70:84:105:120: Difference between revisions

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m moved link to 4:5:6:7 earlier
Address the harmonic sixth chord, mirroring 4:5:6:7 article
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'''70:84:105:120''', the ''subharmonic sixth chord''<ref>[[Flora Canou]]. [[User:FloraC/Analysis on the 13-limit just intonation space: episode ii #Chapter II. Generic Rooted Chord Construction|"Chapter II. Generic Rooted Chord Construction", ''Analysis on the 13-limit Just Intonation Space: Episode II'']]. </ref>, is a [[tetrad]] in [[7-limit]] harmony. It is the inverse of [[4:5:6:7]], the harmonic seventh chord. It can be considered the minor version of 4:5:6:7, and serves as the fundamental [[utonal]] consonance of the [[7-odd-limit]]. On C, it can be notated as Cm(S6), where m is minor and S is supermajor.
'''70:84:105:120''', the ''subharmonic sixth chord''<ref>[[Flora Canou]]. [[User:FloraC/Analysis on the 13-limit just intonation space: episode ii #Chapter II. Generic Rooted Chord Construction|"Chapter II. Generic Rooted Chord Construction", ''Analysis on the 13-limit Just Intonation Space: Episode II'']]. </ref>, is a [[tetrad]] in [[7-limit]] harmony. It is the inverse of [[4:5:6:7]], the harmonic seventh chord. It can be considered the minor version of 4:5:6:7, and serves as the fundamental [[utonal]] consonance of the [[7-odd-limit]]. On C, it can be notated as Cm(S6), where m is minor and S is supermajor.


The 4:5:6:7 chord may be modified to obtain this chord by flattening the [[5/4]] by [[25/24]] and the [[7/4]] by [[49/48]]. The intervals [[25/24]] and [[49/48]] thus serve as chromas, and they are equated when [[50/49]] is tempered out, such as in [[pajara]].
The subharmonic sixth chord may be modified to obtain the harmonic seventh chord by raising the [[5/4]] by [[25/24]] and the [[7/4]] by [[49/48]]. The intervals [[25/24]] and [[49/48]] thus serve as chromas. It can also be modified by inflecting both [[6/5]] and [[12/7]] down by [[36/35]] to get the ''harmonic sixth chord'' [[6:7:9:10|1–7/6–3/2–5/3]].  


{{todo|inline=1|add sound example}}
{{todo|inline=1|add sound example}}

Revision as of 12:03, 18 December 2025

Chord information
Harmonics 70:84:105:120
Subharmonics 1/(12:10:8:7)
Intervals from root 1/1–6/5–3/2–12/7
Cents from root 0¢–316¢–702¢–933¢
Step intervals 6/5, 5/4, 8/7
Step cents 316¢, 386¢, 231¢
Color names gu ru-6 or g,r6
sub-6 or s6
Prime limit 7
Genus 3⋅5⋅7 (105)
Intervallic odd limit 7
Otonal odd limit 105
Utonal odd limit 7
Consistent edos (d ≥ 2) 31edo*, 41edo*, 68edo*, 72edo*

70:84:105:120, the subharmonic sixth chord[1], is a tetrad in 7-limit harmony. It is the inverse of 4:5:6:7, the harmonic seventh chord. It can be considered the minor version of 4:5:6:7, and serves as the fundamental utonal consonance of the 7-odd-limit. On C, it can be notated as Cm(S6), where m is minor and S is supermajor.

The subharmonic sixth chord may be modified to obtain the harmonic seventh chord by raising the 5/4 by 25/24 and the 7/4 by 49/48. The intervals 25/24 and 49/48 thus serve as chromas. It can also be modified by inflecting both 6/5 and 12/7 down by 36/35 to get the harmonic sixth chord 1–7/6–3/2–5/3.

Todo: add sound example

References

  1. ↑ Flora Canou. "Chapter II. Generic Rooted Chord Construction", Analysis on the 13-limit Just Intonation Space: Episode II.

See also

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