17/12: Difference between revisions

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'''17/12'''
{{Infobox Interval
|-2 -1 0 0 0 0 1>
| Icon =
| Ratio = 17/12
| Monzo = -2 -1 0 0 0 0 1
| Cents = 603.00041
| Name = larger septendecimal tritone
| Color name =
| Sound = jid_17_12_pluck_adu_dr220.mp3
}}


603.0004 cents
In [[17-limit]] [[just intonation]], '''17/12''' is the "larger septendecimal tritone", measuring very nearly 603¢. Its inversion is the "first septendecimal tritone," [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.


[[File:jid_17_12_pluck_adu_dr220.mp3]] [[:File:jid_17_12_pluck_adu_dr220.mp3|sound sample]]
17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].


In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]], 17/12 is the "second septendecimal tritone," measuring very nearly 603¢. Its inversion is the "first septendecimal tritone," [[24/17|24/17]], and the interval that separates them is the small [[Comma|comma]] [[289/288|289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[EDO|EDO]] system contains a close approximation to these intervals.
''See also: [[Gallery of just intervals]]''


17/12 is the [[mediant|mediant]] between the two septimal tritones [[7/5|7/5]] and [[10/7|10/7]].
[[Category:17-limit]]
 
[[Category:Tritone]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
[[Category:Interval]]

Revision as of 10:11, 9 June 2020

Interval information
Ratio 17/12
Subgroup monzo 2.3.17 [-2 -1 1⟩
Size in cents 603.0004¢
Name larger septendecimal tritone
FJS name [math]\displaystyle{ \text{d5}^{17} }[/math]
Special properties reduced
Tenney height (log2 nd) 7.67243
Weil height (log2 max(n, d)) 8.17493
Wilson height (sopfr(nd)) 24

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 17/12 is the "larger septendecimal tritone", measuring very nearly 603¢. Its inversion is the "first septendecimal tritone," 24/17, and the interval that separates them is the small comma 289/288, about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered EDO system contains a close approximation to these intervals.

17/12 is the mediant between the two septimal tritones 7/5 and 10/7.

See also: Gallery of just intervals

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