Counterpoint — from the Latin punctus contra punctum, "note against note" — is the art of writing multiple independent melodic lines that sound good against each other. The technique was perfected in the high Renaissance polyphony of Palestrina (~1550–1590) and reached its absolute summit in the fugues of Johann Sebastian Bach — particularly The Well-Tempered Clavier (two books, 48 preludes-and-fugues, 1722 and 1742) and The Art of Fugue (1740s, unfinished). Bach's death in 1750 is conventionally dated as the end of the high Baroque and of contrapuntal music as the European mainstream. The technique has never died — it survives in fugal passages, hymn settings, choral writing, and as a training discipline in conservatories — but it has not been the dominant style of European art music for nearly three centuries.
Species counterpoint — the pedagogical method codified by Johann Joseph Fux in Gradus ad Parnassum (1725) — teaches counterpoint in five graded species, each adding rhythmic complexity. First species: note-against-note, both lines moving in equal whole notes — the strict-est constraint, where consonance is paramount and dissonance forbidden. Second species: two-against-one — the ornamenting line moves twice as fast, opening up passing tones and neighbor tones (controlled dissonance). Third species: four-against-one. Fourth species: suspensions — held notes that create dissonance and resolve. Fifth species: florid counterpoint, combining all of the above. The constraints are about intervals (consonant intervals — third, fifth, sixth, octave — are stable; dissonant ones — second, fourth tritone, seventh — must resolve) and motion (parallel fifths and octaves are forbidden because they sound "empty"; contrary motion is preferred for independence). Imitation: a melodic motif stated in one voice is restated in another, possibly transposed, possibly inverted, possibly in augmentation or diminution. Canon is strict imitation — every note of the second voice is determined by the first. Fugue is the genre that organizes imitation at the largest scale: a subject (the main motif) is stated alone, then answered in another voice (typically transposed up a fifth), then a countersubject enters, and the piece develops by alternating expositions (subject-and-answer episodes) with episodes (developmental passages, often modulating). Bach's fugues are complete in a way that has barely been matched: the Bᴀᴄʜ spelling-fugue (B♭-A-C-B♮) in The Art of Fugue, the six-voice ricercar in The Musical Offering, the G minor fugue of WTC II — all are masterpieces of constructive ingenuity, where the formal constraints somehow produce music of overwhelming emotional density.
Counterpoint training is still a core part of music conservatory curricula — every composer of art music who has gone through the standard pedagogy has done species counterpoint, fugue, and chorale-style harmonization. Film scoring uses contrapuntal techniques (Bernard Herrmann, John Williams's Imperial March with its competing motifs, Hans Zimmer's Inception score). Pop music increasingly does too: the Beatles, Queen ("Bohemian Rhapsody"), Radiohead ("How to Disappear Completely"), Kendrick Lamar (the contrapuntal vocal layering on To Pimp a Butterfly) all incorporate genuinely contrapuntal moments. Algorithmic composition — Markov-chain generators, neural-net music systems — has historically failed at counterpoint because the constraints span large time scales (a voice's melodic logic must cohere across measures while harmonizing with others); modern transformer-based music models (MuseNet, MusicLM) handle short contrapuntal passages credibly but rarely sustain Bach-level coherence over a full fugue. The discipline is, as Bach demonstrated, one of the few formal systems in art that resists exhausting study — every generation of composers has found new ground inside it.