78/55: Difference between revisions

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Created page with "{{Infobox Interval | Ratio = 78/55 | Monzo = 1 1 -1 0 -1 1 | Cents = 604.85101 | Name = larger tridecimal tritone<br> larger gassormic tritone | Color name = tholugu 5th | FJS..."
 
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m Normalising usage of Infobox Interval
 
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{{Infobox Interval
{{Infobox Interval
| Ratio = 78/55
| Name = larger gassormic tritone
| Monzo = 1 1 -1 0 -1 1
| Cents = 604.85101
| Name = larger tridecimal tritone<br> larger gassormic tritone
| Color name = tholugu 5th
| Color name = tholugu 5th
| FJS name = d5<sup>13</sup><sub>55</sub>
}}
}}


In [[13-limit]] [[just intonation]], '''78/55''' is the '''larger tridecimal tritone''', measuring about 604.9¢. It is [[275/273]] (gassorma, about 12.6¢) flat of [[10/7]]. Its inversion is the smaller tridecimal tritone, [[55/39]], 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 tridecimal tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.
In [[13-limit]] [[just intonation]], '''78/55''' is the '''larger gassormic tritone''', measuring about 604.9¢. It is [[275/273]] (gassorma, about 12.6¢) flat of [[10/7]]. Its inversion is the smaller gassormic tritone, [[55/39]], 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 16:56, 25 October 2022

Interval information
Ratio 78/55
Factorization 2 × 3 × 5-1 × 11-1 × 13
Monzo [1 1 -1 0 -1 1
Size in cents 604.851¢
Name larger gassormic tritone
Color name tholugu 5th
FJS name [math]\displaystyle{ \text{d5}^{13}_{5,11} }[/math]
Special properties reduced
Tenney height (log2 nd) 12.0668
Weil height (log2 max(n, d)) 12.5708
Wilson height (sopfr(nd)) 34
Open this interval in xen-calc

In 13-limit just intonation, 78/55 is the larger gassormic tritone, measuring about 604.9¢. It is 275/273 (gassorma, about 12.6¢) flat of 10/7. Its inversion is the smaller gassormic tritone, 55/39, 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