13/11: Difference between revisions
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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 [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 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]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7. | 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 [[harmonic]]s. The (octave-reduced) 11th harmonic ([[11/8]], about 551.3¢) and 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]] perfect fifth between 33 and 22. Compare this to 22:26:32 (11:13:16), which has the much more dissonant [[16/11]] as the outside interval in place of 3/2. The latter triad sounds more like a xenharmonic version of a diminished triad, and could not be confused with simpler diminished triads such as 5:6:7. | ||