17/16: Difference between revisions

Line 6:

| Name = large septendecimal semitone

| Color name = 17o2, iso 2nd

| FJS name = m2<sup>17</sup>

| Sound = jid_17_16_pluck_adu_dr220.mp3

}}

In [[17-limit]] [[just intonation]], '''17/16''' is the 17th [[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 [[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.

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.

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.

There exists a disagreement in different notation systems on whether 17/16 should be notated as a diatonic semitone or a chromatic semitone. In [[Functional Just System]], it is a diatonic semitone, whereas in [[Helmholtz-Ellis notation]], it is a chromatic semitone.

== See also ==

* [[32/17]] – its [[octave complement]]

* [[32/17]] its [[~~inverse interval~~]]

* [[24/17]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

[[Category:17-limit]]

@@ Line 6: / Line 6: @@
 | Name = large septendecimal semitone
 | Color name = 17o2, iso 2nd
+| FJS name = m2<sup>17</sup>
 | Sound = jid_17_16_pluck_adu_dr220.mp3
 }}
-In [[17-limit]] [[just intonation]], '''17/16''' is the 17th [[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 [[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.
-/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.
+/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.
+There exists a disagreement in different notation systems on whether 17/16 should be notated as a diatonic semitone or a chromatic semitone. In [[Functional Just System]], it is a diatonic semitone, whereas in [[Helmholtz-Ellis notation]], it is a chromatic semitone.
 == See also ==
+* [[32/17]] – its [[octave complement]]
-* [[32/17]] its [[inverse interval]]
+* [[24/17]] – its [[fifth complement]]
 * [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
 [[Category:17-limit]]