Further response to Charles Francis's third paper

...continued from my survey of "Bach" temperaments....

Dated 1 July 2005 (but released around July 14th) Charles Francis has posted a third informal paper on the internet, both at the Bach Cantatas Website of non-academic enthusiasts, and at Eunomios. It clarifies some of the vague ideas in his second one (see above). This time Francis presents a 1/14 PC shaving of my proposed pattern (like Kellner's shaving of Werckmeister; see above). This is done by assuming--without explication from Bach's drawing--that the A#-F diminished 6th should be 1/14 PC narrow, rather than pure or 1/12 PC wide. If Bach had wanted that size to be the same as the others, why did he not simply draw that onto the diagram with the other 5ths? To get around this, Francis in Figures 1 and 3 cuts off the left or right side of Bach's diagram, in turn, and he explains this by claiming that the diagram encodes two separate temperaments....

Through several graphs (Figures 18-20) and tables, Francis's presentation gives a red-herring impression that my 1/12 PC and 1/13 PC readings of Bach's drawing (see the survey) are nothing but a bumpy and inept misreading of Bach's pure theoretical "Cornet-ton" solution (i.e. whatever Francis fancies because it gives a smoother graph). His choice of 1/14 as a comma fragment cites vague principles of esoteric gematria (his footnote 36) to assert that this is Bach's preference. Francis's citation of a "Sorge" temperament is so vague (Figure 10 and footnote 39), and without explication, that one must read other materials to find out that it's specifically the 1758 temperament--the one that I gave special prominence in my own article.

As with Francis's first paper, the 19th century Hopkins anecdote (more than 100 years after Bach's death...) is pressed ahead of 18th century evidence, even though it's merely stashed quietly into footnote 16 instead of the text. Therefore Francis's Ab-C is assigned to be smaller than it is in equal temperament, giving a remarkably suave A-flat major triad at the expense of E-G#. (Might we expect, then, that Bach should have composed some organ music in A-flat major or D-flat major at some point, to take advantage of this?) In the other major thirds in the flat side, Bb-D becomes calmer than G-B.

Francis's "Cammerton" layout, by comparison, is simply the way this same layout would sound to an orchestra playing a tone lower, transposing the organ's "Cornet-ton" temperament (i.e. reminiscent of my "Ensemble music" discussion in part 1, but uncredited here...unless his extremely laconic footnote 41 counts as citation!). Francis does not make it clear which of these two layouts solo keyboardists should prefer in practice, for example in playing the Well-Tempered Clavier. He states only (footnote 34) that "The cammerton and cornet-ton temperaments are exact transpositions," which should be obvious already, but that doesn't tell us anything about making a musical decision between them. Clearly the organ repertoire would be played in the "Cornet-ton" version, at least at Leipzig. But what about solo harpsichord music such as the suites, Goldberg Variations, or inventions/sinfonias? Would that be the "Cammerton" version where only at A=417.997 Hz is allowable? And what should an ensemble harpsichordist use where a Chorton organ is not involved, for example in the Brandenburg Concertos or harpsichord concertos?

As for Francis's comparisons with other temperaments, giving some impression of scientific rigor with "Euclidean distance in cents": his metric at Figures 10-13 is simply to assume that his own extreme position is (arbitrarily) the correct one, and everything else is then measured as deviation from it. This proves what, other than the failure of 18th century people to anticipate Charles Francis? Notably, three of the layouts best-known to current harpsichordists (namely Werckmeister 3, Kirnberger 3, and Young 2) are represented as being some of the most divergent from Francis's bases. Is this a slap in the face against musical practitioners with classic harpsichord training at university, where these temperaments are taught? Whether there has been deceptive intent or not, by Francis, a result is the deceptive impression that all these other temperaments have been measured and found wanting, in some important way. I notice also that many of the results and ideas in this Francis paper (and his two preceding papers), not credited to me, were my own original ideas as I posted in May 2004 to a discussion group where Francis saw them...right down to the types of measurement that might be interesting in such a paper and the general harmonic shape that works best for Bach's music....

