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The Keyboard Temperament of J. S. Bach

John Charles Francis, BSc (Hons), MSc, PhD
CH-3072 Ostermundigen, Switzerland

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Charles Francis wrote (July 16, 2004):
[To John Pike] I categorically deny all of Brad's allegations. I consider his unjust attacks on my integrity are damaging to my personal and professional reputation. Moreover, I note that in the past, he has similarly attacked other list members.

Check the publicly available newsgroup archives and you will discover my interest in tuning goes back many years. I have been a member of both the Alternative Tuning and Tuning Maths group for over three years, something you can easily verify by joining the group and checking the dates for yourself. I was, moreover, invited to join a privately run tuning group by Dr. Kellner, a man with 51 publications on Bach's tuning under his belt, and someone recognised as the world leader in this area (guess how many organs worldwide have Kellner temperament). OK, Bradley trashes the peer-reviewed publications of Dr. Kellner as smoke and mirrors, but that is par for the course. Incidentally, Bradley's approach is far from scientific: would a scientist refer to a tentative hypothesis of his own as "Bach's Temperament"? If he achieves 51 publications like Dr. Kellner, will it be Bach's Temperament. What then of Dr. Kellner's claim to have discovered Bach's temperament?

I hope Bradley stops this kind of behaviour right away, because it contradicts the guidelines of the BCML/BRML and the good spirit which has characterised these music lists for so long.

I would not like waste the time of the members on personal arguments. Therefore, I say no more about this topic and hope Brad does likewise.

John Pike wrote (July 16, 2004):
[To Charles Francis] I was aware that Charles was interested in tuning and that he was a member of at least one tuning group. I admire the knowledge he does have on this subject....certainly a lot more than me. However, I do not think his knowledge, skills and expertise were of a sufficient level to produce this paper and my criticisms of his paper still stand. Although fully qualified as a doctor and as a general practitioner, I would never dream of writing a paper on any aspect of general practice since I know that I just don't have the necessary expertise. This despite being a professional in my field. To have a keen amateur interest in something and to know a fair amount of knowledge in a particular subject is one thing, but to claim to have the expertise to write an original paper on a subject (which implies being a leading authority on that subject) that will stand up to formal peer review, is quite another. Brad's paper has been through a very rigorous peer review process and ! has been accepted for publication. Charles has had the good grace to congratulate him on a significant achievement. Why does he now seek to undermine that act by further criticism of his work in such paragraphs as: "Incidentally, Bradley's approach is far from scientific: would a scientist refer to a tentative hypothesis of his own as "Bach's Temperament"? If he achieves 51 publications like Dr. Kellner, will it be Bach's Temperament. What then of Dr. Kellner's claim to have discovered Bach's temperament?"

While acknowledging Dr Kellner's expertise in this area, and that of others, and while acknowledging the significant achievement of 51 papers in this field, I am sure he would be the first to accept that new evidence may come to light that would change previous beliefs about that field. Any professional is always on the look out for new material that may change the way we think about things. No-one would be so rash as to dismiss something without having first studied it. We are not in a position to do that yet since Brad's paper has not yet been published. Brad claims to have found new evidence, his paper has been accepted, and we should all wait now to see what effects his work has on Bach performance. Anyone with a serious interest in this field would do no less.

Bradley Lehman wrote (July 16, 2004):
[To Charles Francis] I respond here to this, although (as experience on the BRML/BCML has shown) it most likely will not be taken seriously by the people who most should do so. Let it serve also as a personal introduction to the group; other members here should perhaps also offer personal histories about training and experience in musicology and performance, so we know the practical and scholarly background which each brings to the discussion of Bach's music.

My concern is, foremost, with the accuracy of material as presented. Bach scholarship is a serious scientific field of inquiry; so is performance practice. There are professionals, and amateurs, with huge amounts of dedication/time/training/money/careers invested in this expertise, and the academic credentials earned through it. The formal training is a serious thing, and it shows both a level of competence in the material and the licence to teach it at accredited institutions, beyond merely scattering ideas upon unmoderated internet discussion groups. I relish the reading of oddball ideas as much as anybody does, but when such assertions clearly cross the verifiable scientific findings in these fields, I speak up and gently suggest where one can go find out more about it: the university programs and peer-reviewed reference books, articles, and dissertations. Academic verification of ideas is worth quite a lot.

