Comments for the "BachRecordings" mailing list

7/13/04 to 7/14/04; (c) Dr Bradley Lehman, 7/14/04, all rights reserved.
7/15 section added.

Basically, my comments at
boil down to several of the most relevant points, including some new comments here today:

1. Anyone who claims to do research has a responsibility to understand and acknowledge the work that has already been done in a field both to avoid ghastly mistakes (ones that only show the writer's own ignorance and disregard for others' serious work), and to understand the nature of the problem(s) to be solved in the first place. In this case, the problem of keyboard temperament is much more subtle and deep than Charles has acknowledged. All he has done, in effect, is to fool around with sharpening/flattening notes or groups of notes on his synthesizer until he has found something that he feels sounds reasonably good; and then to try to force it to look like it came from any evidence of Bach (and Werckmeister, in the emphasis on archaic-1/3 comma fifths, shuffled around differently). This is hardly different from harpsichord/organ/clavichord tuners (whether in the 17th century or now) moving individual notes of the scale around arbitrarily until finding something that sounds inoffensive to themselves, and then claiming triumphantly to have found something meaningful; it's merely creativity, not research. Without a clearly stated musical purpose (that is, a definite improvement on all other available possibilities) it's meaningless! The use of synthesizer instead of harpsichords, clavichords, and organs simply makes it easier for him to convince himself that he's got something, without actually having to understand how to tune or play any of the instruments Bach knew! The Korg simply makes it easier not to think, easier to be a "knight of the [electronic] keyboard": merely plug in some cents values from wherever, listen to some automatically generated results, and convince oneself that something has been learned or achieved. Such a failure to discern value doesn't mean that nobody else can discern value, by musical standards! Werckmeister and his cantor Bendeler both in the 1690s published 1/3 comma solutions that are better balanced musically than Charles' solutions are; Charles hasn't shown how his own manipulations are appreciably any improvement (if he was even aware of Bendeler's work at all, until I mentioned it in review of his paper).

2. When evidence is used (and it must be!), it must be used consistently and completely. One cannot simply leave out the conditions one does not wish (or understand) to satisfy; or use the evidence illogically, either. In Charles' paper, one of the most illogical bits is his inconsistent treatment of ornaments. He takes a mordent in some places in BWV 924 as prescriptive of pure fifths, and on another note (E) he takes the same ornament to mean a 1/3-flattened fifth. Why, unless the whole thing is a farce of forcing evidence to say what he wishes it to say? It becomes obvious he is simply using BWV 924 to his own ends, as a framework on which to hang his own invention and implicate Bach in the anti-musical crime. Why should signed ornamentation in Bach's music (mordents, various types of trills, etc) mean anything more than face value, anyway? Why derive tuning instructions from such an arbitrary thing, and then do it inconsistently to boot, unless the aim is to lampoon the value of real scholarship? Did Charles expect that no readers are astute enough to notice the logical problems in his method?

3. A temperament that is marketed as a "Bach" derivation simply cannot cast F major as the worst available major key; this goes against all the musical and historical evidence. It makes tonal music sound like a farce, with the notes arbitrarily sharp or flat as the music is played no orderly progression of keys as the music modulates. That was a top priority of 17th and 18th century tuners/players/listeners making the most commonly-used keys (especially C, F, and G major) the best in tune, with any contrasts moved out to the more exotic areas as special effects. The claim that Bach tuned the way of Charles' "Temperament IV" (or any of those) is, more deeply, a claim that Bach didn't understand anything about normalcy, and didn't care if his music sounded random. All Charles has done to arrange his scale is to force the triad of A-flat major to be much smoother than it normally would be in any 17th/18th century method, artificially, to suit an 1855 anecdote (yes, 105 years after Bach's death) which he has misattributed to 1895 (even worse). Again, that's not research; it's just a creative forcing of the little bits of evidence he has brought to the project, while ignoring the whole body of 17th/18th century music and its history.

