Introduction

We have so far met major and minor triads as well as dominant seventh chords. In this section, we learn about another type of triad: the diminished triad.

The diminished triad

The diminished triad is made up of two minor thirds stacked on top of each other. It is named after the interval between the root and the fifth of this chord: a diminished fifth. Check that you understand this, by working out the intervals in the diminished triad below:

The construction of the diminished triad

Note that this triad is different from the major triad and the minor triad, in that it is built from two minor thirds; the major triad is built from a major third with a minor third on top, and the minor triad is built from a minor third with a major third on top.

Labelling

In the Roman numeral system, diminished triads are written (like minor triads) in lower case, together with a small ° symbol, for example: vii°

In the alternative system, in which C refers to a chord of C major, and Cm refers to C minor, we simply add the word dim for diminished chords or triads. A diminished chord or triad on B would therefore be Bdim.

In major keys

You may remember that there were some blanks when we first looked at the triads on different scale degrees. We can now fill in these blanks!

The chord degree built on the 7th degree of both the major and (harmonic) minor scale is a diminished triad. Here is the complete list of triads by degree in C major:

The complete set of triads in C major

Notice that we have also introduced the triads ii, iii and vi. These are all straightforward minor triads when in the major key.

In minor keys

The triads are a little more complicated in minor keys. The triad on the 7th degree is, as stated above, a diminished triad identical to vii° in the equivalent major key (for example, vii° is identical in C major and C minor).

The triad on the supertonic is also diminished: ii°, and the triads on the 3rd and 6th degree are, unexpectedly perhaps, major triads: III and VI. This is the opposite to the major key, in which thoe triad on the 6th degree is minor.

Here are all the triads by degree in C minor:

The complete set of triads in C minor

As we have said above, look at the triad vii° in both C major and C minor: it is exactly the same.

Functions and substitutes

The triad on the 2nd degree has many functions in harmony.

For instance, we saw in Cadences that an imperfect cadence consists of any chord followed by V, and ii (in a major key) frequently precedes chord V.

It is often also used as a substitute in any situation where we might otherwise use IV, as it shares two out of three notes with IV, and can therefore form a cadence reminiscent of the plagal cadence when followed by I. The triad ii in a major key is therefore very useful.

Similarly, we can use iii as a useful substitute for I or V, as it shares two notes with both of those triads.

Here are both ii and iii in use as substitutes in the hymn tune harmonisation we have used a few times in our study of harmony. Notice how we could easily have used IV instead, but introducing ii moves beyond the primary triads and adds more harmonically interest to the music.

A harmonisation using ii instead of IV and iii instead of I

In addition, look at how the alto part is suddenly more interesting - take a look at what it was like when we used only primary triads!

The diminished triad, by contrast, requires more careful use. It is inherently somewhat unstable, and the 5th usually "resolves" down by a semitone while the root usually resolves up by a semitone, a convention which requires careful thought when used in four-part writing (and is therefore not recommended until you are very confident with four-part harmonisations!)

The diminished triad can, like ii and iii, be used as a substitute, typically for V. The reason becomes clear when you consider that vii° contains the same notes as V7, minus the 5th degree itself.

For instance, in G major (or, indeed, G minor!), vii° consists of F sharp, A, and C; and V7 is the same, plus the note D.

The following example by J.S. Bach shows the use of vii° as a substitute for V, in the unusual time signature of 24/16 (it might help to think of this as similar to 12/8, but with each duration halved!):

Using vii° as a substitute for V in J.S. Bach, Prelude in G major from The Well-Tempered Clavier

The note G in the bass in this example is called a pedal note, which is simply a note that is held over several changes in harmony.

At the moment where our vii° substitute occurs, the pedal note is actually dissonant (non-harmonic), and it "resolves" (becomes harmonic again) when the harmony moves to I. Rather, the rest of the music "resolves" around the pedal tone. This interesting technique is frequently found in the music of J.S. Bach!

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