Musical Time

The arithmetic that turns a tempo into seconds and seconds back into a position you can say out loud: a typed table of note divisions from a whole note to a 1/32 in plain, dotted and triplet flavours, each carrying its length in beats, its seconds and its rate in Hz; MPC-convention swing offsets; a pure tap-tempo reducer with median averaging and a phrase-ending gap rule; grid quantising; and 1-based bar.beat.sixteenth formatting. Beat conversion is echo-train's, imported rather than restated, and the shipped conversions it unifies are pinned bit-identical against verbatim copies. No React, no DOM — testable in Node and safe to format with on the server; and formatDuration, seconds as m:ss.