The "attacks" (as reported by Charles!, from other forums) are not personal attacks! The perception arises in situations of the following pattern: a member of the discussion asserts various things which are simply not true and easily verifiable as untrue (see the above paragraph); the member refuses to admit even the possibility that he or she could be wrong about it; the member refuses to take academic findings seriously, but instead digs in the heels in personal pride of being "unspoiled by academia" (however one wants to put this). In short, it is the elevation of naivete and guesswork above the value of serious learning and experience. At such moments in such discussions, I become exasperated at others' unwillingness to give academic expertise its earned due (whether that's expertise as presented in published materials, or in the discussion itself); and that's when my remarks are sometimes perceived as personal attacks, in that exasperation. But, from my perspective, it's only from running into the brick wall of other people's stubbornness and refusal to take academic scholarship seriously: their arrogant overruling of it whenever the results don't suit their preconceived notions, and their refusal to support their own assertions adequately when the content of them is challenged in discussion.

The current discussion about tuning is yet more of the same. Charles has refused to address any of the technical issues which I presented at:
and: .
Instead, he has tried to recast the discussion as if I have been attacking him, and as if my personal character should be thrown into question. (And, by implication, this would make him completely free of any wrongdoings...if an opponent is shown to be a villain! Well, that's a fallacious method of reasoning, right there.) His posting from today, quoted above, is more of the same: the allegation that it's more important to examine my character than to address the technical and musical problems that have been presented as challenge to his work.


Has Charles been a member of alternative-tuning newsgroups, as claimed? OK, fine. Granted. He's interested in the topic and has some connections with other people, especially with those who play with their own synthesizers and invent new music on new scales; quite a different thing from theresearch into historical tuning methods of the 17th and 18th centuries, but granted. Mere membership in discussions does not denote expertise anyway; it merely offers more opportunities to copy and recycle other people's work, without crediting it adequately, and without working through it sufficiently to make bring it into one's own understanding. Anyone can cite others' comments from anywhere on the internet; the ability to do so does not denote expertise.

The important thing here, always, is accuracy of the work as presented. Can Charles' paper stand on the information as presented, or can't it? My contention (in my professional/expert opinion in this field!) is that it can't, and I've presented the explicit reasons why it falls apart. He has not addressed those reasons, to support his assertions, but has merely counter-attacked with allegations about my character. That's not a proper scientific response by him. His work, if he wishes it to be taken seriously, needs to go through scientific review and be supportable through such a process. I suggested at least 20 technical points on which it already fails such a process; other experts in this same field will probably be able to find additional ones. The point is, the work itself is inadequately prepared and inadequately defended, to be considered for any validity.


As for Dr Herbert Kellner's work, his 50+ publications about his own invention which he claimed was Bach's tuning: again, the problem is in THE WORK. From a scientific perspective, work is either right or wrong on the merits of the evidence, regardless of who presented it or how many times he said it. Anyone can foist faulty premises on the public dozens of times, and still be wrong because the premises are wrong. That's indeed what has happened in Kellner's case. (And Kellner's own degrees were in engineering, not music! Obviously, on the evidence of his publications, he was better equipped to work with numerical business than to address the music and history.) I'm not the only tuning expert who has found his work seriously wanting, in technical/historical details and in (un)musical suitability to the repertoire; among the most notable who have criticized it in print are Mark Lindley and John Barnes. Kellner's methodology is deeply flawed. That's why his results are wrong: they overlook important evidence in both the music and the historical record; and his method to "prove" his points replaces the addressing of that problem with mere pseudo-mystical mumbo jumbo, as if we're not supposed to notice the bits being swept under the carpet. Kellner fell away from his own strengths as an engineer, replacing his own best arguments with pseudo-religion!

