12/7: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| JI glyph = [[File:ji_glyph_12_7.png|x48px]]
| Name = supermajor sixth, septimal major sixth
| Ratio = 12/7
| Monzo = -2 -1 0 1
| Cents = 933.12909
| Name = septimal supermajor sixth
| Color name = r6, ru 6th
| Color name = r6, ru 6th
| Sound = jid_12_7_pluck_adu_dr220.mp3
| Sound = jid_12_7_pluck_adu_dr220.mp3
}}
}}
{{Wikipedia| Septimal major sixth }}


In [[7-limit]] [[Just intonation|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 [[36/25]] -- the septimal quartertone -- a [[superparticular|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 '''septimal (super)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 of [[7/4]] 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: [[Gallery of Just Intervals]]
== See also ==
* [[7/6]] – its [[octave complement]]
* [[7/4]] – its [[twelfth complement]]
* [[Gallery of just intervals]]
* [[:File:Ji-12-7-csound-foscil-220hz.mp3]] – an alternative sound sample


[[Category:7-limit]]]]
[[Category:Sixth]]
[[Category:interval]]
[[Category:Major sixth]]
[[Category:just]]
[[Category:Supermajor sixth]]
[[Category:just interval]]
[[Category:Over-7 intervals]]

Latest revision as of 16:59, 14 April 2025

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
English Wikipedia has an article on:

In 7-limit just intonation, 12/7 is the septimal (super)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 of 7/4 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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