140/81: Difference between revisions

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Rewrite according to its octave complement
m Mention of enneadecal (and replace of old description)
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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.  
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.  


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]].  
It is so 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 ==

Revision as of 05:34, 5 January 2021

Interval information
Ratio 140/81
Factorization 22 × 3-4 × 5 × 7
Monzo [2 -4 1 1
Size in cents 947.3196¢
Names septimal semidiminished seventh,
septimal inframinor seventh
Color name zy7, zoyo 7th
FJS name [math]\displaystyle{ \text{m7}^{35} }[/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 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.

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 temperament targets this progression and uses it as one of the generators.

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

See also