70:84:105:120: Difference between revisions

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{{Infobox Chord|70:84:105:120|ColorName=gu ru-6 or g,r6, sub-6 or s6}}
{{Infobox Chord|70:84:105:120|ColorName=sub-6 or s6, gu ru-6 or g,r6}}
'''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 5-limit 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]].  
 
{{chord edo approximation}}


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

Latest revision as of 04:38, 26 May 2026

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 sub-6 or s6
gu ru-6 or g,r6
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 5-limit 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.


Edo approximations for 70:84:105:120 ▶
intervals: 6/5, 3/2, 12/7 · ≤ 60edo, RMS rel. error ≤ 15%
  Edo Steps Cents (¢) Absolute errors (¢) RMS (¢) RMS (%)
▶ 10 0  3  6  8 0.00 360.00 720.00 960.00 0.00 +44.36 +18.04 +26.87 15.99 13.33
▶ 12 0  3  7  9 0.00 300.00 700.00 900.00 0.00 -15.64  -1.96 -33.13 13.25 13.25
▶ 15 0  4  9 12 0.00 320.00 720.00 960.00 0.00  +4.36 +18.04 +26.87 10.72 13.40
▶ 19 0  5 11 15 0.00 315.79 694.74 947.37 0.00  +0.15  -7.22 +14.24 7.78 12.32
▶ 22 0  6 13 17 0.00 327.27 709.09 927.27 0.00 +11.63  +7.14  -5.86 6.69 12.26
▶ 27 0  7 16 21 0.00 311.11 711.11 933.33 0.00  -4.53  +9.16  +0.20 4.96 11.17
▶ 31 0  8 18 24 0.00 309.68 696.77 929.03 0.00  -5.96  -5.18  -4.10 2.30 5.94
▶ 37 0 10 22 29 0.00 324.32 713.51 940.54 0.00  +8.68 +11.56  +7.41 4.26 13.15
▶ 41 0 11 24 32 0.00 321.95 702.44 936.59 0.00  +6.31  +0.48  +3.46 2.54 8.67
▶ 46 0 12 27 36 0.00 313.04 704.35 939.13 0.00  -2.60  +2.39  +6.00 3.17 12.14
▶ 50 0 13 29 39 0.00 312.00 696.00 936.00 0.00  -3.64  -5.96  +2.87 3.38 14.08
▶ 53 0 14 31 41 0.00 316.98 701.89 928.30 0.00  +1.34  -0.07  -4.83 2.34 10.34
▶ 58 0 15 34 45 0.00 310.34 703.45 931.03 0.00  -5.30  +1.49  -2.09 2.55 12.32
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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