Dr. Kit Music

We’ve almost finished covering most of the chords present in diatonic classical music. If you have any previous experience with chord analysis, there are a couple chords you’re probably wondering about. We’ll discuss diminished triads and seventh chords today.

To start, let’s review some intervals. Intervals like seconds, thirds, sixths, and seventh come in the flavors of major and minor. Octaves, fifths, and fourths we general describe as perfect – except for the tritone that we talked about in the dominant seventh chord. A diminished fifth is one half step smaller than the perfect fifth that happens more often. Technically, any perfect interval can be diminished by shrinking it half a step, but the diminished fifth is more common.

Minor intervals can also be shrunk by half a step to create a diminished interval – a minor third of D to B would become a diminished third if it were D♭ to B. The other most common diminished interval (besides the fifth) is the diminished seventh. Most common diminished intervals use the solfège ti as one of the end points: the diminished fifth is ti fa, the diminished third used above is rah ti (a chromatic alteration we’ll get to soon), and the diminished seventh is le ti.

Diminished triads are those that have a diminished fifth on the outside when close packed, instead of a perfect fifth like the major and minor triads we’ve been seeing. Likewise, diminished seventh chords are those that have a diminished seventh on the outside when close packed. In the music we’re looking at, there are only a few of these occurring within the key without chromatic alteration.

In major, a diminished triad occurs if you go up by third from ti – ti re fa, and a seventh chord that we call diminished-minor or half-diminished if you add one more third, ti re fa la. (Because the fifth is diminished, but the seventh is minor.) Because of the strong draw of ti to do, both of these chords typically function as dominant. We’ll describe them as a dominant seventh (or ninth) missing the root so, using a symbol like this:

This specific constructed example in C major shows that the third of the dominant, ti, is in the bass, the slash thru the D shows the root so is missing and the 7 and 9 indicate extensions in the upper voices, fa and la.

My favorite example of this chord arpeggiated in a song is “Rather Be,” here in the Pentatonix version. The accompanying arpeggios (sung by Mitch) alternate between tonic and slash-D before the melody comes in: https://www.youtube.com/watch?v=OPWPa-HMpj8
The alteration of the dominant without the root weakens the function some, so that while we still feel the pull to the tonic, the pull is not so strong that we anticipate a cadence yet.

In minor, there are two places in the scale where diminished chords occur, the altered dominant missing the root: ti re fa le diminished seventh (or triad), similar to major, but also re fa le (do) – both as a triad and a seventh chord. As a triad, re fa le usually appears as a p⁶, with fa in the bass and re replacing do. So to describe this chord that looks like a seventh chord when stacked in thirds, we’ll start with the p⁶ idea.

Here you see the predominant in A minor as we initially expect, with fa in the bass, with an additional sixth (both re and do). The second chord is the same notes in a different spacing. Now the sixth above the root fa is the lowest note, as indicated by the subscript. Since 6 often replaces 5, the 5 is included above for clarity.

Next time we’ll start to talk about chromaticism, which might take more than one post, we’ll see.

Main Ideas

Diminished triad: a triad made up of two minor thirds stacked, diminished fifth on the outside. Most common examples are slash-D₃⁷ (ti re fa) and p⁶ (fa le re)

Diminished seventh chord: chord made up of three minor thirds stacked, diminished seventh on the outside. Usually slash-D₃⁷⁹(ti re fa le). Symmetrical and rotational.

Half-diminished seventh chord: also called diminished-minor seventh. Two minor thirds (diminished triad) plus a major third, minor seventh on the outside. Usually slash-D₃⁷⁹(ti re fa la).