Music 009: Music Theory Fundamentals

Intervals: thirds

A third is a pitch interval that spans three letter-names in the musical alphabet.

Thus a third is always notated on two adjacent lines or two adjacent spaces.

Like all interval designations, “third” describes a relationship between two pitches. This could be:

The following are all thirds:

[ascending] C – E    D – F       B – D   
[descending] E – C    F – D    D – B
[ascending] C – E-flat    C-sharp – E    C-sharp – E-flat
...and so on.

Quality of thirds: major and minor

The third C–E spans two whole steps (C-D and D-E), or 4 semitones.
It is called a major third (abbr. M3).

The third D–F spans a whole step and a half step (for example, D-E and E-F), or 3 semitones.
It is called a minor third (abbr. m3).

The term for the precise size of a given interval in this sense (major vs. minor) is “quality”.

NOTE: The number of semitones is a simple way to define major and minor thirds, but counting semitones should not be your go-to method for determining third quality. See below for better techniques.

We say “C-E is a major third” and “The quality of the third C-E is major.”
We say “D-F is a minor third” and “The quality of the third D-F is minor.”

The two most common qualities of third are major (M3) and minor (m3). There are others, but we will not concern ourselves with them just yet.

Interval math

Note that in interval math, a second + a second = a third. This is because early (ancient Greek) music theory was concerned with melody only, not harmony, and the original meaning of “third” was in reference to scales. “Second” meant the second note of a given scale, “third” meant the third note, etc. When you reckon intervals this way, you end up including both “endpoints” (the top and bottom notes of an interval) in your “count”, which is why the numbers work out wonky.

Identifying/constructing third quality

There are several ways to go about distinguishing or constructing third quality.

I recommend you use one of the first two methods below.
Methods 3 & 4, though popular in textbooks and online primers, are problematic.

1. Think of a third as comprising two steps

M3 = two whole steps; m3 = one whole and one half step.

If you are constructing a major third above (or below) a given note, you simply go up (or down) a whole step and then another whole step.

If you are constructing a minor third above (or below) a given note, you simply go up (or down) a whole step and then a half step. (The order doesn’t matter, so if it’s easier you can reckon half-step/whole-step instead of whole-step/half-step.)

2. Compare all thirds to white-note thirds

This method takes a little longer to internalize, but clicks for some people and is better for developing fluency than methods 3 & 4 below.

Consider the white notes only. Notice that the thirds built above C, F, and G are major, while the others are minor.

Memory aid: the three natural-note major thirds are built on degrees 1, 4, and 5 of the C-major scale, which are the tonic, dominant, and subdominant. I, IV, and V are also the three chords of the basic 12-bar blues progression.

Once you know the qualities of all white-note thirds, it is simple to reckon the quality of any third, as in the examples below.

B-D is a m3. Lowering the bottom note (only) to Bb widens the interval one half-step, making a M3.
G-B is a M3. Sharping both notes does not change their relationship, so G#-B# is a M3.
F-A is a M3. Either lowering the top note (only) or raising the bottom note (only) would narrow the interval one half step, yielding a m3.

3. (Think of a major scale)...

I discourage this method!
Click to reveal if you want to see it anyway

Think of a major scale built on the lower note of a third.
If the top note of the third matches the third degree of the major scale (mi), the third is major;
if it is a chromatic half-step below mi, the third is a minor.

So what's wrong with this method? A few things, I think.

For one, it asks you to imagine a major scale that may have nothing to do with the actual musical context, which is potentially confusing. For example, if you are looking at a piece in the key of E major and are trying to determine tha quality of the third C#–E, you need to think about the scale of C-sharp major&nmdash; which has nothing to do with the situation at hand, and may confuse you about the actual key signature in effect.

And what if you were looking instead (still in the key of E) at the third G#–B: you would have to start thinking about the key of G-sharp major, which does not really exist.

Finally, if you are trying to determine a third below a given note (such as "what is the note a major third below C", this method does not work, or requires some further elaboration, or requires a corollary rule for finding descending intervals, further complicating the situation.

By contrast, if you use method 1, you can always choose your steps to fit the scale you are actually in. For example, again considering the interval C#-E in the key of E major, you can reckon thus: "C#-D# is a whole step; D#-E is a half step: so C#-E is a minor third". Whereas if you were reckoning G#-B, you would go up G#-A, then A-B (also a minor third). And if you need to reckon an abstract descending interval (as in "what is the note a major third below C") you can choose whatever steps/spellings are most convenient: a whole step below C is Bb; another whole step below Bb is Ab; so Ab is a major third below C.

4. (Count half steps)...

I discourage this method!
Click to reveal if you want to see it anyway

This method is popular because it is easy to remember: a m3 has three semitones, a M3 has four semitones, and we're done.

So what's wrong with it? A couple of things. First of all, counting semitones is the long way around: you have to count off 3 or 4 different pitches to determine the quality of just one interval; the more steps there are in your reckoning method, the more chances there are to get off track. This may not feel like a big problem for thirds, but it sets up a bad habit for reckoning quality as we progress to larger intervals (4ths, 5ths, 6ths), which span 5-9 semitones.

Trust me, you do not want this to be your go-to method for reckoning interval quality! It may seem easy at first but will come back to bite you.

Also, counting semitones is not a particularly musical way of thinking. Most music is diatonic, which means that it is made up of mostly whole steps or larger skips. When you think about all the "in-between" half steps, you are taking yourself out of the musical context.

Recognizing third quality by ear

One way to learn to recognize major and minor thirds is to associate them with familiar tunes.

Here is a very cool customizable tune-list tool for learning to hear intervals.

Here is another good list.

Spelling counts!

A third is always spelled with two non-adjacent letter names.

Equivalently, it is always notated on two adjacent staff lines or two adjacent staff spaces.

The interval A-flat—B is not a third, even though it spans 3 semitones. A-flat to B is an augmented second. It is enharmonically equivalent to a m3, but it is not “the same”.

Likewise, the interval C-sharp—E-flat is not a major second, but a diminished third. It is enharmonically equivalent to a M2, but it is not “the same”.