To summarize the argument as he presented it in his own published papers: Kellner's premise is that Andreas Werckmeister had a secret unpublished system reserved for his own use (rather like keeping the best wine hidden away in the cellar, away from all guests) but that Bach somehow knew about it, and Kellner himself "discovered" it in the 1970s. Simply, Kellner has taken Werckmeister's most famous published temperament (having 1/4 Pythagorean comma fifths C-G-D-A and B-F#) and shaved it down to 1/5 comma, so it goes C-G-D-A-E and B-F#. This indeed smooths out the musical landscape a bit; but so what? And John Barnes, in 1979, did the same thing again by shaving it once more to 1/6 and putting it to F-C-G-D-A-E and B-F#. In the other direction, J P Bendeler (Werckmeister's own professional colleague) had given one with 1/3 comma fifths as C-G-D and B-F#. All these temperaments are essentially the same in character, putting the one piece into B-F# (where it does some nice things for the sharp-side major thirds) and all the rest in the core of the natural notes: where Werckmeister's own goal was to convert the sound of regular meantone temperaments to something more circulating, with a minimum of work (pipe-cutting and rebuilding). Werckmeister indeed achieved his objective, with this and another somewhat workable solution; so did Kellner and Barnes, by smoothing him out. But has anything of this to do with Bach? No! And, all these temperaments fail technically for the same reason: for the way they mistreat the keys with flats, according to the evidence of Bach's music. No amount of gematria will address that problem. (Nor do the new bits of gematria offered in Charles Francis' article...they equally prove nothing, because that method of proof/reasoning itself is flawed...but we digress.)

Kellner, for his part, spent the remaining 30+ years of his life writing article after article to market his own invention. As a salesman he did convince some people. But his "proofs" as he offered them elevate truisms about the equal-beating of all 1/5 PC systems, without showing that such truisms are necessarily any better than the similar properties of 1/6 or other systems: either for mystical reasons or for the music. Another truism of his is the coincidence that his B-major triad has some proportional beating in it: because of the way he's laid out his circle, and decided where to put his final fifth into B-F#! Truisms are truisms, and all Kellner has done is to assign undue significance to them, and then to make alleged connections to Bach through numerology (which can be forced to say whatever one wishes it to say). For example, one of Kellner's papers in French spends pages and pages on the search for the number 369, counting notes and beats in Bach pieces; and claims triumphantly that this "proves" his own temperament. How so? Well, it's all made up, that's how so. Other papers of his document his enterprising searches for the magic numbers 5 and 7, which supposedly prove that his solution could be the only correct one; overlooking the fact that there are thousands of ways to distribute readings of 5 and 7 numerology into other temperaments than his own.

Serious musicology--as in consideration of history and the music--does not need to fall back upon numerology, gematria, and coincidences. Kellner's work is a mockery of serious research, whether he or his peer reviewers who passed it ever realized that. Lindley certainly realized that problem, and that's why he is so dismissive of Kellner's "findings" in the articles in The New Grove Dictionary of Music and Musicians. Kellner's temperament sounds pretty decent, musically, in repertoire that never strays far from 17th century norms of the meantone environment, staying mostly in the keys with fewest sharps or flats, with the occasional accidentals brought in from outside the Eb-Bb-F...B-F#-C#-G# core. Of course it does: as a recycling of Werckmeister (whose temperament had the same musical goal) the results are rather smooth in that repertoire.

But, again, that's not Bach's repertoire. His music goes much further afield than that, even from the earliest years of his career. So does some other people's. The proof of a Bach temperament has to be much more substantial than Kellner (or, indeed, Charles Francis) has offered. Arbitrary gematria, beat-counting, ornament-counting, and the like: it's all smoke and mirrors to elevate truisms and make them appear more important than they really are.

The more papers are published to recycle the same mumbo-jumbo and invent new pseudo-mystical business, the more it looks like a desperate attempt to save face (instead of simply admitting that the original results were mistaken because of poor premises and poor use of the evidence, and moving on to do something real scientists do when they're able to admit that their work was in error). That's my perception of Kellner's published work; and now also my perception of Charles Francis' internet paper as well.

