Each step up the cycle of fifths adds one sharp; each step down adds one flat — encoding all 12 major keys

The cycle of fifths arranges all 12 major keys in a circle where each adjacent key is a perfect fifth apart. Moving clockwise (up a fifth): each new key adds one sharp to its key signature (C=0, G=1#, D=2#, A=3#, E=4#, B=5#, F#=6#). Moving counterclockwise (down a fifth): each new key adds one flat (C=0, F=1b, Bb=2b, Eb=3b, Ab=4b, Db=5b, Gb=6b). At the extreme points, F# major (6#) and Gb major (6b) are enharmonically equivalent. Adjacent keys share the most notes and are easiest to modulate between. Sharp keys tend to sound bright; flat keys darker.

Examples

D major has 2 sharps (F# and C#). Bb major has 2 flats (Bb and Eb).

Assessment

Without looking up, state the key signatures of A major, Eb major, and B major. Use the cycle of fifths to explain how to modulate from C major to A major efficiently.