13/11
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- This revision was by author Andrew_Heathwaite and made on 2011-10-01 09:25:47 UTC.
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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>