55/39: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 55/39
| Name = smaller gassormic tritone
| Monzo = 0 -1 1 0 1 -1
| Cents = 595.14899
| Name = smaller tridecimal tritone<br> smaller gassormic tritone
| Color name = thuloyo 4th
| Color name = thuloyo 4th
| FJS name = A4<sup>55</sup><sub>13</sub>
}}
}}


In [[13-limit]] [[just intonation]], '''55/39''' is the '''smaller tridecimal tritone''', measuring about 595.1¢. It is [[275/273]] (gassorma, about 12.6¢) sharp of [[7/5]], and is the interval between [[13/11]] and [[5/3]]. Its inversion is the larger tridecimal tritone, [[78/55]], and the interval that separates them is the small [[comma]] [[3042/3025]], about 9.7¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both tridecimal tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.
In [[13-limit]] [[just intonation]], '''55/39''' is the '''smaller gassormic tritone''', measuring about 595.1¢. It is [[275/273]] (gassorma, about 12.6¢) sharp of [[7/5]], and is the interval between [[13/11]] and [[5/3]], and also the sum of [[11/9]] and [[15/13]], intervals often equated to an exact neutral third and semifourth, respectively. It is also [[936/935]] flat of [[24/17]]. Its inversion is the larger gassormic tritone, [[78/55]], and the interval that separates them is the small [[comma]] [[3042/3025]], about 9.7¢. This difference can be negligible, and tempering out this comma allows the 600¢ half-octave to function as both gassormic tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.


== See also ==
== See also ==
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* [[Gallery of just intervals]]
* [[Gallery of just intervals]]


[[Category:13-limit]]
[[Category:Tritone]]
[[Category:Tritone]]

Latest revision as of 04:45, 5 October 2025

Interval information
Ratio 55/39
Factorization 3-1 × 5 × 11 × 13-1
Monzo [0 -1 1 0 1 -1
Size in cents 595.149¢
Name smaller gassormic tritone
Color name thuloyo 4th
FJS name [math]\displaystyle{ \text{A4}^{5,11}_{13} }[/math]
Special properties reduced
Tenney norm (log2 nd) 11.0668
Weil norm (log2 max(n, d)) 11.5627
Wilson norm (sopfr(nd)) 32
Open this interval in xen-calc

In 13-limit just intonation, 55/39 is the smaller gassormic tritone, measuring about 595.1¢. It is 275/273 (gassorma, about 12.6¢) sharp of 7/5, and is the interval between 13/11 and 5/3, and also the sum of 11/9 and 15/13, intervals often equated to an exact neutral third and semifourth, respectively. It is also 936/935 flat of 24/17. Its inversion is the larger gassormic tritone, 78/55, and the interval that separates them is the small comma 3042/3025, about 9.7¢. This difference can be negligible, and tempering out this comma allows the 600¢ half-octave to function as both gassormic tritones. Thus, every even-numbered EDO system contains a close approximation to these intervals.

See also