# The circle of fifths

**Scales & modes:** [Scales](theory.md) · [Modes](modes.md) · [Beyond scales](beyond-scales.md) · Circle of fifths

The circle of fifths is a map of all twelve keys arranged so that each step **clockwise** jumps up a
**perfect fifth** and adds exactly one sharp to the key signature. Go **counter-clockwise** and you add
one flat. It shows how keys relate, where sharps and flats come from, which minor key shares each major
key's notes, and why chords move the way they do.

> Start at **C** (no sharps or flats) at the top. One step clockwise to **G** gains one sharp (F♯);
> another step to **D** adds C♯. Neighbours on the circle share **six of their seven notes**, which is
> why they sound closely related.

The interactive [circle-of-fifths.html](circle-of-fifths.html) shows a clickable wheel: pick any major
key (outer ring) or its relative minor (inner ring) to hear the scale and light up its two neighbours
(its IV and V) plus its relative minor. Playback follows the metronome tempo.

## Why each step adds a sharp (or flat)

A perfect fifth is seven half-steps (C up to G). Build the major scale on the new root and every note
matches the old key except one, which must be raised to keep the W-W-H-W-W-W-H pattern — that's the new
sharp.

- **C major** = C D E F G A B — no sharps or flats.
- Up a fifth to **G major** = G A B C D E **F♯**. Only F changed.
- Up again to **D major** = D E **F♯** G A B **C♯**.

Going the other way flattens one note per step (C → F adds B♭, F → B♭ adds E♭). Sharps accumulate in the
order **F C G D A E B**; flats in the reverse **B E A D G C F**. The two sides meet at the bottom:
**F♯ major** (6 sharps) and **G♭ major** (6 flats) are the same keys spelled differently (enharmonic).

## Relative minors — the inner ring

Every major key shares its seven notes with the minor key built on its **6th degree** (its relative
minor). C major and **A minor** use the same notes, key signature, and diatonic chords — only home
differs. Quick trick: count **down three half-steps** from the major tonic to find its relative minor
(C → A, G → E, F → D).

## Neighbouring keys & chord motion

A key's closest relatives are its two neighbours: its **IV** (one step counter-clockwise) and **V** (one
step clockwise). With the relative minors these give the six chords behind most songs — **I, IV, V** and
**vi, ii, iii**. Chords love to move counter-clockwise (falling fifths): the jazz cadence **ii → V → I**
and the classic **V → I** resolution are motion toward home along the circle. See it on the
[chord cheat-sheet](chord-cheatsheet.md) and [play-along songs](songs.md).

## How to use it

- **Read key signatures instantly** — 2 sharps = D major (or B minor).
- **Transpose** by rotating every chord the same number of positions around the wheel.
- **Practise in all keys** clockwise — the [Circle of Fifths Grind](routines.md) routine.
- **Build progressions** by borrowing a key's neighbours and relative minors.

## All twelve at a glance

| Major | Signature | Relative minor | Notes |
|-------|-----------|----------------|-------|
| C  | no sharps or flats | Am  | C · D · E · F · G · A · B |
| G  | 1 sharp (F♯) | Em  | G · A · B · C · D · E · F♯ |
| D  | 2 sharps (F♯ C♯) | Bm  | D · E · F♯ · G · A · B · C♯ |
| A  | 3 sharps (F♯ C♯ G♯) | F♯m | A · B · C♯ · D · E · F♯ · G♯ |
| E  | 4 sharps (F♯ C♯ G♯ D♯) | C♯m | E · F♯ · G♯ · A · B · C♯ · D♯ |
| B  | 5 sharps (F♯ C♯ G♯ D♯ A♯) | G♯m | B · C♯ · D♯ · E · F♯ · G♯ · A♯ |
| G♭ | 6 flats (B♭ E♭ A♭ D♭ G♭ C♭) · = F♯ | E♭m | G♭ · A♭ · B♭ · C♭ · D♭ · E♭ · F |
| D♭ | 5 flats (B♭ E♭ A♭ D♭ G♭) | B♭m | D♭ · E♭ · F · G♭ · A♭ · B♭ · C |
| A♭ | 4 flats (B♭ E♭ A♭ D♭) | Fm  | A♭ · B♭ · C · D♭ · E♭ · F · G |
| E♭ | 3 flats (B♭ E♭ A♭) | Cm  | E♭ · F · G · A♭ · B♭ · C · D |
| B♭ | 2 flats (B♭ E♭) | Gm  | B♭ · C · D · E♭ · F · G · A |
| F  | 1 flat (B♭) | Dm  | F · G · A · B♭ · C · D · E |