18/13: Difference between revisions

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'''18/13'''
{{Infobox Interval
|1 2 0 0 0 -1>
| Name = tridecimal augmented fourth, low tritone
| Color name = 3u4, thu 4th
| Sound = jid_18_13_pluck_adu_dr220.mp3
}}


563.38234 cents
In [[13-limit]] [[just intonation]], '''18/13''', the '''tridecimal augmented fourth''' is a '''low [[tritone]]''' measuring about 563.4¢. It represents the interval between the 13th and 18th harmonics of the [[overtone scales|harmonic series]].


[[File:jid_18_13_pluck_adu_dr220.mp3]] [[:File:jid_18_13_pluck_adu_dr220.mp3|sound sample]]
The low tritone in [[17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8]] and [[9/8]] are both a little sharp. The inversion of 18/13 is [[13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is [[169/162]], approximately 73.2¢.


In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], '''18/13''' is a low [[tritone|tritone]] measuring about 563.4¢. It represents the interval between the 13th and 18th overtones of the [[overtone_scales|harmonic series]]. The low tritone in [[17edo|17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8|13/8]] and [[9/8|9/8]] are both a little sharp. The inversion of 18/13 is [[13/9|13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is 169/162, approximately 73.2¢.
== See also ==


Other just tritones include [[7/5|7/5]], [[10/7|10/7]], [[45/32|45/32]], [[64/45|64/45]], [[24/17|24/17]], [[17/12|17/12]], [[23/16|23/16]], [[32/23|32/23]], and, of course, infinitely many more intervals.
* [[13/9]] – its [[octave complement]]
* [[13/12]] – its [[fifth complement]]
* [[Gallery of just intervals]]


See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
[[Category:Tritone]]
[[Category:15-limit]]
[[Category:interval]]
[[Category:just_interval]]
[[Category:ratio]]
[[Category:tritone]]

Latest revision as of 12:35, 25 October 2022

Interval information
Ratio 18/13
Factorization 2 × 32 × 13-1
Monzo [1 2 0 0 0 -1⟩
Size in cents 563.3823¢
Names tridecimal augmented fourth,
low tritone
Color name 3u4, thu 4th
FJS name [math]\displaystyle{ \text{A4}_{13} }[/math]
Special properties reduced
Tenney height (log2 nd) 7.87036
Weil height (log2 max(n, d)) 8.33985
Wilson height (sopfr(nd)) 21

[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 18/13, the tridecimal augmented fourth is a low tritone measuring about 563.4¢. It represents the interval between the 13th and 18th harmonics of the harmonic series.

The low tritone in 17edo approximates 18/13 quite well, while 17edo's approximations of 13/8 and 9/8 are both a little sharp. The inversion of 18/13 is 13/9, a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is 169/162, approximately 73.2¢.

See also

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