12/7: Difference between revisions

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reworked: simplified links; introduces infobox interval
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{| class="wikitable"
{{Infobox Interval
|-
| Icon = [[File:ji_glyph_12_7.png|124px]] <small><br/>[[JI glyphs|JI glyph]]</small>
| | [[File:ji_glyph_12_7.png|alt=ji glyph 12 7.png|136x120px|ji glyph 12 7.png]]
| Ratio = 12/7
|-
| Monzo = -2 -1 0 1
| | JI Glyph for 12/7
| Cents = 933.12909
|}
| Name = septimal supermajor sixth
| Sound = jid_12_7_pluck_adu_dr220.mp3
| Color name =
}}


'''12/7'''
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]].
|-2 -1 0 1&gt;


933.12909 cents
See: [[Gallery of Just Intervals]]
 
[[File:jid_12_7_pluck_adu_dr220.mp3]] [[:File:jid_12_7_pluck_adu_dr220.mp3|sound sample]]
 
In [[7-limit|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|5/3]] by [[36/35|36/25]] -- the septimal quartertone -- a [[superparticular|superparticular]] interval of about 48.8¢. It differs from the Pythagorean major sixth of [[27/16|27/16]] by [[64/63|64/63]] -- Archytas' comma -- about 27.3¢. And finally, it differs from the harmonic seventh -- [[7/4|7/4]], about 968.8¢ -- by [[49/48|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|7/6]].
 
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]

Revision as of 22:31, 17 October 2018

Interval information
Ratio 12/7
Factorization 22 × 3 × 7-1
Monzo [2 1 0 -1⟩
Size in cents 933.1291¢
Name septimal supermajor sixth
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 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 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: Gallery of Just Intervals

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