Fretboard

Almost every chord app is a lookup table: a few thousand hand-entered diagrams, keyed by root and quality. It works, it is fast, and it stops dead the moment you drop the low E to D. Alternate tunings are exactly where a player most wants help, and exactly where a table has nothing to say.

Deriving the shapes instead means the tuning is an input rather than an assumption. The same code handles DADGAD, open G, a bass, and a ukulele whose fourth string is tuned above its third — none of which required a single new line.

A fingering is a choice per string: mute it, play it open, or fret it somewhere the hand can reach. Fixing a hand position bounds the fretted options to a span of four frets, which turns the problem into a depth-first walk over the strings with a handful of choices each, repeated for each position on the neck.

Two prunings keep it cheap. Only frets that actually sound a chord tone are ever considered, which removes most of the branching before the search starts. And a branch is abandoned as soon as the strings still to come cannot supply the chord tones still missing. Twelve roots' worth of shapes is comfortably under a frame.

Ranking is where the musical judgement lives. Covering every chord tone dominates; after that the score rewards full voicings, open strings and the root in the bass, and penalises stretches and the number of fretted notes. It is a heuristic, not a theorem — so the test for it is that the shapes guitarists actually play come out on top.

Naming a chord from a set of notes is the harder problem, because the answer is not unique. C-E-G-A is both C6 and Am7, and both are correct; which one you mean depends on the bass and on context.

The recogniser scores every root against every quality: chord tones present earn credit, missing tones and notes the chord cannot explain both cost. That produces a fit score that stays honest — an exact match is always exactly 1 — and leaves preference to the tiebreaks, where the bass note settles it. Under an A it reports Am7; under a C, C6; under an E, a slash chord. The score is unchanged across all three, because the fit genuinely is.