🔍📖 Reference
20 lessons

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.

lesson 2 of 2 in this unit

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.

f = 440 Hz × 2n / 12n = semitones above A4 (negative below); n = 12 gives 880 Hz, n = −9 gives middle C ≈ 261.6 Hz

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.
The German B

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.

🎼 LabThe 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.
C3D3E3F3G3A3B3C4AD4SE4DF4FG4GA4HB4JC5KC♯D♯F♯G♯A♯C♯WD♯EF♯TG♯YA♯U

A' and WP play the keyboard · Z/X shift the octave

Note
C4
Other name
MIDI number
60
Frequency
261.6 Hz
Semitones from C4
0
Key colour
white keys

one name, no accidental

🎼 LabThe 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.

1. Using f = 440 × 2^(n/12): what is the frequency of C5, 3 semitones above A4?
2. How many semitones from C4 (MIDI 60) up to G4 (MIDI 67)?

Check your understanding

1. How many semitones are there in one octave?

2. C♯ and D♭ are…

3. Which pair of white keys has NO black key between them?

4. In equal temperament, each semitone multiplies the frequency by…