What's really important? The music itself, and the SOUND of it, and the ease of performing Bach's repertoire in it, beautifully!


What is my personal background in this topic? I have been working as a professional harpsichord tuner (and, of course, more notably as a performer) since 1983 when I was a university assistant assigned to take care of the institution's instruments. Through my teacher's guidance I studied all the mI could get, and especially the books by Barbour (1951/72), Jorgensen (his first one, Tuning the Historical Temperaments by Ear), and Blackwood (The Structure of Recognizable Diatonic Tunings, as soon as it came out in 1985). And of course I did all this stuff hands-on
in the regular maintenance of the harpsichords and virginal and continuo organ, learning how to tune the instruments in dozens of methods, by ear, counting beats and proportions. I was simultaneously a major in both mathematics and music, so this topic itself suited me especially well: exploring both the theory and practice.

Later, in graduate school 1989-1994, I took it much further: going into the tuning literature and the keyboard repertoire more deeply, and using this topic as one of the major components of my doctoral degree in harpsichord (including public lectures, and the oral defense to my dissertation committee). This was, and remains, the primary topic of my research interests; and, of course, it affects the sound every time I perform anything or am hired to tune for others' gigs...always trying to supply a temperament that will be appropriate to all the music that is to be performed. These are eminently practical things to know, for a player of most of the harpsichord repertoire.

From 1984 to 1994, employed on the side as a professional church organist, I was also responsible to keep the pipe organs in tune and regulation, and to tune additional continuo pipe organs (from scratch) for performances of oratorios and cantatas. In the early 1990s I spent a week assisting an organ builder in the repair of an organ that had had water damage, from a faulty roof: a week I consider very well spent in learning more about the inner workings of pipe organs! And, of course, I have maintained friendships and correspondence with builders of harpsichords and organs during and since graduate school: rather like Bach's network of his own colleagues, I hazard to suggest. All these aspects of the musical and technical arts inform one another: the intermixing of music, mathematics, engineering, and instrument building/maintenance. Some of my closest friends outside music are professors of mathematics and physics; we discuss all this stuff, as well, from mathematical perspectives.

Currently I have at home a harpsichord, a virginal, a clavichord, and a 19th century reed organ; and am course are responsible to keep them in playing shape for myself and my family. These are marvelous tools for experimentation with various temperaments, since it's easy to set temperaments on the harpsichord and virginal in 10-15 minutes (the same amount of time it was reported that it took for Bach), by ear. The clavichord requires a bit more time, since any conversion of temperament requires the bending of some of the tangents to one side or the other: not something one wants to do frequently, for the health of the instrument, as it stresses the metal. Therefore, the goal of a "set it and forget it" temperament for all purposes is especially attractive on the clavichord, for the same reason that it must have been so for Bach. Ditto, on pipe organs: some temperaments are different enough from one another that one simply cannot do it it willy-nilly without adding or removing material from the pipes. Temperaments, within some tolerance for adjustment, must be built into the instrument. That is the point that Werckmeister et al were addressing: the conversion of 17th century regular meantone schemes into more gently circulating temperaments, with a minimum of work rebuilding the instruments.

And, indeed, through my research (which indeed has taken 21 years to get to this point, the current stages of the discovery) I have discovered exactly what Bach's preferred temperament for harpsichords/clavichords/organs was! This discovery is through a thorough examination of the music and other documents extant from Bach's life, and of course also through knowing what is normal and practical on the instruments themselves, as explained above. One has to know all these pieces to grasp it, and to see why it matters, and to see what difference it makes in Bach's music: the problem to be solved is an extraordinarily complex one. In consultation with about a dozen of my expert colleagues (scholars/players/builders) over the past months, I have written this discovery as a formal paper, which has been accepted for publication in a musicological journal in 2005.

