12/7: Difference between revisions

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Now that 42/25 is given a more appropriate name, the "septimal major sixth" name can be used for this
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| Monzo = -2 -1 0 1
| Monzo = -2 -1 0 1
| Cents = 933.12909  
| Cents = 933.12909  
| Name = septimal supermajor sixth
| Name = supermajor sixth, <br>septimal major sixth
| Color name = r6, ru 6th
| Color name = r6, ru 6th
| Sound = Ji-12-7-csound-foscil-220hz.mp3
| FJS name = M6<sub>7</sub>
| Sound = jid_12_7_pluck_adu_dr220.mp3
}}
}}


In [[7-limit]] [[Just Intonation]], '''12/7''' is the '''septimal supermajor sixth''' of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of [[5/3]] by [[36/35]] -- the septimal quartertone -- a [[superparticular]] interval of about 48.8¢. It differs from the Pythagorean major sixth of [[27/16]] by [[64/63]] -- Archytas' comma -- about 27.3¢. And finally, it differs from the harmonic seventh -- [[7/4]], about 968.8¢ -- by [[49/48]] -- the large septimal diesis or slendro diesis -- about 35.7¢. 12/7 is the inversion of the septimal subminor third of [[7/6]].
In [[7-limit]] [[Just Intonation]], '''12/7''' is the '''supermajor sixth''' or '''septimal major sixth''' of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of [[5/3]] by [[36/35]] -- the septimal quartertone -- a [[superparticular]] interval of about 48.8¢. It differs from the Pythagorean major sixth of [[27/16]] by [[64/63]] -- Archytas' comma -- about 27.3¢. And finally, it differs from the harmonic seventh -- [[7/4]], about 968.8¢ -- by [[49/48]] -- the large septimal diesis or slendro diesis -- about 35.7¢. 12/7 is the inversion of the septimal subminor third of [[7/6]].
 
[[File:jid_12_7_pluck_adu_dr220.mp3]]


== See also ==  
== See also ==  


* [[7/6]] -- its [[octave complement]]
* [[7/6]] -- its [[octave complement]]
* [[42/25]] -- a lower septimal major sixth
* [[Gallery of Just Intervals]]
* [[Gallery of Just Intervals]]
* [[Wikipedia:Septimal major sixth|Septimal major sixth - Wikipedia]]
* [[File:Ji-12-7-csound-foscil-220hz.mp3]] an alternative sound sample


[[Category:7-limit]]
[[Category:7-limit]]
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[[Category:Sixth]]
[[Category:Sixth]]
[[Category:Major sixth]]
[[Category:Major sixth]]
[[Category:Supermajor sixth]]
[[Category:Just interval]]
[[Category:Just interval]]

Revision as of 07:25, 1 September 2020

Interval information
Ratio 12/7
Factorization 22 × 3 × 7-1
Monzo [2 1 0 -1⟩
Size in cents 933.1291¢
Names supermajor sixth,
septimal major sixth
Color name r6, ru 6th
FJS name [math]\displaystyle{ \text{M6}_{7} }[/math]
Special properties reduced
Tenney height (log2 nd) 6.39232
Weil height (log2 max(n, d)) 7.16993
Wilson height (sopfr(nd)) 14

[sound info]
Open this interval in xen-calc

In 7-limit Just Intonation, 12/7 is the supermajor sixth or septimal major sixth of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of 5/3 by 36/35 -- the septimal quartertone -- a superparticular interval of about 48.8¢. It differs from the Pythagorean major sixth of 27/16 by 64/63 -- Archytas' comma -- about 27.3¢. And finally, it differs from the harmonic seventh -- 7/4, about 968.8¢ -- by 49/48 -- the large septimal diesis or slendro diesis -- about 35.7¢. 12/7 is the inversion of the septimal subminor third of 7/6.

See also

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