4. Even the most minimal reading list to begin to understand temperament would include the following books and articles.

  • Mark Lindley, "Temperaments" and "Well-Tempered Clavier" in New Grove (2001), for a succinct survey and lots of technical detail as well.
  • Lindley's book Lutes, Viols, and Temperaments for technical background and to see how a top researcher comes to the field, sifting through sources that look contradictory.
  • Easley Blackwood's book The Structure of Recognizable Diatonic Tunings to understand the mathematical (group theory!) nature of the problem, and to pick up all the necessary nomenclature for the tuning literature.
  • Murray Barbour's book Tuning and Temperament (1951; reissued just a few months ago by Dover, by the way) to see the sweep of most of the documented temperaments, grouped together by some of the goals those people had.
  • Rita Steblin's book A History of Key Characteristics in the 18th and 19th Centuries to fill out the history of theory, and to see what goals those people had in musicality and perception in the normal tuning arrangements of keys; she also covers some of the 17th century values, and Mattheson, and the serious theoretical debate between Kirnberger (Bach's student) and Marpurg.
  • Owen Jorgensen's book Tuning, and his earlier Tuning the Historical Temperaments By Ear, to see the full workout of practical recipes (although his books are skewed by his too-light use of sources that are not in English, and several other priorities of his own value judgments that he reads into the evidence).
Has Charles read even one of these standard items in the tuning literature? Not on the evidence of his paper, either from his list of cited references or from his command of the material.

5. There simply is no substitute for tuning instruments by ear (because people listen to music by ear!) to understand how the temperaments are shaped, and then improvise figured-bass progressions and play through the repertoire (both solo and ensemble). Walk in Bach's shoes in that manner; that leads to comprehension of at least the musical aspects of the problem. It's also important to do this if one's aim is to convince other people who are able to do that, to confirm the results for themselves. (Scientifically achieved results are reproducible, right? If not, it's merely anti-scientific nonsense by a guy with a computer.) But, again, Charles hasn't tuned anything by ear or played any of the repertoire; it's not clear that he's ever even met a person who has a harpsichord. All he's done is take MIDI files (assembled by other people!) and plug manipulated cents-values into his synthesizer, and then decide when it sounds good enough to him; this is akin to people changing the speed of published recordings just to suit their own whims, and claiming that they've made the music more listenable. It has nothing to do with performance as Bach knew it; digitally simulated music on computers didn't exist. The acid test here is to listen to performances of Bach's music not generated by Charles himself, and therefore to recognize how abnormal and preposterous are the musical values in his proposed solution. The paper is merely the results of a consumer messing around with other people's music and other people's thoughts superficially, after they've put them out there; and then claiming to know better how to do their jobs than they do/did. Recycled garbage--and some of the material being put in there without attribution before being turned into garbage--is supposed to overthrow serious work.

6. The burden of proof is not on those who would refute Charles' work; the temperament sounds like garbage immediately upon being set up on an appropriate instrument. But, by "publishing" his paper now in at least two places on the web, and attaching an irrelevant doctoral degree (in what? obviously not music or musicology...) after his name to make the numerical voodoo look significant, he's out there to fool people who don't know how to see the difference between garbage and meaning. He makes it look as if he's already proven he's right, through all his impressive-looking numbers that surely must mean something important...until one actually takes a close look at the numbers and sounds and realizes that they make no sense, and don't solve any of the classic problems of tuning. He's invented a temperament that sounds different, and he's tied it tenuously to a piece by Bach. So what? He hasn't proven that Bach did, or outlined any of the reasons why a different-sounding temperament would even be desirable (then or now). All he's done is to recycle comments of mine from the BCML/BRML back into his paper, musical/analytical comments about a quite different temperament, to try to force it all to fit his own invention, and co-opting the analytical methods themselves for his own ends. Again, that's not research. It's merely plagiarism, mockery, and a way to get knowledgeable people to waste their time checking out "research" that on the surface looks halfway plausible.

