Notes, intervals and octaves

A system of twelve steps

On a normally tuned piano, an octave is divided into 12 equal semitone steps. A semitone takes you to the very next key, regardless of colour. E–F and B–C are semitones even though both keys are white. C–D is a whole tone: two semitones. Count the gaps, not the keys including your starting note.

The sign ♯ raises a note by a semitone; ♭ lowers it by a semitone. We use international note names.

Distance and spelling tell you different things

C–E is four semitones and a major third. C–E♭ is three semitones and a minor third. C–G is seven semitones and a perfect fifth. The interval number counts letter names including both ends: C, D, E makes a third. This is why the same keyboard distance can have different interval names depending on its spelling.

Why is a higher C still a C?

One octave up means 12 semitones and twice the frequency. The pitches are different, but they belong to the same pitch class. C3, C4 and C5 can therefore serve the same harmonic role. Equal temperament gives the frequency ratio 2^(n/12) for n semitones. It is a useful model for moving music, rather than a recipe for what sounds good.

Move the relationship and keep the structure

C–E–G has distances of 0, 4 and 7 semitones from C. Add two to each: D–F♯–A. You have transposed the chord to D major. The pattern of white and black keys changes, but the interval structure stays the same. This is transposition.

Here a chord means notes sounding together. C–E–G is an example you can move; we will study how to build it after learning about scales.

Try it at the piano

Play C4, E4 and G4 separately, then C5, E5 and G5. Listen for the same chord identity in a brighter register. In the lab, move the entire chord up or down an octave.