4:5:6:7:9: Difference between revisions

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{{Infobox Chord|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}
{{Infobox Chord|ColorName=yo zo-7 add-9 or y,z7,9, har-9 or h9}}


'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, [[140:180:210:252:315|1/(4:5:6:7:9)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]]. It is an extension of [[4:5:6]] and [[4:5:6:7]].
'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, [[140:180:210:252:315|1/(9:7:6:5:4)]], can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by [[36/35]], so the third becomes [[9/7]] and the seventh [[9/5]]. It is an extension of [[4:5:6]] and [[4:5:6:7]].


== See also ==
== See also ==

Revision as of 08:00, 22 December 2025

Chord information
Harmonics 4:5:6:7:9
Subharmonics 1/(315:252:210:180:140)
Intervals from root 1/1–5/4–3/2–7/4–9/4
Cents from root 0¢–386¢–702¢–969¢–1404¢
Step intervals 5/4, 6/5, 7/6, 9/7
Step cents 386¢, 316¢, 267¢, 435¢
Color names yo zo-7 add-9 or y,z7,9
har-9 or h9
Prime limit 7
Genus 32⋅5⋅7 (315)
Intervallic odd limit 9
Otonal odd limit 9
Utonal odd limit 315
Consistent edos (d ≥ 1.5) 31edo, 41edo*, 46edo, 53edo, …

4:5:6:7:9, the harmonic ninth chord, is a pentad in 7-limit harmony. It serves as the fundamental otonal consonance of the 9-odd-limit, with many chords being a subset of it or one of its inversions. Its utonal inverse, 1/(9:7:6:5:4), can also be seen as a fundamental chord, and subsets can be taken out of it as well. The 4:5:6:7:9 chord can be modified to get its utonal inverse by inflecting both the third and seventh up by 36/35, so the third becomes 9/7 and the seventh 9/5. It is an extension of 4:5:6 and 4:5:6:7.

See also

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