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I was interested in Bradley Lehman's exposition of J. S. Bach's temperament, as interpreted from the ‘sinuous spiral’ drawn as a header to the first volume of the Well-tempered clavier in EM, xxxiii/1 (Feb 2005), pp.3–23. The temperament he proposes is good indeed, just as good as a number of other temperaments (Neidhardt, temperament ordinaire, Vallotti and John Barnes's temperament derived from musical analysis of the ‘48’). However, I am concerned about the number of assumptions made by Dr Lehman in arriving at his solution. First, I see no reason to analyse the diagram upside-down (in which case why did Bach not write the vitally important ‘C’ upside-down as well?). As a harpsichordist who has experimented with many temperaments (one's thinking goes round and round in circles as much as the temperaments themselves), it is plain to me that if one analyses the diagram the right way up the initial ‘casual flourish’ looks like a ‘G’. In which case the ‘C’ further along the line confirms that each of the 11 loops starting from the left implies: thus giving all the 5ths. This is a completely different solution from that advocated by Dr Lehman, who has read the diagram upside-down.
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David Ponsford (2005) studied this question.
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