17/16: Difference between revisions

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'''17/16'''
{{Infobox Interval
|-4 0 0 0 0 0 1>
| Icon =
| Ratio = 17/16
| Monzo = -4 0 0 0 0 0 1
| Cents = 104.95541
| Name = large septendecimal semitone
| Color name = 17o2, iso 2nd
| Sound = jid_17_16_pluck_adu_dr220.mp3
}}


104.9554 cents
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.


[[File:jid_17_16_pluck_adu_dr220.mp3]] [[:File:jid_17_16_pluck_adu_dr220.mp3|sound sample]]
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.


In [[17-limit|17-limit]] [[Just_intonation|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|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.
== See also ==
* [[32/17]] its [[inverse interval]]
* [[Gallery of Just Intervals]]


17/16 is one of two [[superparticular|superparticular]] semitones in the 17-limit; the other is [[18/17|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.
[[Category:17-limit]]
 
[[Category:Interval]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
[[Category:Just interval]]
[[Category:Ratio]]
[[Category:Sound example]]
[[Category:Semitone]]
[[Category:Superparticular]]

Revision as of 22:48, 26 October 2018

Interval information
Ratio 17/16
Subgroup monzo 2.17 [-4 1⟩
Size in cents 104.9554¢
Name large septendecimal semitone
Color name 17o2, iso 2nd
FJS name [math]\displaystyle{ \text{m2}^{17} }[/math]
Special properties superparticular,
reduced,
reduced harmonic
Tenney norm (log2 nd) 8.08746
Weil norm (log2 max(n, d)) 8.17493
Wilson norm (sopfr(nd)) 25

[sound info]
Open this interval in xen-calc

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.

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.

See also

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