Western tonal music — Bach, Mozart, Beethoven, Schumann, Wagner, Mahler, Gershwin, the Beatles, Stevie Wonder, most contemporary pop and film score — is built from chord progressions: sequences of three-or-more-note simultaneities that move toward and away from a tonic. Harmony is the theory of how these chords are constructed, related, and resolved. The system emerged gradually from medieval modal practice, took recognizable shape with Monteverdi around 1600, was codified by Jean-Philippe Rameau in Traité de l'harmonie (1722), and reached full chromatic complexity in Wagner's Tristan und Isolde (1859) before partially dissolving into atonality with Schoenberg in the early twentieth century.
The basic units are triads — three pitches stacked in thirds: a root, a third, and a fifth. Major triads sound bright and stable, minor triads darker and more melancholy, diminished and augmented triads unstable enough to demand resolution. Rameau in 1722 abstracted the system that has organized Western music ever since: a triad has a function in the key it sits in, and chord progressions are heard as motion between functions rather than between specific notes. The tonic (I) is home; the dominant (V) creates tension and demands return; the subdominant (IV) departs in the other direction. The cadence — the harmonic punctuation that ends a phrase — has a small grammar: V→I as the strongest authentic cadence, IV→I as the gentler "amen" plagal, V→vi as the deceptive cadence that frustrates expectation, a half-cadence on V that leaves the phrase open like a question. Modulation, the move from one key to another, is the harmonic analog of plot — leave home, visit a related region, return.
The system buys enormous generative reach from a small grammar. Roman-numeral analysis lets a musician track function through changes of key, and the same handful of progressions — the I-V-vi-IV of countless pop songs, the ii-V-I of jazz, the twelve-bar blues — recur across the popular repertoire. Chromatic harmony extends the basics with secondary dominants that briefly borrow another key's gravitational center, borrowed chords from the parallel minor, and a small zoo of Neapolitan and augmented-sixth chords for particular effects. The grammar reached its limit in Wagner's 1859 Tristan chord — an opening dissonance that refuses to resolve and floats across the entire opera — and the system was finally abandoned by Schoenberg's twelve-tone technique in 1923. Tonal harmony has outlived its abandonment.
Pop music theory is applied functional harmony: the I-V-vi-IV progression underlies hundreds of hit songs (Pachelbel's Canon, "Let It Be", "Don't Stop Believin'", "Someone Like You"); jazz changes are an extended vocabulary on the same backbone, the ii-V-I its workhorse cadence. Music software (Logic Pro, Ableton, GarageBand) ships with chord libraries organized by function. AI composition systems (MuseNet, Suno, Udio) have learned the empirical statistics of common progressions from training data and reproduce them credibly. Neural music-information retrieval reveals that the same dozen progressions recur across decades of popular music — a small grammar with deep generative reach.