A multifaceted structure
The “dominant shape” is extremely versatile. In a tonal context, it can be used to voice all chords that are derived from melodic minor, and most chords that are derived from major (in a modal context, its use is broader yet). The degrees on which each of the chords below function are indicated in the captions below each example.
Transposable formulas (specific arrangements of chord tones and tensions, e.g. “3 13 b7 9”) are also given in the captions for each chord (in each caption, position B is listed first and position A second to be consistent with the music notation). By position A/B, it is meant “dominant shape (voicing used for the V chord) extracted from the major II-V-I progression in position A/B.”
The dominant shape is comprised of the following intervals (listed from the bottom to the top of the voicing): major third, major second, perfect fourth in position A / perfect fourth, minor second, major third in position B.
Tonal use cases
The mixolydian (dominant) chord is listed first, since it is, naturally, the one from which the thought of using the dominant shape to play other chords comes from. Then we have the altered chord, and it is interesting to note that there is a sub V (tritone substitution) relationship between the mixolydian and the altered dominant chords. Eb7 and A7alt, for example, indeed share the same guide tones (G and Db/C#), and their roots are indeed a tritone apart. As a result, one chord can be substituted for the other following the tritone substitution rule.
I have then chosen to list the locrian and minor 6/9 chords, since they are also widely used. In fact, a minor II-V-I can be played entirely using the dominant shapes presented here (e.g. Emi7(b5) = E A Bb D, A7alt = G C Db F, Dmi6/9 = F A B E).
Next up are the lydian and phrygian sounds, which also come in handy, albeit arguably more sporadically than the ones mentioned previously.
Lastly, the mixolydian b13/aeolian sound is probably the least common of all (moreover, it is rather tricky to find an adequate chord symbol for it, so the space has been left blank).
Internalize both shapes by taking them through the cycle of fifths (using different roots in the left hand for example; that way you’ll get the different sounds described above). It’s fine if you have to think about the formulas at first, but try and gradually shift towards using your ears and muscle memory exclusively. It is without question a challenging exercise… But trust yourself in the process: it will be way more fun!
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