48/35: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 48/35
| Monzo = 4 1 -1 -1
| Cents = 546.81538
| Name = septimal superfourth
| Name = septimal superfourth
| Color name = rg4, rugu 4th
| Color name = rg4, rugu 4th
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}}
}}


'''48/35''', the '''septimal superfourth''' (546.8¢), is 385/384 (4.5¢) below the undecimal superfourth of [[11/8]] (551.3¢). It is opposite 1/1 in the octahedral geometry of the [[hexany]] <span style="white-space: nowrap">1/1-8/7-6/5-48/35-8/5-12/7-2/1</span>; hence in the [[Keenanismic_family#Keenanismic|keenanismic temperament]] tempering out 385/384, 11 is an interval of rather low complexity, with [[11/8]] being the interval between [[7/6]] and [[8/5]].
'''48/35''', the '''septimal superfourth''' (546.8{{cent}}), is [[385/384]] (4.5{{cent}}) below the undecimal superfourth of [[11/8]] (551.3{{cent}}). It is opposite 1/1 in the octahedral geometry of the [[hexany]] <span style="white-space: nowrap">1/1-8/7-6/5-48/35-8/5-12/7-2/1</span>; hence in the [[Keenanismic_family#Keenanismic|keenanismic temperament]] tempering out 385/384, 11 is an interval of rather low complexity, with [[11/8]] being the interval between [[7/6]] and [[8/5]].


== See also ==
== See also ==
 
* [[35/24]] – its octave complement
* [[35/24]] -- its octave complement
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[Superfourth]]
* [[Superfourth]]


[[Category:7-limit]]
[[Category:Fourth]]
[[Category:Superfourth]]
[[Category:Superfourth]]
[[Category:Interval ratio]]

Latest revision as of 15:59, 25 October 2022

Interval information
Ratio 48/35
Factorization 24 × 3 × 5-1 × 7-1
Monzo [4 1 -1 -1⟩
Size in cents 546.8154¢
Name septimal superfourth
Color name rg4, rugu 4th
FJS name [math]\displaystyle{ \text{P4}_{5,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 10.7142
Weil norm (log2 max(n, d)) 11.1699
Wilson norm (sopfr(nd)) 23

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Open this interval in xen-calc

48/35, the septimal superfourth (546.8 ¢), is 385/384 (4.5 ¢) below the undecimal superfourth of 11/8 (551.3 ¢). It is opposite 1/1 in the octahedral geometry of the hexany 1/1-8/7-6/5-48/35-8/5-12/7-2/1; hence in the keenanismic temperament tempering out 385/384, 11 is an interval of rather low complexity, with 11/8 being the interval between 7/6 and 8/5.

See also

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