There were two systems of tuning the archicembalo considered by Vicentino: • The most important was the extended quarter-
comma meantone temperament—which, given such a wide gamut of fifths, becomes almost exactly a system of 31 equal divisions of the octave (see
31 equal temperament). This arises because after a cycle of 31 quarter-comma-tempered fifths, the 32nd pitch is remarkably close to a pitch that already exists in the system. Thus, five of Vicentino's 36 possibilities became practically redundant in this system. He suggested that these five be tuned instead according to the second manner described below. • Vicentino offered an alternative tuning in which the upper keyboard was tuned a quarter-comma higher than the lower, allowing pure fifths by playing chords across the manuals, giving a limited system of triadic
just intonation. This tuning still permits
modulation to a wide range of keys, but not in a completely circular fashion as with the first tuning described above, and still only modulates by the meantone-tempered fifth, not by the pure fifth. The observation that extended quarter-comma
meantone temperament almost exactly approximates 31 equal was recognized by Huygens in 1661, published in 1691. He says that after making this discovery, he found an earlier mention of the idea in Salinas' report on a 31 tone Italian keyboard, presumably Vicentino's archicembalo. Vicentino's description of his first tuning has some puzzling statements if it is understood as 31 equal. He says that the
major third from C to E is made closer to pure if it uses the slightly lower pitched C on the front keyboard with the slightly higher pitched E from the back keyboard. This is puzzling because in pure 31 equal all the major thirds should have been almost exactly pure already. Karol Berger's analysis of this suggests that he may actually have used a somewhat unequal tuning for his extended meantone system, varying perhaps from 0.2 comma smaller than pure to comma larger than pure. == Uses ==