112/75: Difference between revisions

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'''112/75'''
{{Infobox Interval
|4 -1 -2 1>
| Ratio = 112/75
| Monzo = 4 -1 -2 1
| Cents = 694.2435
| Name =  marvelous fifth
| Sound = jid_112_75_pluck_adu_dr220.mp3
}}


694.2435 cents
'''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]] [[:File:jid_112_75_pluck_adu_dr220.mp3|sound sample]]
 
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.
[[Category:interval]]
[[Category:interval]]
[[Category:just_interval]]
[[Category:just_interval]]

Revision as of 22:51, 11 October 2018

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
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 (694.7¢), 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.