Triads

Just like scales are named sets of notes, so are chords. There are just fewer notes in a ‘chord’-set than there are in a ‘scale’-set. On this page I’ll tell you about triads, which are three-note chords. Here are a few:

On this page, I put the names of the chords above the note clusters, but this is not a requirement for a chord to be a chord 1 – it’s only about the notes themselves. The first of these sets is a \(C\)-major, the second a \(D\)-minor, and the third a \(B\flat\)-major.

The system for naming these chords is similar again to naming scales. The chord names have two components: the root and the character.

\[\underbrace{\quad B\flat \quad}_{\text{root}}\quad \underbrace{\text{ minor}}_{\text{character}}\]

The character tells you which intervals you should add to the root to assemble the full chord. So, seeing the notation ‘\(B\flat \text{minor}\)’, we know the root is a \(b\flat\) and the character is minor. Now we need to know the set of intervals that belong to such a triad. Here they are for minor and major.

Name

Notation

Intervals

Major

None

\(\{P1, M3, P5\}\)

Minor

\(m\)

\(\{P1, m3, P5\}\)

To assemble a \(B\flat \text{ minor}\) chord (\(B\flat_m\), for short), we add all the intervals to the root:

\[\begin{aligned} b\flat &+ P1 = &b\flat\\ b\flat &+ M3 = &d\\ b\flat &+ P5 = &f\\ \end{aligned}\]

That’s already it! It’s pretty much exactly like assembling scales from their names.

You can see in the table that major and minor triads differ by only one interval: the third. It’s a major third for major chords and… You guessed it: a minor third for minor chords. The decision tree for recognizing the triads we know so far in the wild looks like this:

digraph G {
    s [label="Start"]
    M [label="Major"]
    m [label="Minor"]
    s -> M [label="M3"]
    s -> m [label="m3"]
}

There are more different triads. Here they are in a table with their names and intervals:

Name

Notation

Notation example

Intervals

Major

None

\(C\)

\(\{P1, M3, P5\}\)

Minor

\(m\)

\(C_m\)

\(\{P1, m3, P5\}\)

Diminished

\(\circ\)

\(C^{\circ}\)

\(\{P1, m3, d5\}\)

Augmented

\(+\)

\(C^+\)

\(\{P1, M3, A5\}\)

If you know about intervals from you may have noticed that I sneaked in two intervals that I did not mention previously! The diminished fifth (\(d5\)) and the augmented fifth (\(A5\)). Fortunately these are not so new after all – the \(d5\) is enharmonically the same as the tritone (\(TT\)) I did tell you about, and the \(A5\) is enharmonically the same interval as a minor sixth (\(m6\)). 2

Why do we write them this way then? Well, triads are _actually_ defined _not_ just as chords with three notes, but specifically as chords with exactly one root, one third and one fifth. So, in order to stick with this scheme, we shrink down a perfect fifth by one semitone into a diminished fifth (\(d5\)) for a diminished chord. Or we stretch the \(P5\) out to an augmented fifth (\(A5\)).

For example: a set of notes like \(\{b\flat, c, a\}\) with root \(b\flat\) is not technically a triad, because it’s built from the intervals \(\{P1, M2, M7\}\). But \(\{b\flat, d, f\sharp\}\) is a triad. Can you name the intervals that it consists of?

To wrap up this post, let’s add the augmented and diminished triads to the decision tree of how triads can be identified.

digraph G {
    s [label="Start"]
    MA [label="Major or augmented"]
    md [label="Minor or diminished"]
    M [label="Major"]
    m [label="Minor"]
    A [label="Augmented"]
    d [label="diminished"]
    s -> MA [label="M3"]
    s -> md [label="m3"]
    MA -> A [label="A5"]
    MA -> M [label="P5"]
    md -> d [label="d5"]
    md -> m [label="P5"]
}

I’ll also add some extra examples of different triads. They are unordered by design. Play around with them. Maybe you can even identify some enharmonic anomalies here and there, like an \(e\sharp\) that would otherwise be written as an \(f\).

Footnotes

1

In styles of music that lean to the classical side you won’t see chord names above the staff, whereas in jazz you’ll only see chord names and the notes that make up those chords won’t be on the staff. It’s a good idea to become comfortable with the mapping both ways.

2

Two notes, intervals, scales or chords are enharmonic equivalents if they have different names but have the exact same notes. Imagine a building. The ceiling of the first floor and the floor of the second floor are the same thing, but the naming is different depending on your point of view.