Keyboard Geometry

Where the keys of a piano are and which one you hit, as pure maths: a key rectangle per MIDI note over any range in a unit coordinate box, black keys placed by the equal-white-tops derivation rather than the lumpy uniform approximation, hit-testing back from a point with black-over-white priority, white-key indexing both ways, and the press-height velocity a touch surface needs because a screen has no key bed. No React, no DOM — testable in Node and safe to draw with on the server.