17/16: Difference between revisions

Line 10:

}}

In [[17-limit]] [[just intonation]], '''17/16''' is the 17th [[~~Overtone~~ series|~~overtone~~]], [[octave reduced]], and may be called the '''large septendecimal semitone'''. Measuring about 105¢, it is close to the [[12edo]] semitone of 100¢, and thus 12edo can be said to approximate it closely. In a chord, it can function similarly to a jazz "minor ninth" – for instance, 8:10:12:14:17 (although here the interval is 17/8, which is a little less harsh sounding than 17/16). In 17-limit JI, it is treated as the next basic consonance after 13 and 15.

In [[17-limit]] [[just intonation]], '''17/16''' is the 17th [[Harmonic series|harmonic]], [[octave reduced]], and may be called the '''large septendecimal semitone'''. Measuring about 105¢, it is close to the [[12edo]] semitone of 100¢, and thus 12edo can be said to approximate it closely. In a chord, it can function similarly to a jazz "minor ninth" – for instance, 8:10:12:14:17 (although here the interval is 17/8, which is a little less harsh sounding than 17/16). In 17-limit JI, it is treated as the next basic consonance after 13 and 15.

17/16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18/17]], which measures about 99¢. The difference between them is [[289/288]], about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out.

@@ Line 10: / Line 10: @@
 }}
-In [[17-limit]] [[just intonation]], '''17/16''' is the 17th [[Overtone series|overtone]], [[octave reduced]], and may be called the '''large septendecimal semitone'''. Measuring about 105¢, it is close to the [[12edo]] semitone of 100¢, and thus 12edo can be said to approximate it closely. In a chord, it can function similarly to a jazz "minor ninth" – for instance, 8:10:12:14:17 (although here the interval is 17/8, which is a little less harsh sounding than 17/16). In 17-limit JI, it is treated as the next basic consonance after 13 and 15.
+In [[17-limit]] [[just intonation]], '''17/16''' is the 17th [[Harmonic series|harmonic]], [[octave reduced]], and may be called the '''large septendecimal semitone'''. Measuring about 105¢, it is close to the [[12edo]] semitone of 100¢, and thus 12edo can be said to approximate it closely. In a chord, it can function similarly to a jazz "minor ninth" – for instance, 8:10:12:14:17 (although here the interval is 17/8, which is a little less harsh sounding than 17/16). In 17-limit JI, it is treated as the next basic consonance after 13 and 15.
 /16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18/17]], which measures about 99¢. The difference between them is [[289/288]], about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out.