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Werckmeister Temperment
ament Werckmeister temperaments are the tuning systems described by Andreas Werckmeister in his writings.[1][2][3] The tuning systems are numbered in two different ways: the first refers to the order in which they were presented as "good temperaments" in Werckmeister's 1691 treatise, the second to their labelling on his monochord. The monochord labels start from III since just intonation is labelled I and quarter-comma meantone is labelled II.
Werckmeister also gave a table of monochord lengths for this tuning, setting C=120 units, a practical approximation to the exact theoretical values[ citation needed]. The resulting scale has rational frequency relationships, so it is mathematically distinct from the irrational tempered values above; however in practice, both involve pure and impure sounding fifths. 6 of Geschichte der Musiktheorie, Wissenschaftliche Buchgesellschaft (Darmstadt 1987).^ A. Werckmeister: Musicae mathematicae hodegus curiosus oder Richtiger Musicalischer Weg-Weiser (Quedlinburg 1686, Frankfurt & Leipzig 1687) ISBN 3-487-04080-8^ A. Werckmeister: Musicalische Temperatur (Quedlinburg 1691), reprint edited by Rudolf Rasch ISBN 90-70907-02-X"A handy guide to choosing temperaments for the practical musician, note 2".
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