7. To understand the arbitrariness of Charles' "Temperament IV", consider the possible layouts available to him in his choice of 1/3 syntonic comma fifths (three of them) plus a schisma (the leftover "2 cents" he seems not to know what to do with, with any definite plan). There are twelve fifths to work with. Arrange all 12 fifths into a fixed sequence, and let "0" represent a pure fifth and "1" a 1/3 comma fifth. Obviously, the possibilities are 000000000111, 000000001011, 000000001101, 000000001110, etc with the 1's progressively walking their way up the line (including symmetric arrangements such as 100010001000, which would yield nicely a pseudo-equal-temperament that Charles appears to prefer anyway, in musical results: all the major thirds equally sharp). 12C3 combinations = 220, as is obvious from elementary knowledge of the field of probability and statistics. And, the schisma could be applied to any one of the 12 fifths (whether the fifth was already tempered, or pure), so multiply all the previous discussion by 12. Clearly, this is quite a big number of possibilities (220 * 12 = 2640), and that's dealing only with 1/3 syntonic comma fifths; one could also work with 1/4, 1/5, 1/6, 1/7, etc comma fifths, or fractions of the other (Pythagorean) comma as Werckmeister did, or mix two or more types of tempered fifths together. And, for that matter, why assume that the comma is being split into several tidy equal portions, or rational portions at all? Musical taste doesn't have to move in discrete chunks like that! The number of combinations here is astronomical. Charles hasn't shown how his preferred "Temperament IV" is appreciably better for the music than the other possibilities are, or indeed why any performers or fans of Bach's music should care about his "research". Furthermore, his spiral graphs, taking his own concoctions as normative, merely show that he's invented solutions sufficiently weird (historically questionable) that nothing else really resembles them. As long as he keeps his tempered thirds spread out somewhat with some pure fifths between them, of course it's going to come up that the closest match is equal temperament; that's a truism. Put weird major thirds and/or fifths into the classically common keys, and voila, equal temperament becomes the closest virtue that the historically verifiable temperaments had the goal of not putting the rubbish heap downtown like that.

8. Charles' posting
, announcing the BCW copy of his paper, contains a number of notions that are obviously there mainly to pique me and other serious musicians.

  • (1) the notion of "Urtext" performance as a virtue (apparently musicians need not attend any sort of school to learn how to perform music, if computers can do it more faithfully to Bach's intentions by simply reproducing some supposedly complete score full of naked notes). Obviously this is an affront to all notions of "gestural" performance as I have described frequently. It is also a reference back to Charles' own regularly posted distaste for any performance practice (such as shortened bass notes in recitative) that requires performers to know expectations that are not written in the score. Basically: if it's not in the score, he (without appreciable musical training) doesn't understand it, and therefore it's not valid. Therefore, "Urtext" performances are to him more valuable than musical ones are; that's what he's re-asserting here, knowing that it will incense any musicians who happen to be reading it.
  • (2) the "unique tetrachords" (directly from my BRML postings)
  • (3) the emphasis on "purity" in the way he has advertised his work (as if no other way is pure?)
  • (4) the "sonorous sound" (whatever that means) as an assertion that the wildly UNsonorous character of F major sounds better than it really does, as I've already pointed out several times in the discussion on the BRML
  • (5) the reference to a practice that "had apparently died out by his time" (on what evidence?). Charles knows very well, if he's read my earlier review of his paper (including my remarks on, that Bendeler's solutions using 1/3 comma fifths were republished in 1739, which is quite a long time after the composition of BWV 924. What's this about a practice dying out? Rather, Charles is simply showing his disdain for my criticisms of his paper; his refusal to take seriously the pointing-out of factual problems with his work.
  • (6) the "conjectured trade-secret of the Bach family" (a reference to my own hypothesis as posted on the BRML, that Bach learned an important tuning method from other relatives of his)
  • (7) the notion that "Temperament IV" is in any way a "Well Tempered system" or the "Well Tempered system"; all it means to Charles on the evidence of his paper is that he's split a wolf into unwolflike pieces; so what? We're supposed to take his assertion here as if he's solved the outstanding problems of "well temperament" once and for all?
  • (8) the "significant technical challenges, which needed time and patience to overcome" (yeah, right: the location of MIDI files to co-opt, and the generation of mp3 files from them...all within scarcely a week! Instant "recordings" of non-performances, to mislead any who would not know any better)
  • (9) the probably deliberate misspelling of Dr Yo Tomita's name as "Jo" Tomita, belittling the name and importance of a major Bach scholar; also implicating Dr Tomita as somehow condoning Charles' project by permitting the use of his files
  • (10) example #19 being in "G sharp major" when Bach wrote it in A-flat, as all musicians familiar with that book know
  • (11) the use of a Contrapunctus from The Art of Fugue as supposed proof of his temperament's superiority...less than a month after I reported playing through the piece myself on harpsichord really tuned in a temperament for which I've found Bach's evidence. Obviously, Charles is trying to make it look here as if (a) he's found what I found, independently; or (b) if my own results sound as rotten as his do in this piece, I must have a tin ear to accept such unmusical sounds. Bach must have been such an insensitive lout, too, if Charles' temperament is to be believed as stemming from Bach?!
There are probably other carefully calculated points in that posting, also, that I haven't even caught! Charles is that devious, regularly, in putting up things that anger musicians and belittle the value of serious work. He does it on the list, too. It's a regular Charles thing to do: put up misleading half-truths and misquotes and false connections, all to make musicians and researchers look stupid, while on the surface his words appear so innocuous that they could not possibly be offensive. His paper itself is more of the same.

