13/11
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Original Wikitext content:
In [[13-limit]] [[Just Intonation]], 13/11 is the tridecimal minor third (or 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, but 13/11 can be likened unto some kind of low minor third. It can even function as such in a relatively consonant 13-limit Neo-Gothic minor triad which goes 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. See: [[Gallery of Just Intervals|Gallery of Just Intonation Intervals]] [[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 (or 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, but 13/11 can be likened unto some kind of low minor third. It can even function as such in a relatively consonant 13-limit Neo-Gothic minor triad which goes 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 /> See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intonation Intervals</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>