Musica mathematica by Pieter Bakkerby Pieter Bakker | Het ORGEL | Year 98 | (2002) | Issue 2
Het ORGEL 98 (2002), nr. 2, 11-14 [summary]
Most of Andreas Werckmeister’s sources can be identified easily. This is not the casewith regard to his irregular circular tunings. It seems, however, that he was inspired bytwo sources. The first one is Musica mathematica of Abraham Bartolus, published atLeipzig in 1614. Bartolus takes over a tuning designed by Andreas Reinhard, published inhis Monochordum (Leipzig, 1604): the phrygian scale is divided into 48 parts andrelated to the proportions of the universe. Bartolus praises this tuning: it would bepossible to make music in all keys. Werckmeister sees that the tuning needs to be temperedfirst. The second source is a disc made by Theophil Staden, studied by Werckmeister inHarsdörffers Mathematische und Philosophische Erquickstunden. It visualisesthe idea of a circulair tuning in a primitive way.
Werckmeister’s tunings known as Werckmeister III and Werckmeister IV are irrigularcircular. He recommended these tunings in particular, and not equal temperament, which isregular circular, because he preferred the thirds to be purer, because the popularmeantone temperament was more related to Werckmeister III en IV, and possibly becauseequal temperament was hard to realize accurately.