4:5:6:7:9: Difference between revisions
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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]]. | 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]]. Meanwhile, the utonal inverse above can be voiced as [[210:252:315:360:560|1–6/5–3/2–12/7–8/3 | 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 == | == See also == | ||
* [[Otonalpentad]] – this chord as a scale | * [[Otonalpentad]] – this chord as a scale, [[octave reduced]] | ||
Latest revision as of 22:46, 4 February 2026
| Chord information |
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. It is an extension of 4:5:6 and 4:5:6:7.
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.
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 1–6/5–3/2–12/7–24/11, which has the inverse 1–5/4–3/2–7/4–11/4. Meanwhile, the utonal inverse above can be voiced as 1–6/5–3/2–12/7–8/3. These four chords form a quadruplet in the 11-odd-limit, all being subsets of 1–5/4–3/2–7/4–9/4–11/4 and 1–6/5–3/2–12/7–24/11–8/3.
See also
- Otonalpentad – this chord as a scale, octave reduced