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Mark Lindley, Bach’s temperament, Early Music, Volume 40, Issue 1, February 2012, Page 167, https://doi.org/10.1093/em/cas026
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I write in belated response to Bradley Lehman’s letter in the February 2010 issue (Early Music, xxxviii/1 (2010), pp.170–1). The delay is due to my having waited until I could mention the posting of a set of webpages about a style of unequal temperament which I regard as more suitable than Dr Lehman's tuning for Part I of the ‘48’. These webpages (with more than 200 audio tracks etc.) can now be accessed at www.sim.spk-berlin.de/wtc.
Dr Lehman's tuning is indeed, notwithstanding his recent denials, mathematically formulated. In his main account of it, Table 1 (Early Music, xxxiii/1 (2005), p.9) specifies various aspects of the tuning by means of some 250 numbers in 20 rows of 12 columns plus another dozen at the bottom. I am among the many who smile at Dr Lehman's claim that the tuning is not of his own devising but was invented by Bach and merely decoded (by Dr Lehman) from an occult message bequeathed by Bach in the guise of a set of decorative loops. Early Music readers may, for instance, examine for themselves the footnotes in Patrizio Barbieri’s 2008 book Enharmonic instruments and music, 1470–1900, and confirm that the one about Dr Lehman is the only one that cites refutations of an alleged finding.
