Bach-style keyboard tuning

Abstract

The chain of reasoning in Bradley Lehman's article in Early music, xxxiii (2005), pp.3?23, 211?31, is full of weak links. The notion that Bach followed a mathematical rule when tuning is contrary to relevant documentary evidence that he did not go in for ?theoretical treatments? and that ?mathematizing would never have led to success in ensuring the execution of an unobjectionable temperament?. An expert and musicianly tuner would indeed temper alike the 5ths C?G?D?A?E, but would not feel obliged (as Lehman imagines) to temper some 5ths exactly twice as much as others. The premise that a mathematically rigid tuning-scheme is hidden cryptically in a decorative scroll on the title-page of WTC I is daft, and Lehman's belief that there is only one musically feasible way to interpret this alleged evidence is disproved by the existence of several other such ways besides his (which was based on misreading a serif as a letter). Lehman misrepresents Sorge's account of a certain theoretical scheme from after Bach's death (which he regards as evidence applicable to Bach). No tuning-theorist close to Bach approved of tempering E?G# as much as Lehman does. Lehman's idea that Bach's secret tuning is uniquely beautiful for music by Frescobaldi et al. is outlandish. His one-size-fits-all approach obscures some relevant facts about church-organ tuning in those days. If Bach advised some organ builders about tuning, Zacharias Hildebrandt would be the most likely one, but the meaning of the statement by Bach's son-in-law that Hildebrandt ?followed Neidhardt?, while clearly ruling out Lehman's scheme, is unclear in some other ways since some of Neidhardt's ideas about tempered tuning changed over the years.