Intervals: the distance between two notes

What an interval is

An interval is the distance between two notes. A melody is a chain of intervals and a chord is a stack of them, so once you can measure them you start reading music in shapes rather than one note at a time.

An interval’s name has two parts. The number comes from counting letter names, both ends included: C to E is a third, because you count C, D, E. F to C is a fifth (F, G, A, B, C), and C to the next C is an octave, eight letters up. The quality, the word in front of the number, comes from counting half steps, because intervals with the same number can differ in size.

Counting half steps

To count half steps, start on the lower note and count every key you move up, black or white, but not the key you start on. From C, C♯ is 1, D is 2, D♯ is 3 and E is 4: C to E is four half steps, a major third. D to F is a third too, but only three half steps, so it is a minor third. If half steps are new to you, the lesson on sharps and flats explains them.

Here are the intervals within an octave, counted upwards, with their size and an example on the white keys:

• Minor second: 1 half step, E to F or B to C
• Major second: 2 half steps, C to D
• Minor third: 3 half steps, D to F or A to C
• Major third: 4 half steps, C to E
• Perfect fourth: 5 half steps, C to F
• Tritone: 6 half steps, F to B
• Perfect fifth: 7 half steps, C to G
• Minor sixth: 8 half steps, E up to C
• Major sixth: 9 half steps, C to A
• Minor seventh: 10 half steps, G up to F
• Major seventh: 11 half steps, C to B
• Octave: 12 half steps, C to the next C

Seconds, thirds, sixths and sevenths come in two sizes, major and minor, the minor one a half step smaller. Fourths, fifths and octaves are called perfect. The tritone, six half steps, splits the octave exactly in half and sounds tense, as if it wants to move on.

Melodic and harmonic intervals

Two notes played one after the other make a melodic interval, the material of tunes. Played together, they make a harmonic interval, the beginning of a chord. The distance is the same either way, only the effect changes: thirds and sixths sound sweet together, fifths and octaves open and hollow, seconds and sevenths crowded and tense.

Intervals on the staff

On the staff you can read the number of an interval at a glance. A second goes from a line to the next space, or from a space to the next line. A third goes from a line to the next line, or a space to the next space. The pattern then alternates: thirds, fifths and sevenths go line to line or space to space, while seconds, fourths, sixths and octaves go from a line to a space or the reverse.

The staff gives you the number; the quality still depends on the half steps between the letters and on any sharps or flats. Above C, every interval in the figure is major or perfect.

Hearing intervals

To recognise intervals by ear, tie each one to a tune you already know:

• Minor second: the first two notes of Für Elise, going down.
• Major second: Ode to Joy, from its third note to its fourth.
• Minor third: the first two notes of Greensleeves.
• Major third: the first two notes of When the Saints Go Marching In.
• Perfect fourth: the first two notes of Here Comes the Bride.
• Perfect fifth: Twinkle Twinkle Little Star, from its second note to its third.
• Major sixth: the first two notes of My Bonnie Lies Over the Ocean.
• Octave: the first two notes of Somewhere Over the Rainbow.

Play each pair on the piano below and hum the tune over it. After a few days the tune comes to mind before you have counted a single half step.

Practise: play the interval

In the exercise, a key lights up: it is the lower note, and the page names an interval. Count the half steps up from the lit key, without counting the key itself, and play the note you land on. A major third above C4 is E4, four half steps up. Only that key counts, not the same note in another octave and not the interval below.

The names are on the keys so you can check yourself, and each note you play appears on the staff. Once counting feels easy, start to see the shapes: on the white keys a third always skips one key, and a fifth spans five. Move on when you can play all eight intervals without a miss and without Show me.