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For the baffled, the relevant Wikipedia entry has a pretty succinct summary:
"In music, consecutive fifths (also known as parallel fifths) involve the concurrence of successive intervals of a perfect fifth between two voices in parallel motion; e.g., a parallel movement from C to D in one voice, and G to A in a higher voice. Intervening octaves are irrelevant to this aspect of musical grammar; for example, parallel 12ths (i.e., as created by successive intervals of an octave plus a fifth) are equivalent to parallel fifths. During the common practice period, the use of consecutive fifths was strongly discouraged. This was primarily due to the notion of voice leading, which stresses the individual identity of voices. Because of the powerful presence of the fifth above the fundamental in the overtone series, the individuality of two parts is weakened when they move in parallel fifths."
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