Bach's temperament, Occam's razor, and the Neidhardt factor
John O'Donnell is Monash University organist and founder/director of Ensemble Gombert. He has performed the complete keyboard works of Bach (organ and harpsichord) and tours Europe regularly as organist, harpsichordist and choral director. He has published a complete edition of the keyboard works of Johann Caspar Kerll, but his research of the past two decades has focused on High Renaissance musica ficta. jdod{at}ozemail.com.au
Bradley Lehman's Bach temperament, its predecessors and successors proceed from a single assumption concerning Bach's diagram: that it represents a circle of 5ths. Some have even followed Lehman in inverting the diagram in order to read it, though there appears to be no logical reason for doing so. Temperaments in Bach's day were commonly notated chromatically from C, no doubt following the model of the monochord, but also because of increasing interest in measuring the equality or otherwise of successive semitones in the quest for equal temperament. It also happens to represent the order in which Bach chose to lay out his preludes and fugues. Can it be that Bach's diagram is to be read in this way? The key to the reading of the diagram is surely the ‘E
/D
’ embedded in the ‘D’ of ‘Das’. The resulting temperament bears strong similarities to Neidhardt's Circulating Temperament no.1 published in 1724, as well as to Sorge's temperament for a Kammerton harpsichord published in 1744, while it is all but identical to The Neidhardt's 3rd-circle no.4 published in 1732. And though we know of no direct association between Neidhardt and Bach, circumstances suggest that they would certainly have been familiar with one another's work. It is proposed, on the principle of Occam's razor, that the linear interpretation given here should supersede all interpretations presented to date.
Key Words: J. S. Bach • G. A. Sorge • The Well-Tempered Clavier • temperament