81/70: Difference between revisions

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m Mention of enneadecal (and replace of old description)
Consolidate interval name
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| Monzo = -1 4 -1 -1
| Monzo = -1 4 -1 -1
| Cents = 252.6804
| Cents = 252.6804
| Name = septimal semiaugmented second, <br>septimal ultramajor second
| Name = septimal ultramajor second
| Color name = rg2, rugu 2nd
| Color name = rg2, rugu 2nd
| FJS name = M2<sub>35</sub>
| FJS name = M2<sub>35</sub>
| Sound = Ji-81-70-csound-foscil-220hz.mp3
| Sound = Ji-81-70-csound-foscil-220hz.mp3
}}
}}
 
'''81/70''', the '''septimal ultramajor second''' is a [[7-limit]] [[interseptimal]] ratio of about 253 cents. It is sharp of a major second [[9/8]] by a septimal quartertone [[36/35]], sharp of a supermajor second [[8/7]] by a syntonic comma [[81/80]], and flat of a subminor third [[7/6]] by a sensamagic comma [[245/243]].  
'''81/70''', the '''septimal semiaugmented second''' or '''septimal ultramajor second''' is a [[7-limit]] [[interseptimal]] ratio of about 253 cents. It is sharp of a major second [[9/8]] by a septimal quartertone [[36/35]], sharp of a supermajor second [[8/7]] by a syntonic comma [[81/80]], and flat of a subminor third [[7/6]] by a sensamagic comma [[245/243]].  


It is also flat of a minor third [[6/5]] by a subminor second [[28/27]]. For this fact it is useful in the [[Canovian chord]] and provides the function of a voice leading up to the minor third. The [[Canou family|canou temperament]] targets this progression and uses it as one of the generators.  
It is also flat of a minor third [[6/5]] by a subminor second [[28/27]]. For this fact it is useful in the [[Canovian chord]] and provides the function of a voice leading up to the minor third. The [[Canou family|canou temperament]] targets this progression and uses it as one of the generators.  
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[[Category:Supermajor second]]
[[Category:Supermajor second]]
[[Category:Interseptimal]]
[[Category:Interseptimal]]
[[Category:Semifourth]]

Revision as of 17:03, 16 November 2021

Interval information
Ratio 81/70
Factorization 2-1 × 34 × 5-1 × 7-1
Monzo [-1 4 -1 -1
Size in cents 252.6804¢
Name septimal ultramajor second
Color name rg2, rugu 2nd
FJS name [math]\displaystyle{ \text{M2}_{35} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.4691
Weil norm (log2 max(n, d)) 12.6797
Wilson norm (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

81/70, the septimal ultramajor second is a 7-limit interseptimal ratio of about 253 cents. It is sharp of a major second 9/8 by a septimal quartertone 36/35, sharp of a supermajor second 8/7 by a syntonic comma 81/80, and flat of a subminor third 7/6 by a sensamagic comma 245/243.

It is also flat of a minor third 6/5 by a subminor second 28/27. For this fact it is useful in the Canovian chord and provides the function of a voice leading up to the minor third. The canou temperament targets this progression and uses it as one of the generators.

It is so perfectly approximated by 19edo (4\19), with an error of 0.05 cents, and hence equally well done by the enneadecal temperament.

See also