<P> Bach's title suggests that he had written for a (12 - note) well - tempered tuning system in which all keys sounded in tune (also known as "circular temperament"). The opposing system in Bach's day was meantone temperament in which keys with many accidentals sound out of tune . (See also musical tuning .) Bach would have been familiar with different tuning systems, and in particular as an organist would have played instruments tuned to a meantone system . </P> <P> It is sometimes assumed that by "well - tempered" Bach intended equal temperament, the standard modern keyboard tuning which became popular after Bach's death, but modern scholars suggest instead a form of well temperament . There is debate whether Bach meant a range of similar temperaments, perhaps even altered slightly in practice from piece to piece, or a single specific "well - tempered" solution for all purposes . </P> <P> During much of the 20th century it was assumed that Bach wanted equal temperament, which had been described by theorists and musicians for at least a century before Bach's birth . Internal evidence for this may be seen in the fact that in Book 1 Bach paired the E ♭ minor prelude (6 flats) with its enharmonic key of D ♯ minor (6 sharps) for the fugue . This represents an equation of the most tonally remote enharmonic keys where the flat and sharp arms of the circle of fifths cross each other opposite to C major . Any performance of this pair would have required both of these enharmonic keys to sound identically tuned, thus implying equal temperament in the one pair, as the entire work implies as a whole . However, research has continued into various unequal systems contemporary with Bach's career . Accounts of Bach's own tuning practice are few and inexact . The three most cited sources are Forkel, Bach's first biographer; Friedrich Wilhelm Marpurg, who received information from Bach's sons and pupils; and Johann Kirnberger, one of those pupils . </P> <P> Forkel reports that Bach tuned his own harpsichords and clavichords and found other people's tunings unsatisfactory; his own allowed him to play in all keys and to modulate into distant keys almost without the listeners noticing it . Marpurg and Kirnberger, in the course of a heated debate, appear to agree that Bach required all the major thirds to be sharper than pure--which is in any case virtually a prerequisite for any temperament to be good in all keys . </P>

Bach prelude and fugue a flat major book 2