I thought perhaps I should create a separate discussion for temperament, as this is unlikely to be of interest to the majority of pianotech subscribers. Perhaps I will, if this leads to more discussion on the topic. But meanwhile I am going to post the following, quite lengthy post setting out some reasons for a statement I made, quoted at the very bottom.
I have stated that I do not believe Lehman's temperament has any historical basis, both on the lists and in my series of articles on temperament history. I have not made that statement lightly, but I have not elaborated because it takes some time to do so. I shall do so now, for those who might be interested.
Let us start by stating Lehman's claims:
1) The decorative design on the title page of the Well-Tempered Clavier is, in fact, a tuning diagram.
2) That diagram should be interpreted in a certain way, the way that Bradley Lehman has set out in an article in Early Music and on his web site.
There are some related arguments/hypotheses that bear strongly on Lehman's claims:
1) The decorative design has interesting features that lead one to believe that it is not merely decorative. These include its asymmetric pattern, and a small letter C that is next to one of the loops, labeling that as a fifth from C, thereby placing the pattern in the circle of fifths.
2) Bach had a specific tuning pattern that was important to him. He taught it to his students, with the decorative design being used as a mnemonic device (this is Lehman's interpretation, and it seems a reasonable one, within the context of his overall story).
3) This decorative device was finally published in connection with the WTC, making it clear to initiates that the series of 24 pieces in all 12 keys should be played in this specific tuning.
Having laid that groundwork (anyone who wishes to know more should consult Lehman's website, or my article in the November, 2006 Piano Technicians Journal), let us begin to analyze these claims and details historically. From the start, we need to state very clearly that not a single shred of historical evidence supports these theories of Bradley Lehman. There is a decorative design, and that is all. Everything else is speculation, laid out in a persuasive way by Mr. Lehman. Mr. Lehman has never offered any further proof, resting the majority of his case on the "fact" that his temperament scheme "sounds right," a purely subjective judgment.
The asymmetry of the decoration seems odd to our modern eyes, suggesting it is not a mere decoration. However, examination of Baroque decorative flourishes reveals that asymmetry was quite common, in fact probably more common than symmetry. Mark Lindley and Ibo Ortgies provided examples from Bach's own hand for their article in Early Music refuting Lehman's claims (I don't have the citation at hand, but around the end of 2006, beginning of 2007). These all look very similar to the WTC decoration, in their free and extravagant style. The extra letter C that is supposed to indicate the position of the note C in the temperament sequence is also refuted rather strongly in that article. A separated serif C was common for initial capital Cs in Bach's handwriting, and Lindley and Ortgies provide examples in Bach's own hand, showing this very clearly. They also point out that a small letter c is never written in that way (see the article for details). The small C above the large C is normal calligraphy, for the time and for Bach specifically.
Supposing that the diagram is mnemonic device for a tuning scheme that was used with Bach's many students, we might expect that some evidence would survive among their writings and manuscripts, or at least a mention. No such evidence has come to light. However, some of Bach's students did copy the WTC in manuscript. Most of those copies omit the decorative design. One includes a similar decoration, but it is not the same pattern. B. C. Kayser's decoration has fewer loops. (My source: J. S. Bach, a Life in Music (2007: Cambridge) by Peter Williams, pp 336-337). To me this is pretty conclusive evidence that the hypothesis of the students and the design is an untenable one.
Bach had many students, some of whom left behind a good deal of writing. Two wrote a great deal, indeed - Bach's son CPE Bach and Johann Philipp Kirnberger - and both wrote about JS Bach and propagated his ideas. CPE Bach took up much of his book (Versuch über die Wahre Art . . .) in explaining his father's keyboard technique and fingering patterns, and in explaining his methods of realizing figured bass. His treatise is long and detailed, and covers a great deal of ground. He does cover tuning briefly, in the course of talking about stringed keyboard instruments. He mentions not one word about his father having a special tuning pattern, and his description is vague enough to admit various interpretations. Interesting. Not conclusive, but very suggestive. If JS Bach considered his tuning method to be very important in its details, one would expect his son to mention this fact, and maybe describe it, at least briefly, in a book devoted largely to the father's legacy.
Kirnberger based much of his career on the fact that he was a student of the "Great Bach." He wrote a book explaining Bach's method and principles of composition. He also wrote voluminously about tuning. One would expect him to espouse or at least mention any particular tuning scheme his mentor may have had. Not a word to that effect. Instead, Kirnberger first proposed a tuning pattern consisting of a string of eleven just fifths, with the whole Pythagorean comma contained in one fifth. When this was roundly jeered and shouted down, he retreated to a scheme of ten just fifths, with the comma shared by two fifths. This temperament he claimed to be appropriate for the music of Bach.
Marpurg, a proponent of equal temperament, argued vociferously with Kirnberger. At one point he "pulled a trump card," stating that the "Great Bach" had used equal temperament, and appealing to CPE Bach to confirm this fact. Apparently CPE Bach demurred, he seemed to have preferred to avoid taking sides in the argument. But what is most telling is the deafening silence that occurred - a deafening silence IF Bach had a particular tuning that was laid out in plain sight on the title page of his WTC and if his students knew about it. Why would none of them say so at this juncture? Why not CPE? Why not Kirnberger? Or any of the others? This was a very public dispute, one everybody knew about. How easy to show off the fact that you knew the inside secret of JS Bach's tuning. But there was nothing.
I am a believer in following the evidence. The evidence in this case is entirely against the speculations of Bradley Lehman, and there is none to support it. He writes in a persuasive way, and has been very successful in converting many, many people to accept his interpretation. His temperament does have a generally authentic shape to it: it is a mild unequal temperament with narrower thirds in the natural keys, wider ones in the flat/sharp keys, as does Vallotti and as do many, many other temperaments. It is mild enough to be innocuous and pleasing to the ear, not enough different from equal temperament to be noticed by most people who have not been told what they are listening to. But in the end, it is pure speculation, fantasy, nothing more. There are no solid grounds to believe Bradley Lehman's story. In the end, his case rests on his musical analysis: "In this piece, this interval only sounds right when it is tuned this way," repeated over and over with example after example. Other writers have made precisely the same kind of argument, supposedly proving that their own temperament patterns "must have been" the one Bach used. This is a matter of subjective judgment, and one that is so susceptible to suggestion as to be utterly useless.
Although this has been rather long-winded for a post to a discussion, these arguments have been stated as briefly and concisely as I could. It would be possible to go into much more detail, particularly as to Lehman's interpretation of the various loops and related matters, and to show the historical context in more detail to make clear how unlikely it is that such a "secret" would be kept for over 150 years, waiting for a brilliant code solver to discover it. However, I think what I have written above suffices to explain my point of view.
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Fred Sturm
University of New Mexico
fssturm@unm.edu "The true sign of intelligence is not knowledge, but imagination." - Einstein
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"Neither Barnes nor Lehman has any real historical basis (though Lehman certainly believes very strongly that his does. Barnes never claimed his had any historical basis)."