Intervals are the distances between any two tones. They form one of the foundations of musical theory and are therefore essential for many other areas of music, such as the theory of triads, tetrachords, chromatic steps, and improvisation.

Every interval has its own tonal character. Sooner or later, you will have to start learning how to identify each interval just by ear.

The theoretical principles are described in the following, to help you identify different intervals on paper.

Chromatic scale with semitones

In order to identify intervals, it’s helpful to know the chromatic scale.

Quarter tones and eighth-tones are often used in other cultures, but semitones are the smallest units in our Western music. On the piano, a semitone is the distance between two directly adjacent keys (e.g. C to C sharp, F to E).

The chromatic scale differs from the major scale in that it only exists of semitones. In other words, the scale contains all notes on the keyboard. The scale always moves to the next adjacent key.

The chromatic scale from Ab’ to Ab’’ is shown in the following illustration:

Octave interval

Let’s start with a large interval: the octave.

An octave is an interval in which the second note is the same note as the first one, but it’s the next lower or higher one.

The octave is made up of 12 semitones.

The illustration shows one octave step upwards, from F’ to F’’, and then again one octave down back to F’.

Diatonic intervals

The illustration shows a major scale from F’ to B’’.

A major scale contains all diatonic intervals from the root (in this case, this is the F note, which is why this is called the F-major scale).

From the root (F’) to

• F’, the interval is called the (perfect) prime (the interval between two equal notes)

• G’, the interval is called the (major) second

• A’, the interval is called the (major) third

• B’, the interval is called the (perfect) fourth

• C’’, the interval is called the (perfect) fifth

• D’’, the interval is called the (major) sixth

• E’’, the interval is called the (major) seventh

• F’’, the interval is called the (perfect) octave

• G’’, the interval is called the (major) ninth

• A’’, the interval is called the (major) tenth (equal to a major third plus an octave)

• B’’, the interval is called the (perfect) eleventh (equal to a perfect fourth plus an octave)

Altered intervals

An altered interval is given by changing a diatonic interval by a semitone. In principle, there are five attributes given to interval names: diminished, minor, major, perfect, augmented.

Moving a major second/third/sixth/seventh down one semitone results in a minor second/third/sixth/seventh.

Moving a major second/third/sixth/seventh up one semitone results in an augmented second/third/sixth/seventh.

Moving a minor second/third/sixth/seventh down one semitone results in a diminished second/third/sixth/seventh.

There is no such thing as a perfect second/third/sixth/seventh. There are only perfect primes/fourths/fifths/octaves.

Moving a perfect prime/fourth/fifth/octave down one semitone results in a diminished prime/fourth/fifth/octave.

Moving a perfect prime/fourth/fifth/octave up one semitone results in an augmented prime/fourth/fifth/octave.

There is no such thing as a perfect prime/fourth/fifth/octave.

Determining intervals using semitone steps

Of course, this all looks very complicated at first sight. There is, however, another way to determine intervals: using semitone steps.

The distance between C’ and C sharp is a semitone step. You start at C and “wander” across the board one key (or one step). This makes C’ and D’ two semitones apart. This way, a certain number of semitone steps can be assigned to each interval:

0 Semitone steps (STS)	Prime
1 STS	Minor second/augmented prime
2 STS	Major second/diminished third
3 STS	Minor third/augmented
4 STS	Major third/diminished fourth
5 STS	Perfect fourth/augmented third
6 STS	Augmented fourth/diminished fifth
7 STS	Perfect fifth/diminished sixth
8 STS	Minor sixth/augmented fifth
9 STS	Major sixth/diminished seventh
10 STS	Minor seventh/augmented sixth
11 STS	Major seventh/diminished octave
12 STS	Perfect octave/augmented seventh
13 STS	Minor ninth/augmented octave (equals minor second plus an octave)
14 STS	Major ninth/diminished tenth (major second plus an octave)
15 STS	Minor tenth/augmented ninth (minor third plus an octave)
16 STS	Major tenth/diminished eleventh (major third plus an octave)
17 STS	Perfect eleventh/augmented tenth (perfect fourth plus an octave)
18 STS	Augmented eleventh/diminished twelfth (augmented fourth plus an octave)

You can use this table to work out how many semitone steps are in an interval.

Enharmonic change

Now, you might be wondering why there is more than one description in the right column of the table? Which description is the right one?

We’ll now discuss these enharmonic changes. An enharmonic change takes place whenever two notes with different names fall on the same key of the keyboard, and sound the same as well.

The reason why there are several descriptions for the same number of semitone steps is because of the altered intervals.

Example enharmonic change

The major second (D) and major third (E) are two semitone steps apart. On the piano keyboard, you can see that there is another key between the two notes. Nevertheless, the major second can be altered one semitone upward (to get an augmented second) and the major third can be altered one semitone down (for a minor third). As a result, both descriptions apply to the key between them.

The notation indicates which description applies here:

On the left side of the illustration, there is an augmented second; on the right side is a minor third.

To the left, the diatonic interval “major second” (C to D) is altered one semitone up by the # sign. This results in an augmented second (C to D sharp).

To the right, the diatonic interval “major third” (C to E) is altered one semitone down by the b sign. This results in a minor third (C to E flat).

This principle, of both tones looking the same but appearing differently on the notation, is called an enharmonic change.

Exercise to determine intervals

Try to recognise the intervals in the bars of the following illustration.

The solutions (intervals) of the 12 bars (from left to right) are given beneath the illustration.

(Don’t cheat!)

Solutions:

1. Perfect fifth

2. Major second

3. Minor sixth

4. Major third

5. Minor second

6. Diminished fifth

7. Minor seventh

8. Perfect fifth

9. Major ninth

10. Minor tenth (equals minor third plus an octave)

11. Augmented eleventh (equals augmented fourth plus an octave)

12. Perfect prime