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The Keyboard Temperament of J. S. Bach
John Charles Francis, BSc (Hons), MSc, PhD
CH-3072 Ostermundigen, Switzerland
Francis@datacomm.ch
Feedback to the Article - Part 2

Continue from Part 1

Bradley Lehman wrote (July 14, 2004):
Bach’s Temperament

At 01:26 PM 7/14/2004 +0200, Charles wrote:
(...)
7) June 29, 2004, Bradley reports the publication of my paper to the Bach Recordings Group. The paper is, in fact, based on BWV 924, although Bradely does not mention it.
(...)
The chronological list by Charles is at:
http://launch.groups.yahoo.com/group/BachRecordings/message/15008
making counter-accusations against me.
A few steps of the chronology have been cleverly omitted here by Charles. For example:

- On 6/25/04 Charles announced his paper on alt.music.j-s-bach, upon its appearance on Eunomios.org. He did not announce it at all on the BRML/BCML. I heard about it from a professional colleague who got the news through alt.music.j-s-bach, and told me about it on 6/28; he knew already about my paper on a similar topic, which I had already submitted for publication. I spent the evening 6/28 and some of the next day collecting my questions/challenges about Charles' paper into a file for a web page (see the next point).

- In my review of the paper, posted 6/29/04 at: http://www-personal.umich.edu/~bpl/francis-paper.htm
I brought up more than 20 serious objections (as a scientifically astute reader of it) to the allegedly factual material of the paper, and to the methodology it displays. These are serious challenges to the material as presented: giving the paper the expert review that (on the surface) it appears to deserve. At that time I also posted a link to that in the Eunomios forum at: http://www.eunomios.org
and to alt.music.j-s-bach referring members (including Charles himself) to the review. That Usenet thread on alt.music.j-s-bach is still available to the public at: http://tinyurl.com/6jlf3
Charles' response in that thread was patronizing nonsense that I probably didn't tune it correctly, "which is fully understandable as it takes practice to master a new procedure"...claiming therefore that the 10-year-old Wilhelm Friedemann Bach could do this as a beginner, but that I (with 20+ years of professional experience as a harpsichord tuner) could not. Preposterous!

- I brought this material over to the BRML also (with links both to Charles' article and to my review) because I thought it was an interesting creative piece; and because I thought other members here might like to see the way that various on-list comments have been recycled into it by Charles. Since the ideas were stated here in the first place, obviously, they deserve to be discussed here; several members have and had expressed quite a bit of interest in Bach's method of tuning keyboards. Most notably, Charles himself: repeatedly grilling me for information about the project on-list from April to June, and especially requesting that I simply hand him all the cent values from my research so he could try it out. (Which I didn't do, of course!)

- The fact remains: BWV 924 is a red herring (of Charles' own devising!) and has no special meaning as a source of Bach's temperament. I did not mention that piece here on the BRML because it's moot and redundant: anyone who looks at the paper can see immediately what it's based on. Indeed, I was as surprised and shocked as anybody to open his paper on 6/28 and read that he's constructed an entire fantasy world on BWV 924 and on a proposed temperament that makes no musical sense: offering a method that simply would not occur to musicians. Charles' advocacy of BWV 924, and his April notes on-list that it's used in a piece by Sting, is merely of amusing interest but of no import to serious Bach research. Ditto for the use of signed ornamentation as prescriptions for tuning instructions. That is one of many reasons why the solution is so silly, as outlined in my review, in questions which have not been answered by Charles. And, as I have pointed out several times, BWV 924 has not even been used consistently with regard to its ornaments, in Charles' paper; he's forced it to look like evidence that really is unsupportable, once one notices the way he has manipulated the note E. The derivation simply makes no logical sense as presented: even if his explanation of ornaments were valid in any way, he still hasn't used HIS OWN LOGIC correctly to explain his placement of the note E! I pointed all this out on 6/29 but Charles has not addressed any of the problems, in response, either privately or in any forum...or shown that he even understands the technical points of the questions. Instead, he's tried to make me look like a villain for pointing out clear problems in his paper, for giving his work an expert review that should have happened with any experts of his choice, BEFORE publication.

- The main idea for my own paper stems in fact from e-mail conversations with several other people who are not members of the BRML/BCML at all, in private conversation about my own temperament-analysis spreadsheet that has been available on the web since 1997: http://how.to/tune
That was on 3/29/04 and in the first several weeks of April, with several professional colleagues, where I discussed with them the primary pieces of evidence (which indeed have nothing to do directly with BWV 924). And, I have credited them in my footnotes and acknowledgments. I haven't cited BWV 924 at all in my paper, for the simple reason that it doesn't contribute anything to the argument about Bach's temperament. (It's a simple little piece in C major, and all pieces in C major work in all reasonable temperaments; that's not significant one way or another!) The fact that Charles has an inflated sense of self-importance in this is not my concern; he chose to lift whatever he could (probably sparked by my announcement on BRML/BCML that I've found something), and he's misled himself in several egregious ways (mainly by not understanding the material before launching the project, and by taking a coincidental discussion about BWV 924 as if it meant anything). That's his problem, not mine.

