Hearing intervals

Twinkle, Twinkle, Little Star opens with a jump from C to G, seven keys up. Musicians call that distance a perfect fifth.

Counting the distance between notes

An interval is the distance between two notes. The smallest step on the piano is from one key to the very next key, black or white. That step is called a semitone (or half step). Counting semitones gives every interval a precise size. From C to E is 4 semitones: C to C sharp, D, D sharp, E. From C to G is 7. From one C to the next C is 12, the octave you met in the first unit.

Two semitones make a whole tone, also called a whole step. Most neighbouring white keys are a whole tone apart, because a black key sits between them. Two pairs have no black key in between, E and F, and B and C, so each of those pairs is only a semitone apart. That is why the black keys come in groups of two and three.

The names count letter names, not semitones. C to E is a third because it covers three letters, C, D and E. Major and minor tell you which of two sizes it is: a major third has 4 semitones, a minor third only 3. Fourths, fifths and octaves are called perfect, because there is one standard size of each that sounds especially stable.

Intervals also have a sound you can learn to recognise. An octave sounds like the same note, higher. A perfect fifth sounds open and hollow, like the start of Twinkle, Twinkle. A major third sounds bright. One way to practise is to tie each interval to a tune you already know and sing its first two notes in your head when you hear a new pair.

There is a reason these intervals sound smooth. An octave doubles the frequency, a ratio of 2 to 1. A perfect fifth is very close to 3 to 2: on a piano, G4 at about 392 Hz is 1.498 times C4 at 261.63 Hz. Simple ratios like these make the vibrations of the two notes line up often, which our ears hear as calm.

Play the intervals

Play C, then E, then G, then the C above, and listen to each pair. Then try C with F and C with A.

Ear training

Press Play again. Two notes play one after the other; choose the interval you heard. Start with three intervals that sound very different, the major third, the perfect fifth and the octave. When you get most of them right, move on to the second set, which adds closer pairs.

Sing a broken chord

Singing intervals trains the ear from the inside. Sing C, E, G and the C above, one at a time. Each step is a different interval: a major third, then a minor third, then a perfect fourth.