6:7:8: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Overthink (talk | contribs)
Redirected page to 4:6:7
Tag: New redirect
 
Overthink (talk | contribs)
replaced redirect with info on semiquartal harmony
Tag: Removed redirect
Line 1: Line 1:
#REDIRECT [[4:6:7]]
{{Infobox chord}}
'''6:7:8''' is a 7-limit triad consisting of the intervals [[7/6]] and [[8/7]] stacked on top of each other. This chord deviates from traditional harmony in that the intervals divide the [[4/3|perfect fourth]] rather than the [[3/2|perfect fifth]]. The 7/6 and 8/7 intervals contrast by [[49/48]], similarly to how [[5/4]] and [[6/5]] contrast by [[25/24]] in [[4:5:6]]. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being [[21:24:28|1/(8:7:6) = 21:24:28]]. The 6:7:8 chord may be better voiced as 4:7:12 in order to place the root on the bottom and avoid clashes. It's rotation [[4:6:7]] is a subchord of [[4:5:6:7]], the harmonic seventh chord.
{{Todo|expand}}

Revision as of 04:29, 14 December 2025

Chord information
Harmonics 6:7:8
Subharmonics 1/(28:24:21)
Intervals from root 1/17/64/3
Cents from root 267¢498¢
Step intervals 7/6, 8/7
Step cents 267¢, 231¢
Prime limit 7
Genus 37 (21)
Intervallic odd limit 7
Otonal odd limit 7
Utonal odd limit 21
Consistent edos (d ≥ 2) 5edo**, 10edo*, 22edo*, 26edo*, …

6:7:8 is a 7-limit triad consisting of the intervals 7/6 and 8/7 stacked on top of each other. This chord deviates from traditional harmony in that the intervals divide the perfect fourth rather than the perfect fifth. The 7/6 and 8/7 intervals contrast by 49/48, similarly to how 5/4 and 6/5 contrast by 25/24 in 4:5:6. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being 1/(8:7:6) = 21:24:28. The 6:7:8 chord may be better voiced as 4:7:12 in order to place the root on the bottom and avoid clashes. It's rotation 4:6:7 is a subchord of 4:5:6:7, the harmonic seventh chord.