Until it is issued, there is not a lot I can say about its technical details: especially since, as is apparent, people exist who are both eager and unscrupulous enough to try to scoop the findings for themselves, and spray them out there without me. That is what has already happened, I allege, with the "publication" of Charles Francis' paper on the "Eunomios" web site: one which has bypassed all layers of scientific peer review and indeed which is bunk, on the technical and methodological problems in the paper. My earlier remarks about my own paper on the Bach Recordings and Bach Cantatas lists have turned up with all too much familiarity (but some incorrectly forced interpretations) for this to be a coincidence.

But again, my main quarrel is with THE WORK and its validity, wherever any author happened to get his materials; regardless of the alleged honesty or dishonesty of an author, the work has to be able to stand on the evidence as presented, and on valid logical methods where the existing tuning literature and historical literature is also taken into due account. The problem to be solved is so complex, and so multi-faceted, that it really does take at least 15 years of background and experience to encounter and understand all the pieces that matter, from a practical point of view. That, as I explain in part of my own paper, is why this hasn't been discovered before: those who have worked on it have brought faulty premises and additional assumptions into the material, preventing them from seeing the necessary connections and possibilities in the evidence.

This is all a scientific inquiry, not to be taken lightly or to be fluffed through by any who haven't brought the interdisciplinary background to the problem (especially, the hands-on ability to play through all Bach's keyboard repertoire and determine empirically what works and what doesn't). Synthesizer knock-offs of MIDI sequences simply don't do it, as they don't give the hands-on experience tuning and playing the intervals, and hearing them in the complex interactions of physically vibrating strings. One also has to understand how tonal music is put together in the first place (with extensive background in counterpoint and other music theory), understand the normal field of tuning possibilities before and during Bach's lifetime, and only then begin to see how Bach's solution offers something useful and exciting. That's why the project is such an overwhelming bit of work, and why I have been careful to have all stages of it checked out with fellow experts before publication: that's the scientific process of such a discovery, proceeding through the proper steps for scientific publication.


Charles' conjecture above, allegations about my own scientific methods, is yet more fluff to belittle me. He hasn't seen my paper, and therefore is in no position whatsoever to judge what is said in it. His on-list instructions to me to stop my allegedly unscientific behavior? It just looks to me like a sideways complaint that I've found embarrassing scientific problems with his work that he's not prepared to refute, and (once again) is merely trying to make me look like the unscientific one here. To try to save face, he is counter-attacking my person instead of supporting his work. And, his supplying of further MIDI samples does not support the work, in any meaningful way; the problems as presented are ones of logic and research method, and historical and technical objections with the paper. The MIDI stuff is just a further attempt to distract a public away from the importance of those problems: misdirection! Serious musicology has been turned into a stage show here, as if that's all that research en: distraction away from responsibility to the material.

Of course he's eager not to have me continue pointing out the problems with the unsupportable work he's offered; he hasn't yet addressed the ones already presented (where if he had brought any experts into his research in the first place, the work wouldn't be so full of technical errors). This isn't a personal attack, by me, but simply a call for responsibility to the material. It's the scientific review that is merited by the material as presented; no more, no less. He's of course welcome and encouraged to get this checked out with additional experts...but the same problems will continue to come up until he fixes them or retracts the piece altogether. Scientific responsibility in a scientific field!


To return to the topic of a personal introduction: I'm interested in discussing other Bach topics as well...with people who take the scientific inquiry of musicology and historical performance practice seriously. The work itself is meaningful to me, and I'm concerned with both the scientific accuracy and the art of it; music is both, with neither side of it to be excluded.

If, instead, all this is to be turned into a sideshow where the fields themselves are belittled and mocked by those who refuse to study them, such a farce is a waste of my time. That is exactly why I am not currently active on the Bach Cantatas list anymore: it became such an anti-academic and anti-scientific carnival, that in my opinion the music suffered too much. I also couldn't stand to see the regular bashing of my friends and professional colleagues (and my potential employers, as a freelance musician!), at the hands of people who are not qualified to judge the validity of work in the first place. I'm interested in serious discussion in which expertise is respected as meaningful, and not simply overruled willy-nilly by people who wish it were worthless.

Cara Peterson wrote (July 16, 2004):
Charles Francis wrote:
< I hope Bradley stops this kind of behaviour right away, because it contradicts the guidelines of the BCML/BRML and the good spirit which has characterised these music lists for so long. >
Thank you very much, Charles!!

