140/81: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 140/81
| Name = septimal inframinor seventh
| Monzo = 2 -4 1 1
| Cents = 947.3196
| Name = septimal semidiminished seventh, <br> septimal inframinor seventh
| Color name = zy7, zoyo 7th
| Color name = zy7, zoyo 7th
| FJS name = m7<sup>35</sup>
| Sound = Ji-140-81-csound-foscil-220hz.mp3
| Sound = Ji-140-81-csound-foscil-220hz.mp3
}}
}}


'''140/81''', the '''septimal semidiminished seventh''' or '''septimal inframinor seventh''' is a [[7-limit]] [[interseptimal]] ratio of about 947 cents. It is flat of a minor seventh [[16/9]] by a septimal quartertone [[36/35]], flat of a subminor seventh [[7/4]] by a syntonic comma [[81/80]], and sharp of a supermajor sixth [[12/7]] by a sensamagic comma [[245/243]].  
'''140/81''', the '''septimal inframinor seventh''' is a [[7-limit]] [[interseptimal]] ratio of about 947 [[cent]]s. It is flat of a minor seventh [[16/9]] by a septimal quartertone [[36/35]], flat of a subminor seventh [[7/4]] by a syntonic comma [[81/80]], and sharp of a supermajor sixth [[12/7]] by a sensamagic comma [[245/243]].  


It is also sharp of a major sixth [[5/3]] by a subminor second [[28/27]]. For this fact it is useful in the [[Canovian chord]] and provides the function of a voice leading down to the major sixth. The [[Canou family|canou temperament]] targets this progression and uses it as one of the generators.  
Notice it is also sharp of the just major sixth [[5/3]] by a subminor second [[28/27]]. For this fact it is useful in the [[sensamagic dominant chord]] where it functions as a dissonance yet to be resolved down to the major sixth. The [[Canou family|canou temperament]] targets this progression and uses it as one of the generators.  


The interval is so perfectly approximated by [[19edo]], with an error of 0.05 cents. There are a number of edos that do this equally well, [[171edo]] to name one. The first edo that does this better than 19-edo with patent val is [[660edo]].  
== Approximation ==
It is perfectly approximated by [[19edo]] (15\19), with an error of 0.05 cents, and hence equally well done by the [[enneadecal]] temperament.  


== See also ==
== See also ==
Line 19: Line 16:
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]


[[Category:7-limit]]
[[Category:Interval]]
[[Category:Ratio]]
[[Category:Seventh]]
[[Category:Seventh]]
[[Category:Subminor seventh]]
[[Category:Subminor seventh]]
[[Category:Interseptimal]]
[[Category:Interseptimal intervals]]
[[Category:Semitwelfth]]

Latest revision as of 03:27, 28 April 2023

Interval information
Ratio 140/81
Factorization 22 × 3-4 × 5 × 7
Monzo [2 -4 1 1⟩
Size in cents 947.3196¢
Name septimal inframinor seventh
Color name zy7, zoyo 7th
FJS name [math]\displaystyle{ \text{m7}^{5,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 13.4691
Weil norm (log2 max(n, d)) 14.2586
Wilson norm (sopfr(nd)) 28

[sound info]
Open this interval in xen-calc

140/81, the septimal inframinor seventh is a 7-limit interseptimal ratio of about 947 cents. It is flat of a minor seventh 16/9 by a septimal quartertone 36/35, flat of a subminor seventh 7/4 by a syntonic comma 81/80, and sharp of a supermajor sixth 12/7 by a sensamagic comma 245/243.

Notice it is also sharp of the just major sixth 5/3 by a subminor second 28/27. For this fact it is useful in the sensamagic dominant chord where it functions as a dissonance yet to be resolved down to the major sixth. The canou temperament targets this progression and uses it as one of the generators.

Approximation

It is perfectly approximated by 19edo (15\19), with an error of 0.05 cents, and hence equally well done by the enneadecal temperament.

See also

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