Chromesthesia is the form of synesthesia most tied to music. Pitch, timbre, key, or loudness triggers color: a saxophone is amber, E minor is deep green, a cymbal is a white flash. The visual events themselves are called photisms.
What maps to what differs per person, but within one person the pairings hold for decades. Loudness commonly maps to brightness, attack to sharpness of shape, and timbre to color family.
We wrote a full explainer at What is chromesthesia?, covering how researchers verify it and which musicians have described it. Photism, our visualizer for Ableton Live, borrows its logic: color and structure driven by the sound itself.