75/56: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 75/56
| Ratio = 75/56
| Monzo = -3 1 2 -1
| Monzo = -3 1 2 -1
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| Sound = Ji 75-56-csound-foscil-220hz.mp3
| Sound = Ji 75-56-csound-foscil-220hz.mp3
}}
}}
 
'''75/56''', the '''marvelous fourth''' (505.8{{cent}}), is [[225/224]] (7.7{{cent}}) 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.
'''75/56''', the '''marvelous fourth''' (505.), is [[225/224]] (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 ==
== See also ==
* [[:File:jid_75_56_pluck_adu_dr220.mp3]] – another sound example
* [[:File:jid_75_56_pluck_adu_dr220.mp3]] – another sound example
* [[112/75]] - its [[octave complement]]
* [[112/75]] - its [[octave complement]]
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[[Category:7-limit]]
[[Category:7-limit]]
[[Category:Interval ratio]]
[[Category:Just interval]]
[[Category:Fourth]]
[[Category:Fourth]]
[[Category:Marvel]]
[[Category:Marvel]]

Revision as of 17:22, 23 March 2022

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