In short, vis-a-vis his 1/14 PC version, Francis is taking my article's results (and my excited public remarks about my own work in spring 2004, early in the publication process) as basically correct in shape, tacitly, right down to the way that his "Cornet-ton" version would sound like the "Cammerton" version to an orchestra reading in a different key. But Francis's wording of all this gives my article and web site as little credit (and as vague a credit) as possible for my original work; and then he's off to spin the whole thing with equal-beating, see below. Well, he will have to answer for his own soul as to morality and ethics in his treatment of my material; but let us focus on objective and technical assessment of his presented results.

To be clear here: my own article, and larips.com, proposes that Bach used a consistent basic pattern of intervals (the one that Francis's "Cornet-ton" layout most resembles) at various pitches, as a standard. It does not have any fixed starting pitch; the whole temperament transposes to whatever starting pitch is necessary for the other instruments in an ensemble. My alternate version on pages 17-18 of my article only comes up for the benefit of modern players reading from vocal-music parts that have been transposed since Bach's lifetime, eliminating the transposing nature of the Chorton organ.

His "equal-beating" slant...

But the main focus of this third Francis paper is to press an ahistorical premise: that Bach used only a specific arbitrary pitch-level at which the beat-rates are forced to be exactly 1 or 2 per second in particular octaves. The frequencies shown here are drawn directly from Francis's Table 1; compare with the shape of his own theoretical reading, above. The notes are pushed slightly higher or lower from the theoretical 1/14 PC positions, by Francis, to yield the type of equal-beating intervals discussed in some vague references to Owen Jorgensen's book Tuning. Therefore it results in the irregular layout shown here, with ten different sizes of fifths, and it works only at the unexplained "Cornet-ton" pitch level of A=468.497 Hz and C=279.331 Hz (his Table 1). Note the "Per4" and "Per5" columns: all the beat-rates are exactly one second, in some octave or other. Voila!

The recipe here: formulate Sparschuh's premise into some mathematical equations, mix in a dose of Jorgensen's "equal-beating" (vs "theoretically correct") tuning shortcuts, stir in Lehman's musical findings, overrule them a bit with Hopkins, run the whole thing through Mathematica to find the closest match, and voila! write up the superficial results! Never mind testing any of this on harpsichords and organs, or with any expert colleagues on other instruments or voices, but just run it on MIDI files with a synthesizer. And all these other researchers had to do the real work behind the Francis solutions that are therefore proposed here, with only token credit given to each real expert.

Compare with Francis's theoretical formulation of 1/14 and 1/7 PC, above. Where Francis had G-B and Eb-G as equally sized major thirds in that one, Eb-G is now considerably smaller than G-B; and F-A in this equal-beating layout has become smaller than C-E. Never mind that his own paper asserts (top of p12) that he is "placing the best thirds in the key of C".... No, both his "Cornet-ton" versions here are skewed toward making the 19th century Hopkins source look like the trump card of the argument about Bach's preferences.

The most questionable premise in this Francis paper is this notion of equal-beating, coupled with this insistence on a fixed pitch standard without historical evidence. In effect: Johann Sebastian and Carl Philipp Emanuel Bach--expert musicians by anyone's standards--are not allowed to have understood that the regular fourths and fifths of any meantone layout beat properly at 3:2 ratio, rather than 1:1 as Francis asserts with the equal-beating insistence. The Bach family allegedly boxed themselves in tightly with this one-beat-per-second premise, and that was their special angle to music. Owen Jorgensen's musing about amateur-tuning shortcuts (constant beat rates that disrupt geometrically regular layouts of fifths, through approximation) has therefore become a limit on what the Bachs were allowed to understand.

The broader point here is: Francis is hedging his bets (this is the "Texas sharpshooter fallacy": take multiple shots at a barn, then draw a target later around the best concentration of hits...). In that reshaping of the major 3rds pattern from his theoretical to his equal-beating methods, he presents as basically equivalent these two layouts that are seriously different from one another in musical behavior. His comma method is in his paper for handy theoretical comparisons against everybody else's temperaments, showing that his ideas are smoother and that Lindley would therefore approve of them; but that should be irrelevant if Francis is really pressing his equal-beating layout. (That is, he hasn't graphed his own bumpy layout against his smooth one! Exercise for the reader?)

