Chords » A Half-Diminished 7th (3rd inversion)

This chord is an inversion of the A Half-Diminished 7th chord, so construction is a little different from standard chords. An inversion is the same as the base version of a chord, though its notes are played in a different order. For this inversion, you'll start with the notes of the base chord (A, C, D#, G), then count 3 to the right to find the lowest note of this chord (G). The rest of the notes to the right of this continue this chord, and then we 'wrap around' to the beginning, until we have reached our new first note. After all of this, we end up with the final notes for this inversion: G, A, C, D#.

You can also use the more traditional methods described below, though you'll need to start from the lowest note as described above to find your starting point. The scale degree and interval stack listed above are from the perspective of this interval, so they'll produce the same notes as the base chord, but in the order required by this inversion.

Using the scale degree formula, we first start with the G major scale, and number each note in the scale starting from 1 - these are the scale degrees. Next, we use the scale degree formula, in this case 1-2-4-#5, to select notes from our enumerated scale. When a chord requires notes that are not in the scale, this is indicated with a flat (♭) or a sharp (#) along with the scale degree; a ♭3, for instance, would be one half-step down from the 3rd scale degree.

Alternatively, we can use the interval stack to construct our chord. With this approach, we first start with the lowest note of the chord (G), then move our first interval (M2), which brings us to our second note in the chord (A). We repeatedly apply each of the remaining intervals in the stack to get the full list of notes for our chord.

The diagram below shows how both the scale degree formula and interval stack methods result in the same selection of notes: