14:21:24: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Creation
 
Overthink (talk | contribs)
a few fixes
Line 2: Line 2:
'''14:21:24''' is a [[7-limit]] [[chord]] found as a subset of the subharmonic sixth chord, [[70:84:105:120]], or of the septimal major sixth chord, [[14:18:21:24]]. Due to having no fives, it is the first utonal chord that deviates from traditional harmony. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.
'''14:21:24''' is a [[7-limit]] [[chord]] found as a subset of the subharmonic sixth chord, [[70:84:105:120]], or of the septimal major sixth chord, [[14:18:21:24]]. Due to having no fives, it is the first utonal chord that deviates from traditional harmony. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.


Its first rotation, '''21:24:28''', is significant because it consists of the intervals [[8/7]] and [[7/6]] stacked on top of each other. The intervals in this chord divide the [[4/3|perfect fourth]] rather than the [[3/2|perfect fifth]], and 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 8/7 and 7/6, we get the otonal inverse of 21:24:28, that being [[6:7:8]].  
Its first rotation, '''21:24:28''', is significant because it consists of the intervals [[8/7]] and [[7/6]] stacked on top of each other. The intervals in this chord divide the [[4/3|perfect fourth]] rather than the [[3/2|perfect fifth]], and contrast by [[49/48]], similarly to how [[6/5]] and [[5/4]] contrast by [[25/24]] in [[10:12:15]]. By swapping the order of 8/7 and 7/6, we get the otonal inverse of 21:24:28, that being [[6:7:8]].  


Another notable setting is the open voicing 7:12:21, which shares the property with 6:7:8 that its intervals, [[12/7]] and [[7/4]], contrast by 49/48, but they divide the [[3/1|perfect twelfth]] instead. This also has the advantage of avoiding the unresolvedness of a dominant seventh chord that occurs in the 6:7:8 and 4:6:7 voicings. Its otonal version is 4:7:12, an open voicing of [[4:6:7]].
Another notable setting is the open voicing 7:12:21, which shares the property with 21:24:28 that its intervals, [[12/7]] and [[7/4]], contrast by 49/48, but they divide the [[3/1|perfect twelfth]] instead. Its otonal version is 4:7:12, an open voicing of [[4:6:7]].


Its second rotation, '''12:14:21''', is also significant because it functions as the fifthless version of the septimal minor seventh chord, [[12:14:18:21]].
Its second rotation, '''12:14:21''', is also significant because it functions as the fifthless version of the septimal minor seventh chord, [[12:14:18:21]].

Revision as of 20:54, 22 January 2026

Chord information
Harmonics 14:21:24
Subharmonics 1/(12:8:7)
Intervals from root 1/13/212/7
Cents from root 702¢933¢
Step intervals 3/2, 8/7
Step cents 702¢, 231¢
Prime limit 7
Genus 37 (21)
Intervallic odd limit 7
Otonal odd limit 21
Utonal odd limit 7
Consistent edos (d ≥ 2) 5edo**, 10edo*, 22edo*, 26edo*, …

14:21:24 is a 7-limit chord found as a subset of the subharmonic sixth chord, 70:84:105:120, or of the septimal major sixth chord, 14:18:21:24. Due to having no fives, it is the first utonal chord that deviates from traditional harmony. As such, it is a candidate for metallic harmony, a form of extraclassical tonality that employs 7 instead of 5 as its other prime.

Its first rotation, 21:24:28, is significant because it consists of the intervals 8/7 and 7/6 stacked on top of each other. The intervals in this chord divide the perfect fourth rather than the perfect fifth, and contrast by 49/48, similarly to how 6/5 and 5/4 contrast by 25/24 in 10:12:15. By swapping the order of 8/7 and 7/6, we get the otonal inverse of 21:24:28, that being 6:7:8.

Another notable setting is the open voicing 7:12:21, which shares the property with 21:24:28 that its intervals, 12/7 and 7/4, contrast by 49/48, but they divide the perfect twelfth instead. Its otonal version is 4:7:12, an open voicing of 4:6:7.

Its second rotation, 12:14:21, is also significant because it functions as the fifthless version of the septimal minor seventh chord, 12:14:18:21.