Polyphonic music with separate melodies

There are several different forms of counterpoint, including imitative counterpoint and free counterpoint. Imitative counterpoint involves the repetition of a main melodic idea across different vocal parts, with or without variation. Compositions written in free counterpoint often incorporate non-traditional harmonies and chords, chromaticism and dissonance.

Work initiated by Guerino Mazzola (born 1947) has given counterpoint theory a mathematical foundation

In counterpoint, the functional independence of voices is the prime concern

Some examples of related compositional techniques include: the round (familiar in folk traditions), the canon, and perhaps the most complex contrapuntal convention: the fugue. All of these are examples of imitative counterpoint.

A number of popular songs that share the same chord progression can also be sung together as counterpoint. A well-known pair of examples is "My Way" combined with "Life on Mars".

JS Bach's 3-part Invention in F minor combines three independent melodies: Bach 3-part Invention BWV 795

One spectacular example of 5-voice counterpoint can be found in the finale to Mozart's Symphony No 41 ("Jupiter" Symphony).

Species counterpoint was developed as a pedagogical tool in which students progress through several "species" of increasing complexity, with a very simple part that remains constant known as the cantus firmus (Latin for "fixed melody"). Species counterpoint generally offers less freedom to the composer than other types of counterpoint and therefore is called a "strict" counterpoint. The student gradually attains the ability to write free counterpoint

Broadly speaking, due to the development of harmony, from the Baroque period on, most contrapuntal compositions were written in the style of free counterpoint.

Nonetheless, according to Kent Kennan: "....actual teaching in that fashion (free counterpoint) did not become widespread until the late nineteenth century."

Why JS Bach?

you don't have to be a musical sophisticate to comprehend and even enjoy counterpoint; ask any child who's sung "Row, Row, Row Your Boat" or "Frere Jacques" as a round

The pleasure involved is actually rather primitive at base, a dizzy buzz in the face of simultaneity. It may be enhanced by the more meditated impression that, in following more than one melody at once, we're enjoying an expansion of our normal capacities: "I didn't know I could do that!" something in us exclaims.

Counterpoint is ubiquitous in Bach

Bach's fundamental commitment to counterpoint gives rise to a wealth of particularized contrapuntal techniques. These can be grouped, biota-like, into two "kingdoms": the imitative and the nonimitative.

in the course of what develops into an enormous triple fugue. The secondary subjects don't just differ greatly from the main one but considerably from one another, a multi-heterogeneity that helps us follow all three subjects at once when, as the triple fugue concept dictates, Bach eventually presents them simultaneously.

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