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

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'''4:5:6:7:9''', the ''harmonic ninth chord'', is a [[pentad]] in [[7-limit]] harmony.

'''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. It is an extension of [[4:5:6]] and [[4:5:6:7]].

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]].

4:5:6:7:9 (1–5/4–3/2–7/4–9/4) can be modified by inflecting the [[5/4]] down by [[25/24]], the [[7/4]] down by [[49/48]], and the [[9/4]] down by [[33/32]] to get an [[11-limit]] utonal minor counterpart [[770:924:1155:1320:1680|1–6/5–3/2–12/7–24/11]], which has the inverse [[4:5:6:7:11|1–5/4–3/2–7/4–11/4]]. Meanwhile, the utonal inverse above can be voiced as [[210:252:315:360:560|1–6/5–3/2–12/7–8/3]]. These four chords form a quadruplet in the [[11-odd-limit]], all being subsets of [[4:5:6:7:9:11|1–5/4–3/2–7/4–9/4–11/4]] and [[2310:2772:3465:3960:5040:6160|1–6/5–3/2–12/7–24/11–8/3]].

== See also ==

* [[Otonalpentad]] – this chord as a scale, [[octave reduced]]

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 {{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.
+'''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. It is an extension of [[4:5:6]] and [[4:5:6:7]].
+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]].
+:5:6:7:9 (1–5/4–3/2–7/4–9/4) can be modified by inflecting the [[5/4]] down by [[25/24]], the [[7/4]] down by [[49/48]], and the [[9/4]] down by [[33/32]] to get an [[11-limit]] utonal minor counterpart [[770:924:1155:1320:1680|1–6/5–3/2–12/7–24/11]], which has the inverse [[4:5:6:7:11|1–5/4–3/2–7/4–11/4]]. Meanwhile, the utonal inverse above can be voiced as [[210:252:315:360:560|1–6/5–3/2–12/7–8/3]]. These four chords form a quadruplet in the [[11-odd-limit]], all being subsets of [[4:5:6:7:9:11|1–5/4–3/2–7/4–9/4–11/4]] and [[2310:2772:3465:3960:5040:6160|1–6/5–3/2–12/7–24/11–8/3]].
+== See also ==
+* [[Otonalpentad]] – this chord as a scale, [[octave reduced]]