112/75: Difference between revisions

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'''112/75'''
{{Infobox Interval
|4 -1 -2 1>
| Name = marvelous fifth
| Color name = zgg6, zogugu 6th
| Sound = Ji 112-75-csound-foscil-220hz.mp3
}}


694.2435 cents
'''112/75''', the '''marvelous fifth''' (694.2¢), is [[225/224]] (7.7¢) below the just fifth [[3/2]]. It often arises in just intonation scales, for instance as the interval from [[15/14]] to [[8/5]], or 5/7 to 16/15. Tempering out 225/224 from the scale can be used to make it much less flat, but it is usable as it is, being only half a cent flat from the [[19edo]] fifth of 11\19. Considered as a [[meantone]] fifth, it is approximately 5/14-comma meantone.


[[File:jid_112_75_pluck_adu_dr220.mp3]] [[:File:jid_112_75_pluck_adu_dr220.mp3|sound sample]]
== See also ==


112/75, the marvelous fifth (694.7¢), is 225/224 (7.7¢) below the just fifth [[3/2|3/2]]. It often arises in just intonation scales, for instance as the interval from 15/14 to 8/5, or 5/7 to 16/15. Tempering out 225/224 from the scale can be used to make it much less flat, but it is usable as it is, being only half a cent flat from the [[19edo|19edo]] fifth of 11\19. Considered as a [[Meantone|meantone]] fifth, it is approximately 5/14-comma meantone.
* [[:File:jid_112_75_pluck_adu_dr220.mp3]] – another sound example
[[Category:interval]]
* [[75/56]] - its [[octave complement]]
[[Category:just_interval]]
* [[Gallery of just intervals]]
 
[[Category:Fifth]]
[[Category:Marvel]]

Latest revision as of 16:32, 8 February 2023

Interval information
Ratio 112/75
Factorization 24 × 3-1 × 5-2 × 7
Monzo [4 -1 -2 1⟩
Size in cents 694.2435¢
Name marvelous fifth
Color name zgg6, zogugu 6th
FJS name [math]\displaystyle{ \text{d6}^{7}_{5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 13.0362
Weil norm (log2 max(n, d)) 13.6147
Wilson norm (sopfr(nd)) 28

[sound info]
Open this interval in xen-calc

112/75, the marvelous fifth (694.2¢), is 225/224 (7.7¢) below the just fifth 3/2. It often arises in just intonation scales, for instance as the interval from 15/14 to 8/5, or 5/7 to 16/15. Tempering out 225/224 from the scale can be used to make it much less flat, but it is usable as it is, being only half a cent flat from the 19edo fifth of 11\19. Considered as a meantone fifth, it is approximately 5/14-comma meantone.

See also

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