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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = septimal subfourth, narrow fourth, 8ve-reduced 21st harmonic |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-14 21:22:12 UTC</tt>.<br>
| | | Color name = z4, zo 4th |
| : The original revision id was <tt>254175870</tt>.<br>
| | | Sound = jid_21_16_pluck_adu_dr220.mp3 |
| : 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>
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| <h4>Original Wikitext content:</h4>
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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">21/16, the septimal sub-fourth, is an interval of the [[7-limit|7 prime-limit]] measuring approximately 470.8¢. It can be thought of as the 21st overtone, octave reduced. Since 21 is 3*7, 21 can be 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|4/3]] and 21/8 (an octave above 21/16) sounds more consonant than 21/16.
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| 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 (about 80.5¢) to 11/8. These are all movements that assume a stable fundamental, of course, and other movements are possible. | | '''21/16''', the '''septimal subfourth''', is a [[7-limit]] interval measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of [[4/3]] by [[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]] between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths ([[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. |
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| | 21/16 is [[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]], the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an [[11-limit]] system, [[11/8]] is also nearby, so that 21/16 can step up by the small semitone of [[22/21]] (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible. |
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| 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. |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | In [[septimal meantone]], this interval is represented by the augmented third. |
| <h4>Original HTML content:</h4>
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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>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 can be thought of as the 21st overtone, octave reduced. Since 21 is 3*7, 21 can be 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 <a class="wiki_link" href="/4_3">4/3</a> and 21/8 (an octave above 21/16) sounds more consonant than 21/16.<br />
| | == See also == |
| <br />
| | * [[32/21]] – its [[octave complement]] |
| 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 22/21 (about 80.5¢) to 11/8. These are all movements that assume a stable fundamental, of course, and other movements are possible.<br />
| | * [[8/7]] – its [[fifth complement]] |
| <br />
| | * [[Gallery of just intervals]] |
| 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 />
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| | [[Category:Subfourth]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | [[Category:Fourth]] |