13/11: Difference between revisions
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Wikispaces>Andrew_Heathwaite **Imported revision 260455354 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 260456498 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-01 09: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-01 09:25:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>260456498</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">In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third ( | <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">In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic ([[11_8|11/8]], about 551.3¢) and the 13th harmonic ([[13_8|13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit [[Neo-Gothic]] minor triad of 22:26:33, with a [[3_2|3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16_11|16/11]] in place of 3/2. The latter triad sounds more like a very xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7. | ||
13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6_5|6/5]] and [[7_6|7/6]], and can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. It is [[78_77|78/77]] (about 22.3¢) wider than 7/6 and [[66_65|66/65]] (26.4¢) narrower than 6/5. It is also [[352_351]] (about 4.9¢) narrower than [[32_27|32/27]], the minor third in Pythagorean ([[3-limit]]) tuning. | |||
See: [[Gallery of Just Intervals|Gallery of Just Intonation Intervals]], [[gentle chords]], [[List of root-3rd-P5 triads in JI]] | See: [[Gallery of Just Intervals|Gallery of Just Intonation Intervals]], [[gentle chords]], [[List of root-3rd-P5 triads in JI]] | ||
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[[http://dkeenan.com/Music/NobleMediant.txt|The Noble Mediant]] (earliest description of 13:11 as the "Neo-Gothic" minor third)</pre></div> | [[http://dkeenan.com/Music/NobleMediant.txt|The Noble Mediant]] (earliest description of 13:11 as the "Neo-Gothic" minor third)</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>13_11</title></head><body>In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/11 is the tridecimal minor third ( | <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>13_11</title></head><body>In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic (<a class="wiki_link" href="/11_8">11/8</a>, about 551.3¢) and the 13th harmonic (<a class="wiki_link" href="/13_8">13/8</a>, about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit <a class="wiki_link" href="/Neo-Gothic">Neo-Gothic</a> minor triad of 22:26:33, with a <a class="wiki_link" href="/3_2">3/2</a> perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant <a class="wiki_link" href="/16_11">16/11</a> in place of 3/2. The latter triad sounds more like a very xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.<br /> | ||
<br /> | |||
13/11 is the classic <a class="wiki_link" href="/mediant">mediant</a> between the simpler and more familiar ratios <a class="wiki_link" href="/6_5">6/5</a> and <a class="wiki_link" href="/7_6">7/6</a>, and can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. It is <a class="wiki_link" href="/78_77">78/77</a> (about 22.3¢) wider than 7/6 and <a class="wiki_link" href="/66_65">66/65</a> (26.4¢) narrower than 6/5. It is also <a class="wiki_link" href="/352_351">352_351</a> (about 4.9¢) narrower than <a class="wiki_link" href="/32_27">32/27</a>, the minor third in Pythagorean (<a class="wiki_link" href="/3-limit">3-limit</a>) tuning.<br /> | |||
<br /> | <br /> | ||
See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intonation Intervals</a>, <a class="wiki_link" href="/gentle%20chords">gentle chords</a>, <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">List of root-3rd-P5 triads in JI</a><br /> | See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intonation Intervals</a>, <a class="wiki_link" href="/gentle%20chords">gentle chords</a>, <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">List of root-3rd-P5 triads in JI</a><br /> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://dkeenan.com/Music/NobleMediant.txt" rel="nofollow">The Noble Mediant</a> (earliest description of 13:11 as the &quot;Neo-Gothic&quot; minor third)</body></html></pre></div> | <a class="wiki_link_ext" href="http://dkeenan.com/Music/NobleMediant.txt" rel="nofollow">The Noble Mediant</a> (earliest description of 13:11 as the &quot;Neo-Gothic&quot; minor third)</body></html></pre></div> | ||
Revision as of 09:25, 1 October 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2011-10-01 09:25:47 UTC.
- The original revision id was 260456498.
- 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:
In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic ([[11_8|11/8]], about 551.3¢) and the 13th harmonic ([[13_8|13/8]], about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit [[Neo-Gothic]] minor triad of 22:26:33, with a [[3_2|3/2]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16_11|16/11]] in place of 3/2. The latter triad sounds more like a very xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7. 13/11 is the classic [[mediant]] between the simpler and more familiar ratios [[6_5|6/5]] and [[7_6|7/6]], and can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. It is [[78_77|78/77]] (about 22.3¢) wider than 7/6 and [[66_65|66/65]] (26.4¢) narrower than 6/5. It is also [[352_351]] (about 4.9¢) narrower than [[32_27|32/27]], the minor third in Pythagorean ([[3-limit]]) tuning. See: [[Gallery of Just Intervals|Gallery of Just Intonation Intervals]], [[gentle chords]], [[List of root-3rd-P5 triads in JI]] [[http://dkeenan.com/Music/NobleMediant.txt|The Noble Mediant]] (earliest description of 13:11 as the "Neo-Gothic" minor third)
Original HTML content:
<html><head><title>13_11</title></head><body>In <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 13/11 is the tridecimal minor third (a Neo-Gothic minor third), measuring about 289.2¢. It is the difference between the 11th and 13th harmonics. The 11th harmonic (<a class="wiki_link" href="/11_8">11/8</a>, about 551.3¢) and the 13th harmonic (<a class="wiki_link" href="/13_8">13/8</a>, about 840.5¢) are both quite xenharmonic and demand new interval categories, while 13/11 can be likened unto some kind of relatively complex minor third. It can even function as such in a 13-limit <a class="wiki_link" href="/Neo-Gothic">Neo-Gothic</a> minor triad of 22:26:33, with a <a class="wiki_link" href="/3_2">3/2</a> perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant <a class="wiki_link" href="/16_11">16/11</a> in place of 3/2. The latter triad sounds more like a very xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7.<br /> <br /> 13/11 is the classic <a class="wiki_link" href="/mediant">mediant</a> between the simpler and more familiar ratios <a class="wiki_link" href="/6_5">6/5</a> and <a class="wiki_link" href="/7_6">7/6</a>, and can be given as (6+7)/(5+6). This puts in between the latter ratios, slightly closer to 7/6. It is <a class="wiki_link" href="/78_77">78/77</a> (about 22.3¢) wider than 7/6 and <a class="wiki_link" href="/66_65">66/65</a> (26.4¢) narrower than 6/5. It is also <a class="wiki_link" href="/352_351">352_351</a> (about 4.9¢) narrower than <a class="wiki_link" href="/32_27">32/27</a>, the minor third in Pythagorean (<a class="wiki_link" href="/3-limit">3-limit</a>) tuning.<br /> <br /> See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intonation Intervals</a>, <a class="wiki_link" href="/gentle%20chords">gentle chords</a>, <a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI">List of root-3rd-P5 triads in JI</a><br /> <br /> <a class="wiki_link_ext" href="http://dkeenan.com/Music/NobleMediant.txt" rel="nofollow">The Noble Mediant</a> (earliest description of 13:11 as the "Neo-Gothic" minor third)</body></html>