Music theory provides the foundation for understanding how chords are constructed, and the physics of vibrating strings determines the geometry of the fretboard that chord diagrams represent.

Chords are built from intervals, the distance in pitch between two notes. The most fundamental intervals are defined by frequency ratios: an octave is a 2:1 frequency ratio, a perfect fifth is 3:2, and a major third is 5:4. Western music divides the octave into 12 equal semitones using equal temperament tuning, where each semitone represents a frequency multiplication of the twelfth root of 2 (approximately 1.0595). A major chord consists of a root note, a major third (4 semitones above), and a perfect fifth (7 semitones above). A minor chord lowers the third by one semitone to a minor third (3 semitones). Seventh chords add a fourth note: a major seventh (11 semitones) for major seventh chords, or a minor seventh (10 semitones) for dominant seventh chords. These interval patterns determine which frets must be pressed to produce the correct notes on each string.

Fretboard geometry follows a logarithmic spacing pattern derived from the equal temperament tuning system. Each fret shortens the vibrating string length by the factor 1/2^(1/12), producing a pitch one semitone higher. The first fret is positioned at a distance of L - L/2^(1/12) from the nut (where L is the scale length), and subsequent frets follow the same ratio from the previous fret. This means frets get progressively closer together toward the body of the instrument. A standard guitar has 6 strings typically tuned to E2, A2, D3, G3, B3, E4 (standard tuning), while a ukulele has 4 strings tuned to G4, C4, E4, A4, and a bass guitar has 4 strings tuned to E1, A1, D1, G1.

Chord voicings refer to the specific arrangement of chord tones across the instrument's strings and frets. The same chord can be played in many different positions on the fretboard, each producing a different tonal quality and character. Open voicings use open strings (unfretted) and typically occur in the first few frets, producing resonant, full-sounding chords that are the first shapes beginners learn. Barre chords involve pressing one finger across all strings at a single fret to create a movable "nut," allowing the same chord shape to be transposed to any key by sliding up or down the neck. The chord diagram notation system captures all this information in a compact visual format: a grid representing the fretboard from above, with dots showing finger placements, a thick line or arc for barre positions, X symbols for muted strings, and O symbols for open strings.