General Principles
In its most general aspect, counterpoint involves the writing of musical lines that sound very different and move independently from each other but sound harmonious when played simultaneously. In each era, contrapuntally organized music writing has been subject to rules, sometimes strict. By definition, chords occur when multiple notes sound simultaneously; however, harmonic, "vertical" features are considered secondary and almost incidental when counterpoint is the predominant textural element. Counterpoint focuses on melodic interaction—only secondarily on the harmonies produced by that interaction. In the words of John Rahn:
It is hard to write a beautiful song. It is harder to write several individually beautiful songs that, when sung simultaneously, sound as a more beautiful polyphonic whole. The internal structures that create each of the voices separately must contribute to the emergent structure of the polyphony, which in turn must reinforce and comment on the structures of the individual voices. The way that is accomplished in detail is...'counterpoint'.The relationship and separation of harmony and counterpoint has developed over time. During the Medieval period, modes strictly defined harmonic changes and composers of that period had to fit the different voices of their compositions into these modes. By the Baroque period, however, harmony could extend to any key as long as simultaneous voices were in the same key. This retained until the modern period, where polytonality and atonality were introduced; Glenn Gould's String Quartet in F minor, Opus 1, for example, is a fugue with nearly full atonality.
There is a clear distinction between polyphony and counterpoint. Counterpoint generally refers to different motifs used against each other, and cycled through in each voice (of which there are at least two) of the piece, whereas polyphony means simply two or more independent melodies played simultaneously. For example, Giga from J. S. Bach's Partita no. 1, BWV 825, includes a voice that stretches several octaves, and supplementary voice, with much narrower intervals. These are two independent voices played both throughout the piece, which makes the movement polyphonic, but not contrapunctal, since there is no motif shared by the voices, and their relation is theoretically incidental.
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