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Polyphonic music is music where harmonic progression is secondary to the progression of relatively-independent voices. The primary forms of polyphonic music commonly heard today (outside of the historically-informed-performance, HIP, movement) are fugues and Jazz.

The origins of modern Western music lie in the second century after Christ. While the Church was investing its efforts in Chant, a single-voiced form, folk musicians were believed to be 'having fun' with common songs and chant melodies by taking two relatively-unrelated melodies and performing them at the same time. As time progressed, more art was brought to the process, and composers began to exert their efforts to make the disparate melodies work together better.

Eventually, this led to polyphony, where the voices are in agreement most of the time, but still stand independent of each other. Polyphony reached it's peak in the motets of the Netherlands composers, Josquin Des Pres being the most famous (and arguably the most talented) of them. This form of music flourished through the middle of the second millennium.

When the Baroque period began, the focus moved from independence of voices to harmonic progressions. The older system of modes was simplified to the modern system of keys and major vs. minor. The solo aria took the place of the solo song of the renaissance, and the accompaniment simplified to successions of chords, rather than horizontal movement of intervals. This brought theorists to build a new set of rules which was chord-based and chord-progression based, although this 'classical' 4-part harmony technique retained many of the 'old rules' about interval motion in the voices.

At the same time, the technique of 'simple imitation', where one voice would state a melody and another voice would echo it later, became formalized in canons: a single line of music with a rule describing how to make a multi-voiced piece. Sometimes canons stood on their own, sometimes they were incorporated into pieces using other techniques. The rules were often stated as puzzles (my favorite being in Odhecaton, the Des Pres "De Tous Bien Playne", which has three parts: the third part is labeled "Peter and John running, by a punctus", the punctus being one note length! This meant to have two play that one part, with one starting just after the other. Canons could be at the unison, or at any other interval, fourths and fifths being popular.

The fugue, which grew from these rule-canons, involves more than one voice, with each successive voice starting with the same opening theme, but a fifth higher (or fourth lower) and coming in after a period of time. The master of the Fugue, Johann Sebastien Bach, wrote fugues in great number, for organ and harpsichord and clavichord, orchestra and chamber group, lute and violin. (Yes, one violin playing multiple voices!) He wrote most of his best fugues after the style had already gone out of fashion, but his music was discovered again and Mozart and others found out about it and incorporated fugues into their own work.

Modern Jazz uses the same approach to polyphony that the earliest music did in the last millenium: relatively independent melodic lines are combined, often without concern for exact concordance, with the intention that momentary collisions will add to the music rather than merely detracting. The variety of Jazz that really started this rolling was Dixie Land: the trumpet would play a melody, the Clarinet would embroider it with runs and whole sections learned from French marchine music, while the Trombone would wander through various other thoughts. The bass, whether tuba or string bass would work with the drums to establish the rhythmic foundation on which the others would build a kind of dynamic harmony.

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