String picked up — and suddenly math hums alongside music. Quiet demonstration, loud curiosity. For a thirteen‑year‑old violin beginner, building a Pythagorean C on a monochord teaches ears to hear ratios, hands to feel octaves, and minds to trust proportion. Calculating frequencies links pitch to measurement; converting repeating decimals to fractions sharpens notation and tuning accuracy. Unit 1 dramatizes discovery: halve, multiply, listen. Unit 2 builds discipline: round carefully, translate decimals back to exact ratios, justify choices. Together they scaffold a practice habit: compare tunings, compute interval sizes, document progress against standards, and reflect on mistakes. Minimal adult support preserves agency; light nudges teach rounding rules and algebraic tricks. Outcomes: stronger aural discrimination, measurable tuning skills, procedural fluency in number work, neat evidence for reporting, and a confident young musician who grins when a ghostly repeating decimal becomes a tidy fraction. Send more strings. Bravo; curtain call imminent and encore requested.