circle-of-fifths

name	circle-of-fifths
description	Walks through the circle of fifths — key signatures, perfect-fifth relationships, the order of sharps and flats, and the practical use for navigation between keys. Pure catalog skill. Use when a learner asks 'explain the circle of fifths' / 'how do key signatures work' / 'why are some keys sharps and others flats'.
triggers	["circle of fifths","circle of fourths","key signature","order of sharps","order of flats","why sharps","why flats","how many sharps","how many flats"]
license	internal
compatibility	{"agent-framework":">=1.0.0-preview","microsoft-extensions-ai":">=10.5.1"}
metadata	{"authoring-style":"deterministic-catalog","origin":"drafted in skills-dev/ as Tier 2 catalog skill (skill-stewards 2026-05-05)","evidence-kinds":["catalog_lookup"]}

The Circle of Fifths

Reproduce the catalog below verbatim when a user asks about the circle of fifths. Pure pedagogy — the layout is fixed and doesn't need a tool call.

What it is

Twelve major keys arranged so each step clockwise is a perfect fifth up (and each step counter-clockwise is a perfect fourth up, equivalently a perfect fifth down). Adjacent keys differ by exactly one accidental in their key signature.

Clockwise (sharps): adding sharps

Start at C (no sharps), each clockwise step adds one sharp:

Position	Key	Key Signature
12 (top)	C major	(none)
1	G major	F#
2	D major	F# C#
3	A major	F# C# G#
4	E major	F# C# G# D#
5	B major	F# C# G# D# A#
6	F# major	F# C# G# D# A# E#
7	C# major	F# C# G# D# A# E# B# (all 7 sharps)

Order of added sharps: F – C – G – D – A – E – B (mnemonic: Father Charles Goes Down And Ends Battle).

Counter-clockwise (flats): adding flats

From C counter-clockwise, each step adds one flat:

Position	Key	Key Signature
11	F major	Bb
10	Bb major	Bb Eb
9	Eb major	Bb Eb Ab
8	Ab major	Bb Eb Ab Db
7	Db major	Bb Eb Ab Db Gb
6	Gb major	Bb Eb Ab Db Gb Cb
5 (≡ C# major)	Cb major	Bb Eb Ab Db Gb Cb Fb (all 7 flats)

Order of added flats: B – E – A – D – G – C – F (mnemonic: Battle Ends And Down Goes Charles' Father — reverse of the sharps order).

Each major key's relative minor (inner circle)

Each major key shares its key signature with its relative minor — three semitones down (or a minor third), same notes:

Sharp side:

• C major ↔ A minor
• G major ↔ E minor
• D major ↔ B minor
• A major ↔ F# minor
• E major ↔ C# minor
• B major ↔ G# minor
• F# major ↔ D# minor
• C# major ↔ A# minor

Flat side:

• F major ↔ D minor
• Bb major ↔ G minor
• Eb major ↔ C minor
• Ab major ↔ F minor
• Db major ↔ Bb minor
• Gb major ↔ Eb minor
• Cb major ↔ Ab minor

Enharmonic equivalence at the bottom of the circle

At the 6 o'clock position three keys collide:

• F# major (6 sharps) ≡ Gb major (6 flats) — same pitches, different spelling.
• C# major (7 sharps) ≡ Db major (5 flats) — Db is usually preferred (fewer accidentals, no double-sharps).
• Cb major (7 flats) ≡ B major (5 sharps) — B is usually preferred (no Cb / Fb).

Why one publisher writes a piece in Db and another in C# is convention, genre, and instrument-friendliness. Concert-band orchestrators favour flat keys (better for transposing brass); strings often prefer sharp keys; jazz lead sheets follow the composer's choice. The chatbot doesn't pick one over the other — both spell the same harmony.

Why it's useful

• Modulation by fifth is the smoothest key change: only one note changes (the new key's leading tone). C → G changes only F to F#.
• Cadences are often V–I or ii–V–I, which trace the circle counter-clockwise — every dominant resolution is a step counter-clockwise.
• Chord progressions in pop and folk often cycle through circle-of-fifths motion (vi–ii–V–I).

When to call other skills instead

• "Notes in C major scale?" → scale-info skill (canonical).
• "Identify the key of [progression]" → key-identification skill (canonical).
• "What chords are in C major?" → diatonic-chords once that pending tool ships; today, scale-info returns the seven scale notes which is a partial answer.
• "Relative minor of C major?" → relative-key once that pending tool ships; today, the relative-minor pairings table above answers it directly.

When to refuse

• Microtonal or non-12-tone-equal-temperament systems — out of scope.
• "Modal circle of fifths" — modes don't have key signatures in the same sense; offer the major-key equivalent instead.