Piano Roll Geometry

Where a note sits in a pitch × beat plane, and which note a point lands on, as pure maths: a fixed coordinate box resolved from a pitch range and a bar count, note rectangles forward and hit-testing back, a keyboard gutter, and the 1-based bar.beat.sixteenth a transport prints — from a beat position, because a roll never needs the tempo to know where a bar line is. Plus white/black-key classification, default note naming and grid-snap rounding for edits. No React, no DOM, no canvas — testable in Node and safe to lay out on the server.