108/77: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = symbiotic diminished fifth
| Ratio = 108/77
| Monzo = 2 3 0 -1 -1
| Cents = 585.72115
| Name = swetismic augmented fourth
| Color name = 1ur4, luru 4th
| Color name = 1ur4, luru 4th
| Sound = Ji-108-77-csound-foscil-220hz.mp3
| Sound = Ji-108-77-csound-foscil-220hz.mp3
}}
}}


'''108/77''' is 540/539 (3.2 cents) sharp of [[7/5]], and is the interval between [[11/9]] and [[12/7]]. Its [[inverse interval]] is [[77/56]].
'''108/77''' is the 11-limit interval between [[11/9]] and [[12/7]]. It is [[19712/19683]] (symbiotic comma, 2.5 [[¢]]) sharp of the Pythagorean diminished fifth [[1024/729]]. Meanwhile, it is [[540/539]] (swetisma, 3.2 ¢) sharp of [[7/5]].  


:''See also [[Gallery of just intervals]]''
== Terminology ==
This interval could also be called the ''swetismic augmented fourth'' if viewed as fudging from 7/5 instead.
 
== See also ==
* [[77/54]] – its [[octave complement]]
* [[77/72]] – its [[fifth complement]]
* [[Gallery of just intervals]]


[[Category:11-limit]]
[[Category:Interval ratio]]
[[Category:Tritone]]
[[Category:Tritone]]
[[Category:Listen]]
[[Category:Symbiotic]]
[[Category:Sweetismic]]
 
[[Category:todo:expand]]
[[Category:todo:improve synopsis]]

Latest revision as of 11:32, 25 October 2022

Interval information
Ratio 108/77
Factorization 22 × 33 × 7-1 × 11-1
Monzo [2 3 0 -1 -1
Size in cents 585.7212¢
Name symbiotic diminished fifth
Color name 1ur4, luru 4th
FJS name [math]\displaystyle{ \text{A4}_{7,11} }[/math]
Special properties reduced
Tenney height (log2 nd) 13.0217
Weil height (log2 max(n, d)) 13.5098
Wilson height (sopfr(nd)) 31

[sound info]
Open this interval in xen-calc

108/77 is the 11-limit interval between 11/9 and 12/7. It is 19712/19683 (symbiotic comma, 2.5 ¢) sharp of the Pythagorean diminished fifth 1024/729. Meanwhile, it is 540/539 (swetisma, 3.2 ¢) sharp of 7/5.

Terminology

This interval could also be called the swetismic augmented fourth if viewed as fudging from 7/5 instead.

See also