The Twelve Notes
Between one A and the next there are twelve equal steps. Seven of them got letter names, five got sharps and flats — and the piano's black-and-white pattern shows exactly why.
Builds on: 0.1 Pitch: What a Note Is
Slicing the octave
An octave is a doubling, but music needs smaller steps than that. Western music divides every octave into twelve equal steps, and each step is a semitone (or half step). “Equal” means equal in ratio, not in hertz: every semitone multiplies the frequency by the same number, the twelfth root of two, about 1.0595. Twelve of those multiplications make exactly ×2 — one octave. This system is called equal temperament, and it is what pianos, guitars and every digital instrument use.
Seven letters, five black keys
Only seven of the twelve notes have plain letter names: C D E F G A B, the white keys of the piano. The other five sit between them as the black keys. Look at any piano and you see the pattern: black keys in groups of two and three. The white key just left of a group of two is always C. Once you can find C, you can find everything.
Between most neighbouring white keys there is a black key, so the step from C to D is two semitones — a whole step. But look closely: there is no black key between E and F, nor between B and C. Those two pairs are only a semitone apart. That unevenness is not a flaw; it is the fingerprint of the major scale, and Unit 2 will explain it.
Sharps and flats: naming the black keys
A black key has no letter of its own, so it borrows one from a neighbour. The key just above C is C♯ (“C sharp”: C raised a semitone); the very same key is also D♭ (“D flat”: D lowered a semitone). Two names, one pitch — these are enharmonic spellings. Which name you use depends on the key you are in, like choosing between “half past” and “thirty”: same time, different context. Sharps climb, flats descend, and a natural sign (♮) cancels either.
- Sharp keys spell the black notes as sharps: F♯, C♯, G♯…
- Flat keys spell them as flats: B♭, E♭, A♭…
- E♯ and F are the same key, and so are B♯ and C — rare, but you will meet them.
In German-speaking countries the note English speakers call B is written H, and B means B♭. That is why Bach could sign his name in notes: B♭–A–C–B♮ spells B-A-C-H. Switch the interface to DE and the labs spell it the German way.
Two labs: name every key on two octaves of piano (with both spellings), then walk the twelve notes around a circle and count the semitones between any two of them.
🎼 Lab — The Note Namer
Press any key — on screen, on your computer keyboard or on a MIDI keyboard — and read its names, its MIDI number and its frequency.
- Find C4 (middle C): the white key left of the two black keys, MIDI number 60, about 261.6 Hz.
- Press a black key and switch the spelling: C♯ becomes D♭ but nothing else changes.
- Step from E to F and from B to C. No black key in between — one semitone each.
A–' and W–P play the keyboard · Z/X shift the octave
one name, no accidental
🎼 Lab — The Chromatic Circle
The twelve pitch classes arranged in a ring, so that going up an octave brings you back where you started. Click two notes to hear and count the step between them.
- Click C then D: two semitones, a whole step. C then C♯: one semitone, a half step.
- Click E then F: only one semitone, though both are white keys.
- Go all the way round: twelve semitones and you are back at the same letter.
Work it by hand — 0 / 2
No multiple choice here: compute the value and type it. Suffixes like 2.5k or 20m are understood; answers within ±1% count.