SUMMARY: Charles is parading this work around the web with hardly a stitch on it, and we're supposed to be impressed by the mathematical and musical results proposed through this. Musical science be damned; and that's obviously his point. As novice work he's come up with something that convinces and amuses himself; so what? Musical science isn't garbage; but anti-science is. Charles' paper, and his promotion of it, is either a very elaborate (im)practical joke at the expense of Bach and of serious researchers, or it's the delusion that someone with no demonstrable musical training or experience can come up with something as valid as scientific researchers in music do. (And that idea, in turn, was proposed on the BRML on June 20th
and May 15th
by Mats W, both times in messages that cast all academic mastery as garbage and objectivity as a sham, since there's supposedly no "hard" science involved in music). Therefore, the notion of putting up meaningless garbage against the field of musicology isn't even original to Charles; it's a team effort of people seeking to knock down whatever they do not understand as a science!

Additional remarks 7/15/04

At 07:01 AM 7/15/2004 +0200, Charles wrote:

----- Original Message -----
From: "Brad Lehman" <>
To: <>
> - My accusation that he has plagiarized from me is still there especially
> in the area of analyzing the sizes of intervals in "tetrachords" from
> major and minor scales.  Why would Charles even look for that aspect
> of the analysis, unless he's lifted it from me without citation?  It's not
> found in the normal tuning literature (as he'd know IF he were familiar
> with the tuning literature); he simply got it from my on-list remarks!
> I've seen a discussion of "first and second tetrachords" in a 19th century
> American solfege primer, which I duly credited in one of my footnotes.
> Even there it's not about *distinctive* tetrachords, but simply an
> understanding of the way scales can be broken into halves, four notes
> each, to help students understand the reuse of the syllables Do, Re, Mi,
> and Fa. It doesn't have any connection in the tuning literature to any
> differently spaced *intonation* of those notes, except that I've used it
> in one of the sections of my paper, directly CONTRIBUTING TO and
> expanding the tuning literature in that regard (a new way of looking at
> the music, through additional melodic analysis)!  I mentioned the idea
> on-list on May 21st, at
> and yoink, it showed up in Charles' paper scarcely a month later, without
> any attribution, or any footnotes explaining where he got the notion of
> "tetrachords" at all--or why we should care about them.  Looks like
> plagiarism to me.

In revising his tuning paper to take account of reviewers comments, new
inputs, etc., Mr. Lehman, in addition to citing the tetrachordal analysis of
my own paper, may also wish to include a reference to works such as John
Chalmers Divisions of the Tetrachord (which exhaustively details ancient
Greek tunings and lists over 700 historical tetrachordal divisions of the
43 interval, outlining many new intonations), or perhaps to earlier works
such as Ptolemy's Harmonika and the treatise of Aristoxenus.

Several points here:

A. Let me see if I understand the double standard here, correctly. I've mentioned tetrachord analysis in a BRML discussion in May 2004[1], from work in my own paper for a refereed journal. The next month the technique turned up without acknowledgment in a paper on the internet[2] one that has no scientific validity at all[3] and has gone through no pre-"publication" review as to its accuracy[4]. The author of that one, Charles Francis, has not mentioned tetrachords previously in any discussion that I've seen, before this "publication" of his paper. Nor does his paper explain why they're important, or why he's relied on them as part of his proof[5], or where he got the notion to use them at all. They just pop in there as a premise without being crafted into the flow of his logical conclusions, as presented; it's meaningless. (See also (F) below.) Yet, prompted by Francis himself I'm supposed to revise my own paper and cite Francis as a useful source of tetrachord analysis (or, indeed, anything)?! By this bizarre reasoning, a real musicologist (me) is supposedly responsible to cite unscientific and meaningless guesswork (which anyone can put up on the internet, without any checks and balances) as an important source; but writers who don't treat musicology as a valid science are not responsible to cite anything, wherever they happened to get it. If I'm expected to cite Charles Francis on this point about tetrachords, in a serious journal, such a citation would merely condone his plagiarism (whether he got his uncredited ideas from me or elsewhere)! Since when are scientists responsible to credit non-science as sources?

B. How does Charles Francis "know" about the John Chalmers book? Has he actually read and understood it prior to 6/25/04 (in which case it should surely be cited as a reference in his paper, given that his paper places such emphasis on tetrachords as a part of his faulty proof!), or has he simply looked up some internet review of it more recently and summarized the review here to twit me?

