A public-accessible copy of my 7/06/08 posting to "Yahoo! Clavichord", message 8744 in that members-only archive: http://launch.groups.yahoo.com/group/clavichord/message/8744

This was in response to a posting by Andreas Sparschuh, where he claimed that his own work from 1999-2000 (his invention of temperament algorithms based on Bach's WTC title-page drawing) was a hoax and a joke. Sparschuh therefore is trying to dismiss all my work as a misguided avenue of investigation, too.

re: JGW's tuning inspired by Erasthosthenes? (not anymore)

Re: the drawing on Bach's title page, etc.:

Andreas S is welcome to dismiss (or support) *his own* work in any terms he chooses. If he's saying now that *his own* work was just a joke or a hoax, that's for him to decide. It doesn't affect me one way or the other.

My work is absolutely serious academic research. I use my derived temperament from it professionally (have done steadily for the past four years now), and many other fine musicians do so as well. The most important section in my published work, in my own opinion, is on pages 212-222 of the printed "part 2" in the May '05 issue of _Early Music_.
Those pages explain exactly why the temperament sounds so well-matched to the extant music by Bach and his colleagues; and how it fits into the pedagogical standards of the time, too.

Where notes are used with enharmonic equivalence through compositions, the tuning meets and matches the harmonic/melodic tension in the music: which I believe Bach used deliberately as part of the inspiration for his own music. My analysis comes from close study of the notes actually called for in the compositions. The primary evidence is musical. I keep adding to the study of that, at this page:

No one to date has published a cogent argument against any of that material from that chunk of "part 2". The quarrels, rather (both in print and all over the internet, ceaselessly), have been from people flogging their own misunderstandings of my "part 1"...and typically also ignoring or discounting the "supplementary files" and listening examples that were a vital part of that same paper. (And right now I'm working on a response to yet another of these: B Billeter's article in a recent issue of _Ars organi_, which has some good ideas but also some maddeningly superficial points that steer the argumentation away from the music. Billeter's presentation doesn't show any awareness of those "supplementary files" or any of my other internet material since then; it's as if that supportive part of my work doesn't count, since it's in sound or in photons instead of on bound pieces of paper.)

Bach's drawing, I believe, shows a simple hands-on method to tune a keyboard: proceeding note-by-note and nudging the pitch off-spot (from pure) by zero, one, or two little jots of the wrist. It is not necessary to measure *anything* in commas, frequencies, cents, fragments of cents (to three decimals!!), or any other numerical calculations, to get this done. Just knock the notes flatward slightly at each point, listening for quality: it is that simple. The measurements are only to explain the *result* after it is already set up by that analog process working directly at a harpsichord. As I've seen over the past several years, hundreds of people have misunderstood that point. Bach wasn't a numbers guy.

Bach taught by example. He was there to demonstrate his method(s) directly to anyone who needed to know. As I said in that same paper, the reason (I believe) Bach wrote down any details -- in the form of this drawing -- was that he was preparing the book as part of his _curriculum vitae_, applying for his teaching position at Leipzig. (And that hypothesis is from Wolff, not original with me.)

As I've been explaining patiently over the past several years, Bach's *music* itself -- especially in that book of WTC -- constrains any tempering solution to be within a tight range of possibilities...even if he hadn't bothered to do the drawing! Wherever the music uses more than 12 enharmonic notes, with the same key lever on the keyboard serving as (say) D# and Eb in the same piece, the pitch has to be moderated appropriately so it can serve as both. That whole book calls for 27 notes, all sharing space on a normal 12-note keyboard. Couple all this with the basically 1/6 comma naturals common at the time, both in practice and in pedagogy, and this solution is what emerges...with or without the drawing.

The drawing only provides a set of how-to instructions, or a visualization, as we do the process (and check it outward by octaves, testing by the qualities of 4ths/5ths to get the octaves right). The drawing helps us to understand the process of moderating each note in turn to serve appropriately in all the required functions as sharps or flats. I think it was brilliant that Bach illustrated this with a drawing *instead of* with numbers, because the thing really is a harmonic *shape* rather than any pages of calculations. Numbers fall away, in the face of clear concept.

The amount of energy expended by some people, either missing or actively disregarding my main points, has been astounding. Some can't get their minds past the idea of having one *very slightly* wide 5th of +1/12th PC, or can't see any reason why Bach could ever have done such a thing even if it made his music sound fabulous, and (like Billeter) they argue themselves into buckets of red herrings. Some mistakenly think the investigative work is primarily graphology, instead of primarily musical, and they go in directions of interpreting the drawing differently...while disregarding what it does musically on harpsichords and clavichords. (Try http://www.bach1722.com/ on that angle!) Some show no evidence of having tried out any of Bach's music, to understand the enharmonic issue, but rather focus their own argumentation on speculative ideas on paper. Others try to whittle off things they don't like about my writing style, or whatever. But, nobody I've seen yet has even bothered to engage much of my "part 2" theory: my explanation why my proposed solution is the way it is.

That's what I have been explaining in those original papers, and in the follow-up resources: the concept of carefully balanced notes that work in all their required enharmonic functions, as used in the music. None of my work is any joke or hoax, to me. It is a serious examination of the music, along with all other available historical and theoretical clues. I continue to add supporting material to
...which itself has been some thousands of hours of work, along with recordings and video demonstrations.

Brad Lehman