21/16
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- This revision was by author spt3125 and made on 2014-06-08 15:48:04 UTC.
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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 />
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<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>