C. Charles Francis' paper, and his follow-up comments, have indicated that the aim is merely to mock musicology and cast it as a non-science. If Mr Francis believed that it's a science, and considered himself a qualified scientist in this field[6], he would be able and willing to respond to the technical questions that have been presented as challenges to his paper (see both above and my 6/29 review). He also would have had his work checked out by experts before public distribution of it, to make sure it's accurate; that's what scientists do. He would have included recent sources as part of his research, and would have included a section of acknowledgments to experts who assisted with his paper. But instead, he has sought merely to dodge the questions of fact about his material, and to belittle the person (me) who brought them up. Instead of supporting his own work in the follow-up discussion, by answering the questions that challenge its content, it's one dodge after another. What's the opposite of science? Snake-oil sales at a carnival?

D. The Acknowledgments section of my paper thanks people who have been helpful in private discussion of earlier drafts of my work (that is people whom I have trusted enough to show those drafts to, for expert advice!), and people who have helped me to get copies of published materials that I have cited (i.e. reference assistants). Several members of the BRML are already in that submitted list of acknowledgments, for those reasons of off-list assistance and encouragement.

E. As for primacy of ideas in any part of my paper, I'm obviously covered on this one, proceeding carefully from the first day of the project. If it ever becomes necessary to contest the sequence, my defense is easy: various people in my Acknowledgments section have the (always dated) earlier drafts of my paper, as printed and electronic copies. The e-mail trails of my private correspondence with these people still exist, as well; I can trace the ideas as they took shape.

F. Why is Charles Francis even arguing for the first possession of the "unique tetrachords" idea, at all, except to amuse himself and to continue this anti-scientific charade? As demonstrated yesterday[5], the point is insufficient proof anyway, since other temperaments with "unique tetrachords" have already been presented; the creation of a new one proves nothing, in itself. I'll summarize, and see also the "Discussion" and "Conclusions" sections of his paper. Charles has taken as one of his premises the assumption (from where? it's uncredited) that "unique tetrachords" mattered to Bach at all, and that the finding of a temperament whose tetrachords is unique will prove that it originated with Bach. (That's two fallacies right there, so far.) Additionally, he's cited "explicit key colour and variety" as another way of saying that same thing, but again has failed to show why it would matter to Bach; it's just a premise of his own, without sufficiently explaining why (historically, in Bach's milieu) it would matter. Therefore, with his points about "unique tetrachords" he has actually proven nothing. All he has done is to mess around with several alternate readings he has forced from the alleged evidence of BWV 924, and stopped messing around when he found the "unique tetrachords" he sought as his premise, and has claimed that this therefore stems from Bach. Well, it doesn't. The recycling of premises as conclusions isn't proof; any scientist should know that. The obvious corollary here is: Charles Francis does not consider musicology a science, subject to the normal rules of logic and scientific method. Either that, or his own scientific degrees (as claimed) are themselves a sham as well. In the responsibility for accuracy in the material, the field of keyboard tuning, when is Charles Francis going to present an adequate defense of his paper, to demonstrate that it should be taken seriously at all? A simpler and more honorable alternative, of course, would be to retract the entire paper and admit that it was all an anti-scientific hoax. When scientists are wrong, they say so and move on to do something else. To preserve Mr Francis' credibility as a scientist in any area, perhaps that would be the wisest course of action by him here: to get on with his life and stop pretending to be a musicologist. Or, if his indeed has the musicological acumen to support his paper, then by all means let us see it happen.

G. A simple, direct, honest response is deserved to the following question of the tuning literature listed at point (4) above: exactly which ones (if any) has Charles Francis read? And, if so, why are these standard materials not cited anywhere in his paper, along with a discussion of the position in which his alleged discovery should fit into this established field? These sources all contain material that refutes the scientific validity of his proposed temperaments, and conveniently he has not used them. Casting himself as a competent researcher in this field of keyboard tuning, how does he explain this discrepancy?


[1] from 5/21/04

[2] "published" on 6/25/04

[3] The reasons are demonstrated at and

[4] That's according to the claims of the "publisher"; see

[5] The fallacy of using them in the proof is explained at

[6] The citations of scientific degrees at the top of his paper imply that his degrees have something to do with the content to follow...even though he has not made it explicit that they are in any relevant area whatsoever. Details, please.

Brad Lehman