CheatSheet:Introduction to Key Signatures & The Circle of Fifths

1. Key Signatures

1.1 Core Concepts

1.2 Order of Sharps and Flats

• Mnemonic for sharps: "Fat Cats Go Down Alleys Eating Birds"
• Mnemonic for flats: "BEAD Greatest Common Factor" or reverse of sharps
• Sharp and flat orders are reverse of each other

1.3 Major Key Signatures

1.4 Minor Key Signatures

• Each major key has a relative minor that shares the same key signature
• Relative minor is built on the 6th scale degree of the major scale
• Relative minor is a minor 3rd (3 half steps) below the major key

1.5 Identifying Key from Key Signature

1.5.1 Major Keys with Sharps

• The last sharp in the key signature is the 7th scale degree (leading tone)
• Go up one half step from the last sharp to find the tonic
• Example: Last sharp is C♯ → Major key is D

1.5.2 Major Keys with Flats

• The second-to-last flat is the tonic (works for 2+ flats)
• For one flat (B♭), the key is F Major
• Example: Last two flats are A♭ and D♭ → Major key is A♭

1.5.3 Minor Keys

• Find the major key first using the methods above
• Go down a minor 3rd (3 half steps) to find the relative minor

2. The Circle of Fifths

2.1 Structure and Organization

2.2 Clockwise Movement (Sharps)

• Starting at C (top), moving clockwise adds one sharp each step
• Sequence: C → G → D → A → E → B → F♯ → C♯
• Each key is a perfect fifth above the previous
• Number of sharps increases by one: 0, 1, 2, 3, 4, 5, 6, 7

2.3 Counter-Clockwise Movement (Flats)

• Starting at C (top), moving counter-clockwise adds one flat each step
• Sequence: C → F → B♭ → E♭ → A♭ → D♭ → G♭ → C♭
• Each key is a perfect fourth above (or perfect fifth below) the previous
• Number of flats increases by one: 0, 1, 2, 3, 4, 5, 6, 7

2.4 Complete Circle Layout

2.5 Relative Minors on the Circle

• Relative minor keys are placed inside or adjacent to their major counterparts
• Each minor key shares identical key signature with its relative major
• Minor keys follow same fifth relationships as major keys
• Clockwise minor sequence: A → E → B → F♯ → C♯ → G♯ → D♯ → A♯
• Counter-clockwise minor sequence: A → D → G → C → F → B♭ → E♭ → A♭

2.6 Enharmonic Equivalents

3. Applications for Composition

3.1 Key Relationships

3.2 Common Modulation Patterns

• To dominant key: Move one position clockwise (adds 1 sharp or removes 1 flat)
• To subdominant key: Move one position counter-clockwise (adds 1 flat or removes 1 sharp)
• To relative minor/major: Same key signature, different tonal center
• To parallel minor/major: Same tonic, different key signature

3.3 Diatonic Chords and the Circle

• Primary chords (I, IV, V) are adjacent on the circle
• In C Major: F (IV) - C (I) - G (V) appear consecutively
• Moving by fifths creates strong harmonic progressions
• Root movement by fifth is strongest harmonic motion

3.4 Practical Uses

• Transposing: Count positions on circle to determine new key signature
• Chord progressions: Use fifth relationships for strong resolutions
• Modulation planning: Visualize distance between keys
• Scale construction: Quickly identify sharps/flats needed
• Song analysis: Identify key centers and key changes

3.5 Modal Considerations

• Modes share same principle of fifth relationships
• Each mode can be mapped to circle using its characteristic notes
• Parallel modes share tonic but have different key signatures
• Relative modes share key signature but have different tonics

4. Quick Reference Tables

4.1 All Major and Minor Keys

4.2 Key Signature Shortcuts

• Sharps: Last sharp + half step up = major key
• Flats: Second-to-last flat = major key (or memorize F for one flat)
• Minor: Major key down minor 3rd (3 half steps) = relative minor
• Fifths up = add sharp; Fifths down = add flat
• Fourths up = add flat; Fourths down = add sharp