Learning 7th chord inversions, part 1

Using inverted chords is a great way to add some variety to your progressions. However, internalising all the shapes (see here for a good reference) and, in each case, where the root is, can take some time. One trick you may find useful when learning the inversions of the dominant 7th chord revolves around the diminished 7th chord, and its relationship to the dominant 7th.

The diminished 7th (°7) chord is constructed by stacking a sequence of three minor 3rd intervals on top of the root note. This gives it an unusual symmetry - you can consider any diminished 7th chord to be an inversion of three other diminished 7th chords. For example, take this common voicing of E°7:

tabstave notation=false notes (3/1.2/2.3/3.2/4)

As well as being E°7 in root position, this chord is also:

  • Bb°7 with the 5th in the bass
  • Db°7 with the 3rd in the bass
  • G°7 with the 7th in the bass

So how does this help? Let's look at how the diminished 7th and dominant 7th chords are constructed:

  • Diminished 7th: 1, b3, b5, bb7
  • Dominant 7th: 1, 3, 5, b7

Notice that to go from a diminished 7th to a dominant 7th we raise each tone, other than the root, by one semitone. Alternatively, lowering the root of a diminished 7th by a semitone will get us the dominant 7th chord with the root one semitone lower:

tabstave notation=false notes (3/1.2/2.3/3.2/4) $E°7$ notes (4/1.3/2.4/3.2/4) $E7$ notes (3/1.2/2.3/3.1/4) $Eb7$

Now here's the trick - since each diminished 7th chord is actually four different diminished 7th chords, we can create four different dominant 7th chords by lowering any one note of the diminished 7th chord. Usefully, the lowered tone is always the root of the chord we've created:

tabstave notation=false notes (2/1.2/2.3/3.2/4) $Gb7$ notes (3/1.1/2.3/3.2/4) $C7$ notes (3/1.2/2.2/3.2/4) $A7$ notes (3/1.2/2.3/3.1/4) $Eb7$

This works for all other voicings of the diminished 7th chord - here are two other common diminished 7th shapes, and the four corresponding dominant 7th shapes which can be created:

tabstave notation=false notes (3/2.1/3.3/4.2/5) $B°7$ notes (2/2.1/3.3/4.2/5) $Db7$ notes (3/2.0/3.3/4.2/5) $G7$ notes (3/2.1/3.2/4.2/5) $E7$ notes (3/2.1/3.3/4.1/5) $Bb7$
tabstave notation=false notes (2/2.3/3.2/4.3/6) $G°7$ notes (1/2.3/3.2/4.3/6) $C7$ notes (2/2.2/3.2/4.3/6) $A7$ notes (2/2.3/3.1/4.3/6) $Eb7$ notes (2/2.3/3.2/4.2/6) $Gb7$

The same transformation works for arpeggio based licks - this F°7 lick:

tabstave notation=false notes 10/3 9/2 7/1 10p7/1 9s12/2 10/1 13p10/1 12/2 13/3 10/3

can be converted to E7:

tabstave notation=false notes 9/3 9/2 7/1 10p7/1 9s12/2 10/1 12p10/1 12/2 13/3 14/4

or to G7:

tabstave notation=false notes 10/3 8/2 7/1 10p7/1 8s12/2 10/1 13p10/1 12/2 12/3 10/3

...and so on.

Although not quite as elegant, it's possible to use similar tricks to help memorise many of the other types of 7th chord. That will have to wait for another post!