And both of these current Francis lines of temperament, as with his first paper, require the premise that Johann Sebastian Bach was professionally inept. For Francis to be correct, Bach either didn't know or didn't care about normal intonation around him. Bach allegedly just used whatever variants Francis can press (citing gematria?!) to be different from historical precedents, and especially different in surface appearance from anything that Lehman has proposed. Francis's choice is to cite Jorgensen, Sparschuh, and Zapf ahead of anyone who believes that 18th century people (or at least JS Bach and CPE Bach) understood regular tuning with accurately split commas. But Jorgensen, Sparschuh, and Zapf have not attempted to prove that the Bachs only used equal-beating schemes of some manner or other; that part is solely Francis, in his restriction to the specific A=468.497 Hz ("Cornet-ton") or A=417.997 Hz ("Cammerton").

I have some additional personal comments about Francis's methods and his implications, not for posting here or at laripS.com; contact me privately if interested.

And I would still like to know if any of his three claimed degrees "BSc (Hons.), MSc, PhD" have anything whatsoever to do with historical musicology or musical performance. I have asked him about this several times, as early as my public review of his first paper in June 2004 and in several e-mail messages: and he has evaded the question. He will not reveal any direct relevance to music, musicology, harpsichords, organs, clavichords, or historiography. As far as I have been able to determine, he is an electrical engineer of some sort. His claim of scientific degrees (at the top of speculative music papers!) all strikes me as a smoke-and-mirrors show, lending deceptive weight to whatever he's in the mood to invent, in his papers. He just keeps schlocking it out there to Eunomios, a web site that explicitly prides itself on not having any peer review! It is simply a depository, relying on the goodwill and honesty of its contributors, but not checking same.

Additionally, this third paper by Francis has been given a public review by instrument-builder Paul Poletti on HPSCHD-L, 25 August 2005. Francis had joined that group with this first posting in July, bringing his paper out of nowhere, and with no personal introduction to the group.

A later posting by him, on October 3rd, convinces me yet further that he has a personal campaign to smear me, instrument builders, and anyone else who would dare to contradict his pseudo-science in public. His callous but frivolous attitude, as stated there, is that a disgruntled consumer should "use the power of the Internet to make sure the builder never sells another instrument"--where this is some puerile game to harm professional and personal reputations? A game where a consumer need only allege misconduct by an expert (and that the consumer should then be taken more seriously than the expert's work is), with no attitude of accepting circumstances beyond the expert's control?

That is certainly how he has treated me personally, at least in my perception of his activities: by following me around to various internet discussion groups (in both English and German) wherever I've discussed this research project. There he inserts laconic comments: making false allegations against my work, sowing his personal cynicism, and pretending to have discovered things ahead of me (or of doing "more recent" work; whatever is most convenient to his red-herring cases!). As is obvious to me, his speed in getting things sprayed out to the internet comes by dodging academic responsibility and peer review, the better to allege some primacy in this work. I have also seen his posted internet commentaries that musicology itself is--to him--a field of pseudo-science being "little more than informed speculation"; not a particularly good attitude for one who would be taken seriously trying to do some musicology!

Until Charles Francis is willing to show a photo, and to confirm some hands-on tuning of real harpsichords and clavichords (i.e. beyond his mathematical and esoteric speculations, real musical practice by him witnessed by somebody reliable), and to reveal honestly his curriculum vitae vis-a-vis music and musicology: I have found no reason to take his "research" as more than a frivolous attempt to make real musicology look silly or arbitrary. The work in his papers, themselves, hasn't shown itself to be of sufficiently clear or relevant thought, or sufficiently respectful of established expertise. It is a play to provoke people into internet flame-wars, and to mislead any readers not wise enough to see through his specious reasoning: anyone who might be fooled by his brand of speculative pseudo-musicology.

A look at his Usenet postings on various musical topics confirms his regular same style, starting and participating in flame wars on the internet: his pretentious misquotations of other people's ideas, smug rejoinders packed with red herrings, and regular abuse of other people in discussions who know more about the topic than he does.

