Guitar Theory

A practice site for guitarists: thirteen tools covering scales, triads, chords, intervals, ear training, progression analysis, a tuner and a metronome. It installs to the home screen as a progressive web app and keeps working when the connection does not — which is usually where a guitar actually gets played.

• Theory sites hand out lookup tables that break on awkward roots
• Enharmonic spellings taught as interchangeable when they are not
• Practice rooms, rehearsals and studios rarely have usable signal
• Each tool lives on a different site, with a different mental model
• Heavy JavaScript frameworks for what is ultimately arithmetic
• No way to check that the theory a site prints is actually correct

Every note the site prints is generated from letter-and-interval rules rather than looked up in a table. A note is a letter plus an accidental, so a triad is spelled on every other letter name — which is why A♯ major comes out A♯ C♯♯ E♯ and G♭ diminished comes out G♭ B♭♭ D♭♭, instead of the tidy-looking enharmonics a table would return. Because the theory is generated, it can be audited by walking the entire space rather than sampling it.

// The note `letterSteps` letters above the root, `semitones` semitones up.
function spellAbove(root, letterSteps, semitones) {
  var letter  = LETTERS[(LETTERS.indexOf(root.letter) + letterSteps) % 7];
  var desired = (pitchClass(root) + semitones) % 12;

  // How far the plain letter sits from the pitch we need — that gap
  // is the accidental, up to a double sharp or double flat.
  var diff = ((desired - LETTER_PC[letter]) % 12 + 12) % 12;
  if (diff > 6) diff -= 12;

  for (var acc in ACC_OFFSET) {
    if (ACC_OFFSET[acc] === diff) return { letter: letter, acc: acc };
  }
  return null;
}

// A triad is the root plus a third and a fifth — two letters up, then four.
// A# major -> A# C## E#, never A# Db F.
function buildTriad(rootText, intervals) {
  var root = parseNote(rootText);
  return [root, spellAbove(root, 2, intervals[0]), spellAbove(root, 4, intervals[1])];
}

The same primitive spells triads, seven-note scales and chord tones, so one rule keeps every page in agreement.