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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:
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.
In the Roman numeral system, diminished triads are written (like minor triads) in lower case, together with a small ° symbol, for example:
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:
Notice that we have also introduced the triads
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:
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:
As we have said above, look at the triad
vii° in both C major and C minor: it is exactly the same.
A word of warning!
Just as with the triad
V in a minor key,
vii° contains the raised 7th.
This is what makes the triad a diminished triad; if it simply obeyed the key signature it would be a major triad and we would write
The 6th degree
Think for a moment about the triad on the 6th degree. In C major, this triad
vi is A, C, E and is a minor triad.
This particular triad is identical to the triad
I in A minor, which is the relative minor of C major.
Likewise, the triad
III in A minor is C, E, G: that's the same as triad
I in C major, the relative major of A minor.
These relationships between keys are central to our musical system, and are of particular importance in the topic of Modulation.
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
ii (in a major key) frequently precedes chord
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
V, as it shares two notes with both of those triads.
Here are both
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.
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
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!):
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!