Likewise, from autumn 2005 forward, he has edited the Wikipedia article "Well-Tempered Clavier" several times, directly reducing the descriptions of my work to be a series of less-than-half-truths, and promoting his own as somehow superior both chronologically and in quality. What does that Wikipedia article say, on any given day? It depends how recently he has messed with it; check the "history" link at the top to find the occasions where my work has been recast with the faintest possible praise. For example, compare the version that was current on 5 March 2006 with his revision on 8 March 2006, to see how he marginalizes my peer-reviewed and seriously published work...in favor of his self-distributed speculations on the internet!

It's his same old game: play to the people for whom the unmoderated internet is the first (or only) source of information considered, to figure out what is true! Wikipedia can be edited by anybody, and it relies on the goodwill of its users: being unfortunately open to abuse by any self-promoting dodger of academic responsibility.

Let's keep some reasonable perspective on Charles Francis's efforts to undercut or undermine my research, or my honesty; or his frivolous allegations that his work preceded (and/or influenced) mine in any way. My proposed solution was already broadcast in a recital by an expert colleague of mine, on Swiss radio, May 2004; and that's before the first tuning McPaper by Francis was unleashed (June 2004).

Furthermore, a public internet posting by me in April 1994 demonstrates that I already had a strong inkling of the general shape of the solution...ten years before all the recent work, and while finishing my doctoral studies in harpsichord. There in 1994 I surmised that "Bach's well-tempered clavier was actually an advanced form of meantone (complete with a mild wolf), not what we now call well-temperament (where no fifth is wider than pure)." And that's what we have here today: a 1/6 comma meantone on the naturals, modified by making some of the other 5ths less tempered than that, and having a single wide semi-wolf in it.

Francis's "Bach Tuning Website"

Francis in the last week of March 2006 has released what he calls the "Keyboard Tuning of Johann Sebastian Bach" web site advancing his speculations farther. (We are now expected to believe that Bach not only had two secret recipes tuned by beats-per-second, but so did Friedrich Suppig in a 1722 document that is explicitly about other manners of tuning!)

Among other problems, it fails immediately in his putative "Cammerton" tuning instructions from Bach's WTC drawing: where it is alleged that JSB prescribed the (very difficult) upward 4ths from middle C to C-F-Bb, beating once each, as the start of setting the bearings (where it is most important to avoid cumulative initial errors)! This rate is too slow to hear and count reliably, in that octave, at least on real harpsichords.

I have confirmed this myself, on three different harpsichords of various stringing; the octave above middle C is a terrible place to set upward tempered 4ths directly, as slowly as one beat per second, in attempts to establish Francis's temperament. I cannot believe, from practice, that Bach would prescribe such a thing. In my 23 years as a harpsichord tuner by ear, I have set hundreds of other temperaments accurately without problem; but Francis's is absurd as early as its first four notes, for reasonable accuracy. Furthermore, for all the beating to work out correctly to all twelve 5ths, one is constrained to start from a specific starting frequency...which forces Bach to have used some accurate source (but a fictitious one!) for it as well, and an accurate method to measure ticking seconds.

When I have asked Francis directly, three times, if he has ever personally tuned a harpsichord using any of his methods (or at all!) to hear if it actually works in practice, he has consistently evaded the question. (See my public questions on March 31 2006 and April 1 2006, and I had also asked him about this in 2004, vis-a-vis his first paper. In the 2004 occasion he said, with an air that came across as pride, that all his work had been numerical analysis.) I believe that his efforts in this project about "Bach tuning" are nothing but speculation, along with his pressing of mathematical coincidences as if they are meaningful. He is just taking as many bites at the apple as he can think up, whether it is 1/3 comma temperament derived esoterically from BWV 924, or equal-beating layouts derived esoterically from Bach's WTC drawing...and none of it needing to be confirmed as reasonable on any real harpsichords! Francis's speculations about Suppig force specific and arbitrary frequencies, the same way he does to Bach.

- Bradley Lehman, July to October 2005, and April 2006