Chord Theory
Tertian Harmony
A chord is the simultaneous or near-simultaneous sounding of three or more different notes. As Western music has developed through the last few centuries, we as listeners have come to prefer a certain type of chord, namely tertian chords.
Tertian chords are made up of the successive stacking of thirds on top of a root note. Because if how interval theory works, if you stack one third atop another, the outer two notes will be separated by a fifth. A fifth plus a third equals a seventh chord, another third makes a ninth chord, and so on.
- The root note is the most important note of the chord. It is the harmonic anchor.
- The third is the second most important note. It determines whether the chord is a major or minor chord.
- The fifth completes the most basic chord type.
- Further notes are added as needed in order to add coloration to the chord.
As you can see, the chord members are referred to by their respective interval from the root note.
Triads
The most basic chords are called triads (Gr.: "three notes") and consist of just the aforementioned root, third and fifth.
Basic Triads
The two most important triads are the major and minor triads. The difference between them is the third. If it is major, it is a major triad, if it is a minor third, it is a minor chord:
Altered Triads
There are also four possible altered triads, meaning that the fifth has been lowered or raised. There are two altered minor triads and two altered major triads.
However, only two altered triads are commonly discussed: the diminished triad and the augmented triad:
As you can see, the diminished triad has a minor third and a diminished fifth. The augmented triad has a major third and an augmented fifth.
Triad Interval Structure
- Major and minor triads span a total of seven semitones.
- The major triad is built from 4 + 3 semitones, since it consists of a major third and a minor third.
- The minor triad is built from 3 + 4 semitones; the proportions are reversed.
- The diminished triad is made up of six semitones (3 + 3), or two minor thirds.
- The augmented triad is made up of eight semitones (4 + 4), or two major thirds. The augmented triad is symmetrical, because there are four semitones between the aug5 and the octave. This means that the intervals remain the same upon inversion (more on that later).
Most music theory references seem to forget that there are two more triads: the minor augmented fifth triad, and the major diminished fifth triad.
- The minor augmented fifth chord is built up of eight semitones (3 + 5), or a minor third and an augmented third. Enharmonically, it has the same interval structure as a first-inversion major triad, which makes it inherently unstable.
- The major diminished fifth triad is build up out of six semitones (4 + 2), or a major third and a diminished third. The latter interval is enharmonically equivalent to a major second, making the chord close to secundal (as opposed to tertian) harmony.
- The four "official" triads consist of combinations of consonant intervals: minor and major thirds. These two do not.
Four-note Chords
Chords with four or more notes are referred to simply as four-note chords, five-note chords, etc., unless one wishes to specify the exact type, e.g. seventh chords, sixth chords, and so on.
Seventh Chords
A seventh chord is a triad with the addition of a seventh. The seventh winds up a third above the fifth of the chord, since in interval theory, 3 + 3 = 5 and 5 + 3 = 7.
There are two basic triads and you can add either a minor or a major seventh. This gives us four basic seventh chords:
The most common by far is the dominant seventh chord, which is why the term seventh chord most often tends to mean this type of chord and not all four seventh chords collectively.
The dominant seventh chord is a major triad with a minor seventh on top. The minor seventh is not naturally occurring in the major scale, which might be illogical. But: the name "dominant" derives from functional harmony, where the dominant is the chord on the fifth scale degree. If you build a tertian chord from this scale degree, the fourth note will be a naturally occurring minor seventh from the root:
Diminished Seventh
Diminished seventh chords are very special. They consist of a diminished triad to which you add a diminished seventh.
Dim7 chords have all sorts of interesting properties. First and foremost, they are perfectly symmetrical. There are three semitones between each chord member, and when you stack yet another minor third on top of the diminished seventh, you will find yourself back at the octave! This means that any of the notes in the chord can be regarded as the root.
A careful scrutiny of the above music example will reveal that I have taken the liberty of making some enharmonic substitutions in the interest of clarity. B double-flat sounds just like A on an even-tempered instrument.
Sixth Chords
A sixth chord is a major or minor triad with the addition of a major sixth. Please note that the chord always contains a major sixth even if it is a minor chord:
Extended and Altered Chords
Extended Chords
Chords with five or more notes are spread out over more than an octave and are therefore known as extended chords. All extended chords continue the principle of stacking thirds on top of the root:
- A ninth chord is a seventh chord with an added ninth.
- An eleventh chord is a seventh chord with an added ninth and eleventh.
- A thirteenth chord is a seventh chord with an added ninth, eleventh and 13th. (If you look at the notation above, it also just about looks like it's going to require your entire forearm to play.)
When you get to a 13 chord, all seven scale degrees are present in the chord, so no further stacking of thirds is possible. (Or, to quote Nigel Tufnel from Spinal Tap, "by the time you get to 13 the song's over anyway".) There are no 15th chords, because a 15 is a double octave.
Altered Chords
Altered chords are chords where the fifth or any of the extension notes (9th, 11th or 13th) has been chromatically altered. These chords will be discussed in a bit more detail in the essay on chord symbols.
Chord Inversion
Unless otherwise specified, chords are played in root position, i.e. the root note is the lowest note in the chord. When a note other than the root note of a chord is played in the bass, that chord is considered to be inverted.
Triads have two possible inversions, since there are two notes other than the root:
Four-note chords have three, since there is also a seventh:
Inverted chords are often a result of voice leading and are tendency chords. They are not stable, but indicate some sort of movement. A first-inversion chord has a strong secondary dominant tendency, whereas a second-inversion chord has some interesting harmonic stuff going on, which will be discussed momentarily in the article on chord functions.
Chord Relations
In the article on keys, I mentioned the concept of relative keys, i.e. a minor and a major key a minor third apart, that consist of the same notes. It turns out chords can have a similar relation.
Relative chords are chords that are situated three semitones apart and have two notes in common. This always falls so that the major chord is a minor third above the minor chord:
As you can see, the C major triad is relative with A minor (C and E in common), F with Dm (F and A in common) and G with Em (G and B in common).
In C minor, it looks like this:
The C minor triad is related to Eb major (E flat and G in common), Fm with Ab (A flat and C in common) and Gm with Bb (B flat and D in common).
Thus, the upper two notes of the minor chord are common with the lower two notes of the major chord.
This relationship with two notes in common also exists in the other direction. A major triad also has two notes in common with the minor triad that is situated a major third above it:
The C chord has E and G in common with Em. F has A and C in common with Am. G has B and D in common with Bm. (Even though this chord requires a bit of cheating with a sharp in order to make it an unaltered minor triad.)
In C minor above, the Cm triad has C and E flat in common with the Ab triad. Fm has F and A flat in common with Db (which also requires fudging with a flat accidental). Gm has G and B flat in common with Eb.
This relationship has been identified by some theorists as an "opposite" or "counter-relative" chord. It is also referred to as a leading note exchange chord, since the chords are only separated by a leading note (C = C E G, Em = E G B.)
