What does the circle of fifths illustrate in music theory?

The circle of fifths is a fundamental concept in music theory that visually represents the relationships between different keys. It organizes the twelve tones of the chromatic scale into a circle, showing how each key is related to its neighbors by perfect fifths. This layout is particularly useful for identifying key signatures and understanding how to modulate or change from one key to another smoothly.

For instance, moving clockwise around the circle, each key has one additional sharp in its key signature, while moving counterclockwise adds one flat. This structured representation aids musicians in quickly recognizing key signatures and understanding their relative major and minor counterparts, making it an invaluable tool for composers, arrangers, and performers when working with various tonalities and transitions between keys during music creation or performance.