Cara Peterson wrote (July 16, 2004):
[To Bradley Lehman] Mr. Lehman, I see exactly where you are coming from on that, but is it really in your call to decide who gets to participate in these? Again, I am not a professionally trained scholar (we can argue about musicianship, though I'd prefer not to) but I do know a considerable amount about Bach, his life and his music. It makes me wonder: I know a huge amount about what we discuss; but I'm not a scholar, due to being 14 and having a lack of funds. Am I still welcome in your eyes, Mr. Lehman?

Bradley Lehman wrote (July 16, 2004):
[To Cara Peterson] Of course, absolutely! As you said on the BachRecordings list in a similar message, you are eager to learn about the music. As you said over there, "If I don't know anything on the subject, however, I don't make any stupid assumptions. I read to learn more."

That is quite different from the behavior of those who buy a collection of books and recordings, and refuse to enroll in music school (as scholars and/or performers) where they could learn how the music really works. To excuse themselves from any formal training that they could demonstrate, they pontificate forever that they already know the only correct way the music should go, and that they know better than expert performers and researchers how it must be done. The problem is one of pride and arrogance: that refusal to admit that there really are things they don't know, and that experts know better than they do. Instead, they bluff, pontificate, "make stupid assumptions", put up snide and misleading remarks about real experts (to make the experts look stupid), and try to beat down any who would show them the objective reasons why their own assertions are flawed. Anyone who really knows the material automatically becomes the enemy, to such people. Anyone who asks them to substantiate their claims automatically becomes the target of the next attack.

There is always more for everybody to learn, and an appropriate spirit in which to do that is (as you said) to be open to new information. The crucial difference is attitude. Personally, I consider it a joy to learn more about Bach and his music just about every day, through continued study regularly and through playing through all his music, and talking about it with colleagues and other music fans. Such an atmosphere, in my opinion, makes it worthwhile being a member of the discussion.

And, as you also pointed out over there, I'm not the list owner--and the list owner gets to make the rules. I merely suggested a guideline that I think would help to keep the atmosphere here welcoming to any career-serious scholars and performers who might wish to join it. I'd like to invite some experts of my acquaintance, if it's really going to be a safe and meaningful place to talk about serious issues in the music (as the name of the group implies). What would make it worth their time and energy, to the benefit of all here who really are here to have meaningful discussion?

My concern, from several years of participation on BCML/BRML, was that those two lists are not welcoming in that way: and indeed, I have known several expert members who left directly because of the problem. They received hostile personal attacks from other group members, such that it was no longer worth subscribing. Too much time and effort is spent defending the basic validity of the field itself against the postings by several members whose personal agenda is to show that it's all arbitrary and wrong, or that anyone can look up things in reference books (and thereby refute expert points adequately!) without needing any sort of training or experience to understand it. It's that attempt by the naive to assert personal triumph over those who know better. Most notably, there's been a string of regular condemnations of expert singers, continuo players, and conductors who are allegedly too stupid and too misguided by scholarly books to read the music correctly anymore.

The anti-academic climate is made that way by just a few, but it poisons the whole discussion: casting performers and researchers as egotists and charlatans, unable to do their own jobs properly. They also try to make it look as if the whole problem is the fault of those (including myself) who really do bring the experience to the discussion, and none of their OWN responsibility for turning into the mess. I see from your several postings here already that you've already bought into this: that you're chastising me for being the problem! Those who speak our minds frankly and directly, as I do, are seen as the troublemakers. Meanwhile, those who disguise their criticisms (egregiously harsh abuse directly against scholars and musicians) in sweet-sounding language and secretive implications get to make up whatever destructive garbage they want to, and claim that they've done nothing wrong, that they couldn't possibly be the problem. [It reminds me of the double standard in movies: if several foul words are used, or if body parts of nude people are shown, the movie gets a strict rating as warning for those who might be offended; but movies that depict abusive relationships and murders and other violence get by with no restriction at all. Responsibility is turned upside-down.]

