limit</a> system, <a class="wiki_link" href="/11_8">11/8</a> is also nearby, so that 21/16 can step up by the small semitone of <a class="wiki_link" href="/22_21">22/21</a> (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible.<br /> | ||
<br /> | <br /> | ||
The 7-limit is known for its subminor and supermajor 2nds, 3rds, 6ths and 7ths. 21/16 is also an essential interval of the 7-limit and worth distinguishing.<br /> | The 7-limit is known for its subminor and supermajor 2nds, 3rds, 6ths and 7ths. 21/16 is also an essential interval of the 7-limit and worth distinguishing.<br /> | ||
<br /> | <br /> | ||
See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | ||
Revision as of 15:48, 8 June 2014
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author spt3125 and made on 2014-06-08 15:48:04 UTC.
- The original revision id was 513256280.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
**21/16** |-4 1 0 1> 470.7809 cents [[media type="file" key="jid_21_16_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_21_16_pluck_adu_dr220.mp3|sound sample]] 21/16, the septimal sub-fourth, is an interval of the [[7-limit|7 prime-limit]] measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of [[4_3|4/3]] by [[64_63|64/63]], a microtone of approximately 27.3¢. It can be treated as the 21st overtone, octave reduced. Since 21 is 3*7, 21 can be also treated as the 3rd harmonic above the 7th or the 7th harmonic above the 3rd, or both. This identity can be made clear in a chord such as 8:12:14:21, which has a just perfect fifth of [[3_2|3/2]] between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths ([[7_4|7/4]]) in this chord, between 8 and 14 and between 12 and 21. The voicing of this chord is significant, as 3/2 sounds more consonant than its inversion 4/3 and 21/8 (an octave above 21/16) sounds more consonant than 21/16. 21/16 is [[21_20|21/20]] away from [[5_4|5/4]]. This is an interval of about 84.5¢, a small semitone. This introduces the possibility of treating 21/16 as a dissonance to resolve down to 5/4. It can just as easily step up to 3/2 by [[8_7|8/7]], the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an [[11-limit]] system, [[11_8|11/8]] is also nearby, so that 21/16 can step up by the small semitone of [[22_21|22/21]] (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible. The 7-limit is known for its subminor and supermajor 2nds, 3rds, 6ths and 7ths. 21/16 is also an essential interval of the 7-limit and worth distinguishing. See: [[Gallery of Just Intervals]]
Original HTML content:
<html><head><title>21_16</title></head><body><strong>21/16</strong><br />
|-4 1 0 1><br />
470.7809 cents<br />
<!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_21_16_pluck_adu_dr220.mp3?h=20&w=240" class="WikiMedia WikiMediaFile" id="wikitext@@media@@type=&quot;file&quot; key=&quot;jid_21_16_pluck_adu_dr220.mp3&quot;" title="Local Media File"height="20" width="240"/> --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_21_16_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --> <a href="http://xenharmonic.wikispaces.com/file/view/jid_21_16_pluck_adu_dr220.mp3/513250062/jid_21_16_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_21_16_pluck_adu_dr220.mp3/513250062/jid_21_16_pluck_adu_dr220.mp3');">sound sample</a><br />
<br />
21/16, the septimal sub-fourth, is an interval of the <a class="wiki_link" href="/7-limit">7 prime-limit</a> measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of <a class="wiki_link" href="/4_3">4/3</a> by <a class="wiki_link" href="/64_63">64/63</a>, a microtone of approximately 27.3¢. It can be treated as the 21st overtone, octave reduced. Since 21 is 3*7, 21 can be also treated as the 3rd harmonic above the 7th or the 7th harmonic above the 3rd, or both. This identity can be made clear in a chord such as 8:12:14:21, which has a just perfect fifth of <a class="wiki_link" href="/3_2">3/2</a> between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths (<a class="wiki_link" href="/7_4">7/4</a>) in this chord, between 8 and 14 and between 12 and 21. The voicing of this chord is significant, as 3/2 sounds more consonant than its inversion 4/3 and 21/8 (an octave above 21/16) sounds more consonant than 21/16.<br />
<br />
21/16 is <a class="wiki_link" href="/21_20">21/20</a> away from <a class="wiki_link" href="/5_4">5/4</a>. This is an interval of about 84.5¢, a small semitone. This introduces the possibility of treating 21/16 as a dissonance to resolve down to 5/4. It can just as easily step up to 3/2 by <a class="wiki_link" href="/8_7">8/7</a>, the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an <a class="wiki_link" href="/11-limit">11-limit</a> system, <a class="wiki_link" href="/11_8">11/8</a> is also nearby, so that 21/16 can step up by the small semitone of <a class="wiki_link" href="/22_21">22/21</a> (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible.<br />
<br />
The 7-limit is known for its subminor and supermajor 2nds, 3rds, 6ths and 7ths. 21/16 is also an essential interval of the 7-limit and worth distinguishing.<br />
<br />
See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html>