Below is the Wikipedia definition of the French Suites:

The French Suites, BWV 812-817, refer to six suites which Johann Sebastian Bach wrote for the clavier (harpsichord or clavichord) between the years of 1722 and 1725. The suites were later given the name 'French' (first recorded usage by Friedrich Wilhelm Marpurg in 1762) as a means of contrast with the English Suites (whose title is likewise a later appellation). The name was popularised by Bach's biographer Johann Nikolaus Forkel, who wrote in his 1802 biography of Bach, "One usually calls them French Suites because they are written in the French manner." This claim, however, is inaccurate: like Bach's other suites, they follow a largely Italian convention.
There is no surviving "definitive" manuscript of these suites, and ornamentation varies both in type and in degree across manuscripts.
Two additional suites, one in A minor (BWV 818), the other in E-flat Major (BWV 819), are linked to the familiar six in some manuscripts. The Overture in the French style, BWV 831, which Bach published as the second part of Clavier-Übung, is a suite in the French style but not connected to the French suites.
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