75/56: Difference between revisions

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'''75/56'''
{{Infobox Interval
|-3 1 2 -1>
| Icon =
| Ratio = 75/56
| Monzo = -3 1 2 -1
| Cents = 505.75652
| Name = marvelous fourth
| Color name = ryy3, ruyoyo 3rd
| Sound = jid_75_56_pluck_adu_dr220.mp3
}}


505.7565 cents
'''75/56''', the '''marvelous fourth''' (505.8¢), is [[225/224]] (7.7¢) sharp of the just fourth [[4/3]]. It often arises in just intonation scales. Tempering out 225/224 from the scale can be used to make it much less sharp, but it is usable as it is, being only half a cent sharp of the [[19edo]] fourth of 8\19. Considered as a [[meantone]] fourth, it is approximately 5/14-comma meantone.


[[File:jid_75_56_pluck_adu_dr220.mp3]] [[:File:jid_75_56_pluck_adu_dr220.mp3|sound sample]]
== See also ==
* [[112/75]] - its [[octave complement]]
* [[Gallery of just intervals]]


75/56, the marvelous fourth (505.8¢), is 225/224 (7.7¢) sharp of the just fourth [[4/3|4/3]]. It often arises in just intonation scales. Tempering out 225/224 from the scale can be used to make it much less sharp, but it is usable as it is, being only half a cent sharp of the [[19edo|19edo]] fourth of 8\19. Considered as a [[Meantone|meantone]] fourth, it is approximately 5/14-comma meantone.
[[Category:7-limit]]
[[Category:Interval]]
[[Category:Just interval]]
[[Category:Ratio]]
[[Category:Sound example]]
[[Category:Fourth]]

Revision as of 14:14, 27 October 2018

Interval information
Ratio 75/56
Factorization 2-3 × 3 × 52 × 7-1
Monzo [-3 1 2 -1⟩
Size in cents 505.7565¢
Name marvelous fourth
Color name ryy3, ruyoyo 3rd
FJS name [math]\displaystyle{ \text{A3}^{5,5}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.0362
Weil norm (log2 max(n, d)) 12.4576
Wilson norm (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

75/56, the marvelous fourth (505.8¢), is 225/224 (7.7¢) sharp of the just fourth 4/3. It often arises in just intonation scales. Tempering out 225/224 from the scale can be used to make it much less sharp, but it is usable as it is, being only half a cent sharp of the 19edo fourth of 8\19. Considered as a meantone fourth, it is approximately 5/14-comma meantone.

See also

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