Dominant 13th
D13 is a dominant chord built on D. Dominant chords create tension that wants to resolve — they are the engine that drives harmonic motion in jazz (Levine, The Jazz Theory Book). The tritone between the 3rd and b7th gives dominant chords their characteristic pull toward resolution.
24 voicings · dominant
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Melody (B5) doubled an octave below (D4) with chord tones in between
Left Hand
Right Hand
Left hand alternates between bass note and chord
Beat 1 & 3 — D3
Beat 2 & 4 — C, F#, B
Left hand alternates between bass note and chord
Beat 1 & 3 — A3
Beat 2 & 4 — C, F#, B
The dominant seventh chord functions as the V chord in both major and minor keys, creating the strongest harmonic pull toward the tonic (Mulholland & Hojnacki, The Berklee Book of Jazz Harmony). In blues, dominant sevenths also serve as I and IV chords. The tritone between the 3rd and b7th is the defining interval — it resolves by contrary motion to the root and third of the target chord. Understanding this resolution is essential for voice leading on piano (Levine, The Jazz Piano Book).
Mixolydian mode for unaltered dominant chords. The altered scale (melodic minor up a half step) for altered dominants. Lydian dominant (Lydian b7) for #11 sounds. The diminished scale (half-whole) for 7b9 and 13b9 chords (Levine, The Jazz Theory Book).
Dominant chords resolve down a fifth (or up a fourth) to their target chord. D13 most commonly resolves to a chord with a root a fourth above. The tritone substitution allows D13 to be replaced by a dominant chord a tritone away (Levine, The Jazz Theory Book).
ii-V-I
D13 as the V chord, resolving to Imaj7 a fourth above
Dominant cycle
Chain of dominant chords resolving in fourths
Blues
D13 as I7, IV7, or V7 in a blues progression
D13 is a dominant chord containing D, major third, perfect fifth, and minor seventh. The tension between the major 3rd and minor 7th (a tritone) creates a strong pull toward resolution (Levine, The Jazz Theory Book).
Shell voicings (root, 3, b7) are the starting point. Rootless voicings add the 9th or 13th for colour. For maximum tension, upper structure triads place a triad over the tritone — this is the technique of Herbie Hancock and Chick Corea (Levine, The Jazz Piano Book).
The tritone is the interval between the 3rd and b7th of D13. This unstable interval creates the harmonic tension that makes dominant chords want to resolve. The tritone substitution exploits this by replacing D13 with a dominant chord a tritone away (Levine, The Jazz Theory Book).
Upper structure triads are the most sophisticated way to voice dominant chords. Six common upper structures exist per dominant chord, each producing a different colour.
— Levine, The Jazz Piano Book, pp. 115-130
The tritone substitution is based on the fact that two dominant chords a tritone apart share the same tritone interval (3rd and b7th are swapped).
— Levine, The Jazz Theory Book, pp. 260-265