Modulation Path Calculator

Shared notes between the two keys' scales are the biggest factor, since the ear has more familiar pitch content to hold onto during the transition — that's why Common Tones carries the most weight in the Smoothness Score. Keys that sit close together on the circle of fifths and share the same mode (both major or both minor) tend to modulate more smoothly than keys that are harmonically distant or cross from major to minor.

Play or write the pivot chord while it still functions within your starting key, then continue the progression as if you'd been in the ending key all along — the pivot chord is the hinge that belongs to both keys' harmony. This is the classic "common chord" modulation technique; it works best when the pivot chord has a clear, singable function in both keys rather than being a rare or unstable chord in either one.

Because they're relative keys with an identical set of notes, but different modes — C major and A minor use the same pitches yet center on different tonics, which changes the harmonic feel even though nothing needs to change on the page. The Smoothness Score reflects that a same-mode modulation (major-to-major or minor-to-minor) still tends to feel more settled to the ear than a mode change, even one with perfect note overlap.

Circle of Fifths Distance is always calculated as the shortest path between the two keys, so it comes out the same regardless of which one you call the starting key. Common Tones and Smoothness Score are symmetric too, but only if you swap the whole key-plus-mode pair together — swap just the key value while leaving Start Mode and End Mode where they were, and a major-to-minor modulation becomes a different, non-symmetric minor-to-major comparison instead.