false relation (idea)
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|A musical term. The simultaneous or adjacent occurrence of a note in its natural and chromatically inflected (sharp or flat, etc) form in different musical parts (or voices). Mostly found in renaissance and early Baroque music. The two notes in question do not necessarily have to be in the same octave, as demonstrated by the frequent occurrence of false relations between different vocal parts (i.e tenor and soprano).
Simply put, it's when you have both the sharp and the natural of a note present in different voices at the same time, or very close to each other.
An example of a false relation can be seen in the first section of Sweelinck's "Pavana Lachrimae". A more modern example is that of "Eight Days A Week" by the Beatles, whose harmony is based on false relations between G and G sharp. (This shows itself by way of an audible dissonace.)