That's what I object to: the notion that education and experience in the field of music are really worth nothing of value, so nobody need bother with it; and the notion that the academic musicians/scholars are the problem, while the critics and pseudo-scholars get to make up anything they want to, without responsibility or accountability. It prevents there from being any really meaningful discussion about the music and the techniques to perform it. And, after all, wasn't that the point of joining the discussion in the first place?

I am absolutely weary of being forced to defend myself and my professional colleagues against the allegations and "corrections" of critics who can't (and wrefuse to) do the work themselves, and who belittle the value of everything, and who attack personalities rather than discussing the music. That's why I suggested that maybe this group should be for those who really respect musicology and the inquiry into performance practice as serious sciences. As arts, too, of course; but the scientific part shows us how to discern differences between careful/responsible work and made-up garbage.


Somebody, please convince me that I should even go invite other serious musicians/researchers to join the discussion. Will they be subjected to the abuse that I regularly experience on the BRML/BCML, be forced into self-defense, or will this really be a safe and productive place to discuss the music and scholarship as advertised? I've already been insulted directly twice here (at least) today, both times by Charles Francis; what would convince me or anyone else that the same treatment would not happen to any other expert musicians and researchers who join, the moment that they too become targets of his ad hominem method of attack?

His allegation is that I do not understand how to do my job properly as a trained scientist in musicology (even though my degree says that I indeed do); he's offered a whole string of mockeries and scoffs at:
along with a set of personal attacks on my character at: .
He's presumptuously criticizing my work before ever reading the paper; to preempt me from being able to write the paper, as if I'm not smart enough to have done so. That's an ad hominem attack on my person rather than a reaction to my work. I have taken these insults as they quite obviously were intended. What evidence is there that a serious discussion is to had here, if I continue my own membership and possibly invite any colleagues to join?

Bradley Lehman wrote (July 17, 2004):
Charles Francis wrote:
< Bradley's argument is really remarkably simple:
I have the true temperament, a curse on those that have other solutions.Therefore, Kellner, Charles and Barnes are all incompetents. Meanwhile back in the scientific world, Quantum Mechanics, Relativity, Evolution remain as mere theories. (...) >
What's this about "mere" theories? The scientific meaning of the word "theory" is that a hypothesis explains observable reality, offers predictive value for data points yet unknown, and organizes the evidence in a convincing way. The hypothesis is supposed by presentation of the evidence. What's "mere" about all that? The word "theory" doesn't mean "wild and unsupportable GUESS!"

My proposal of the particular reading of Bach's temperament is itself also a theory; obviously! The theory stands on the presentation of evidence, and its ability to explain all that evidence better than any known competing theory would do. My first two hypotheses on the evidence have already been refined or discarded, through the process of consultation with my peers during the writing of my paper; they helped me to find better readings of the material, and to discard my first tentative conclusions as untenable (because the evidence hadn't been considered closely enough and completely enough). I caught the first major error myself in the first several days, and a colleague caught a subtler and less important error a month later and helped me to repair it; I appreciate that, and as a scientist am willing to take such correction seriously in the interest of having the work be correct, instead of trying too hard to save face. This is basic scientific method here, and the paper has already been through three months of this winnowing process with a substantial group of experts, each able to help me with different parts in particular. I've acknowledged all their contributions and assistance, as scientists do. What's the suggestion that I don't understand that? If someone comes up with a better theory later, refining or even overturning my work, so be it; I'll be happy to have catalyzed at least some portion of the inquiry, in the interest of having the work be correct and useful. But, for now, my 35 years of experience as a musician tell me that my theory is right on the mark. So do the confirmations from the other experts who have judged the paper and helped to write it.

And, what's this suggestion that music is NOT part of "the scientific world"?! We see here the honest tipping of the bowl, for once: Charles Francis OPENLY does not believe that musicology is a science. He's admitted it! That's a good first step: the admission that a premise is a premise and should not remain tacit. What does that say for his paper, which on the surface appears to treat the discovery of his own temperament as a scientific process, from an author who OPENLY does not believe that the science doesn't exist? I'll answer that rhetorical question myself: it absolves him from any responsibility of using scientific methods correctly in his own work. To him it is sufficient merely to provide the appearance of scientific validity. Well, that's a problem.

