The Chromatic Circle

A keyboard or a staff lays the twelve notes out in a line. The chromatic circle bends that same line into a loop:

Intervals as distance

On a linear keyboard, where an interval sits changes how it looks - e.g. it can depend on whether we start on a black or a white key. On the circle, an interval is just an angular distance between two points, and that distance is the same wherever the two points happen to sit. A major 3rd starting on C and a major 3rd starting on C♯ are the same arc, just rotated to a different starting point:

Nothing about the shape changes depending on which key you're in, the way the same interval can look visually different in different positions on a keyboard or a staff. The same holds for a chord: a C major triad and a D♭ major triad are the same three-note shape, just rotated to a different starting point.

Inversions become intuitive

The same circle makes both kinds of inversion visible instead of abstract. An interval's inversion is just the same two points read around the circle the other way; a chord's inversion is the same wedges lit up with a different bass note marked.

What about the Circle of Fifths?

This is a question I get a lot. Indeed the Circle of Fifths is a related, well-covered idea - which helps us explore key signatures, which keys share the most notes. It's a useful concept, and plenty of good material already explains it well; it's just not what we're here to explore. The chromatic circle in this app answers a different question: what an interval or a chord actually sounds like, by ear.