< 2) If Barnes method is sufficiently tweaked (to correct the deficiencies noted by Bradley), voila, Bradley's conjectured temperament can be forced to outperform my own. >
Who's tweaking the Barnes experiment? It's flawed, as I said, by having a much too small sample set and ignoring minor-key music. That's quite an obvious observation from the reading of his article itself. To try to fix that, sure, one could shovel many more pieces into it and therefore improve the sample set; but the experiment would remain a statistical analysis on the PREMISE that Bach's music should deliver a linear fit, as to frequency of use of the major thirds. Barnes himself pointed out that one can't expect Bach, an artistic musician, to have done so that reliably; there are so many other musical factors informing Bach's choices and opportunities as a composer. The experiment remains, and must always remain, merely a tool to measure Barnes' own premise there.

There is no need to "correct" Barnes' experiment at all, because the satisfaction of it is not sufficient proof of any Bach temperament anyway, but merely a tool to sift out the most outlandish ones. It already does that well.

Another excellent tool to weed out the outlandish ideas is to play through the pieces that I mentioned at: , among several hundred other pieces. That relies both on absolutely measurable properties of the intervals and chords, and musical taste: the "musical taste" part being defined by the extant reports about Bach's own performances and criticisms of others. That is, it is not sufficiently merely to come up with something that sounds good to us, although that saves a lot of time and effort, helping to discard quickly the junk that could not possibly be right because it sounds awful. The premise, obviously, is that Bach had a fine musical ear and would not put up with junk; and that's documented well, throughout the existing literature about him.

All these tests, including some other tests, are simply a series of differently-shaped sieves to sift out garbage. They're very useful in saving time (throwing out potential solutions that make no musical sense, or come from no historical context around Bach), but not even the whole group of tests together provides sufficient positive proof that a particular result is Bach's. The positive proof is the demonstration of documentation directly from Bach that he had a particular preference, in its historical context. Everything else is corroboration that the reading of Bach's evidence indeed makes musical sense, and therefore that we should care enough about it to it in performance of his music, and therefore to see what it tells us further about that music.

The accusation here today that I don't understand scientific method is noted, by the way, and insult taken. So is the related accusation that musical taste cannot be measured or relied upon in any part of a scientific inquiry. Well, the notion that musicology isn't a science is not my notion, but that of my accuser. His accusation therefore doesn't even make sense, with logical consistency: if (according to him) musicology isn't a science anyway, what's to be gained by alleging that I'm a lousy and incompetent scientist in it?

< Bradley, is of course welcome to respond to correct any misunderstanding on my part! >
Suggestion: why don't you wait for my paper before presuming to criticize what's in it? The time between now and then could be spent usefully by learning how to tune harpsichords by ear and playing Bach's music on them; vital skills in understanding the nature of the work, and indeed the nature of the problem to be solved. The paper can be properly judged only by people who really have expertise in this area, and indeed it already has been. What's this notion that it can also be judged adequately by novices who haven't even read it, and who have never demonstrated any of the requisite background in music theory, history, and performance skill to understand what is being said in it?

As I quoted this morning from Galileo:
"And who can doubt that it will lead to the worst disorders when minds created free by God are compelled to submit slavishly to an outside will? When we are told to deny our senses and subject them to the whim of others? When people devoid of whatsoever competence are made judges over experts and are granted authority to treat them as they please? These are the novelties which are apt to bring about the ruin of commonwealths and the subversion of the state."


Back to the article: The Keyboard Temperament of J. S. Bach [by Charles Francis]

The Keyboard Temperament of J. S. Bach: Article | Music Examples | Feedback: Part 1 | Part 2 | Part 3
Discussions of Temperament / Key Character / Tuning:
Part 1 | Part 2 | Part 3 | Part 4 | Part 5 | Part 6 | Meantone


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Last update: Sunday, May 28, 2017 14:18