- In the proof in my paper, I cite traces of Bach's temperament back as early as the Neumeister chorales, along with dozens of other pieces. Bach's music simply does not work very well with the Werckmeister and related temperaments of the 1690s (Bendeler, et al), for musical reasons which I demonstrate and explain. Obviously, at the beginning of his career, Bach already preferred a tuning in some way other than those. And this is on musical evidence, not the arbitrary gematria of counting ornaments or beats or notes (the same process of nonsense that informed the work of Kellner, and which has led Charles into similar traps). The "Temperament IV" of Charles works even less well in that music than Werckmeister/Bendeler do, as I've already tested empirically as part of reviewing Charles' paper (by playing through Bach's music in his, and in theirs). He has no explanation for this failure to improve upon Werckmeister. Instead, he's fallen back upon the coincidence that he sees 14 ornaments, which doesn't mean a bloody rip as to serious Bach scholarship or to any notions of keyboard temperament; only to the forcing which he has applied to it in his own paper!

- If we're arguing about chronology here, how about this one? A professional colleague of mine, with my permission, used Bach's temperament in a solo broadcast in Europe on May 6th, 2004, playing music by Bach, Handel, and Scarlatti on it. This was (it need hardly be pointed out) seven weeks before the "publication" of Charles' paper on Eunomios. The performer was allowed to use my work on this only by not announcing what it was (he simply plthe music beautifully, without remark about the tuning). This was one of the many practical tests of the work, by myself and expert colleagues, before turning in my own paper to my publisher; practical confirmations that my solution makes musical sense, regardless of ties to any musician living or dead. Another was a performance of the St John Passion, in the first week of June, at the enterprise of another colleague of mine. He tuned both organs for the performance to Bach's temperament, as I had described it to him in an earlier draft of my paper, and he reported back to me that everything went remarkably well. The conductor and the other keyboardist were told only that this is a recently-discovered temperament having some appropriateness to Bach's music. After hearing it in the rehearsal, they chose to use it in the performance also for musical reasons: simply, because it sounds right in the music and makes the orchestra's and singers' performance easier. Of course it does; Bach was an excellent musician who knew what he was doing. [Charles' temperament, by the way, does not do that; with the grossly flat fifths among the natural notes F-C, A-E, and E-B, the string and wind players will mutiny the moment he or anyone else foists this upon them in a practical situation! Has Charles never played any bowed string instruments? How would he propose to instruct a violinist to tune A-E so ludicrously sour, and be taken seriously?]

- I checked out Charles' "Temperament IV" by tuning it on one of my harpsichords and by importing it into a version of my temperament analysis spreadsheet: confirming again that it's preposterous from a musical point of view. It has an artificial harmonic zigzag in forcing Ab-C to be the best major third, while four other major thirds are unacceptably bad, if we are to believe the 18th century theorist Marpurg's assertions about Bach's taste. And, the Ab-C itself is ruined in its triadic context because the Ab-Eb fifth is 33.3% flat: an awful sound on harpsichords, counteracting the improvement he has made to the third. F-A-C is even worse because the F-C is the worst fifth anywhere (42.4% of a syntonic comma flat, since that's where Charles has stuck his schisma without explaining the musical justification of it). C-E is worse than F-A, and both of them are worse than G-B, D-F#, and A-C#; that's just silly, according to the 18th century reports about key organization and key-Affekts. Obviously, "Temperament IV" is a temperament for extremists who don't care about (or perhaps who fancy) random occurrences of harshness as the music goes along...an attempt to make musicians sound incompetent in their musical choices! And, that's not Bach. Bach's temperament has no harshness in it anywhere; and this accords with the historical reports from people who heard his performances.

- Last night, on a whim, I additionally ran the Barnes set of numbers on Charles' "Temperament IV" since I already had all my analytical tools set up that way months ago, to measure the Bach solution for one of my own footnotes. That is: from John Barnes' 1979 article I reproduced all the experimental and statistical numbers from his interpretation of the major-key preludes in the Well-Tempered Clavier, and the way he has plotted them against the relative intonation of the major thirds in various temperaments. Barnes' thesis was that one can plot the number of occurrences of "prominent" major thirds, and extrapolate a linear fit, on the assumption that Bach used the thirds in the common keys more often than the thirds of the classically exotic keys, and that there's something linear about this frequency of doing so. I see now why Charles is so enamoured of his own solution: it fits Barnes' measurements better than the others presented by Barnes do, except for Barnes' own. Indeed, Charles has manufactured his temperament so that it does so: artificially improving Ab major where Barnes says it's important (and Charles has tried to cement this further by citing a document by Hopkins from more than 100 years after Bach's death). Charles' temperament gives an impressively low deviation, by this measurement system. Well, anybody can make up something that suits an existing measurement system in a spreadsheet, and keep fussing around with it until things look good: that's not a musical goal! It's simply the elevation of Barnes' article and experiment above the value of listening to Bach's music, with an ear sensitive to musical detail.

- Evidently Charles has not noticed several other things:

----(1) Barnes' own linear fit for his own proposed temperament (also in the Barnes article) has a creative fib in it: the best linear fit through Barnes' own plotted data is more nearly level through the points than the steep one he published. That is: Barnes' own choice of his line makes it look as if five of the twelve data points fit his linear assumptions perfectly! To reproduce it, I had to force Microsoft Excel to run the linear regression through a forced Y-intercept point instead of letting it calculate the best fit on its own. Yes, I have all the data points reproduced exactly as on all three of his graphs! Barnes' own presentation of his material does not stand up completely to such close scrutiny, through independent reproduction of his own data.

----(2) Barnes' musical sample leading to his data is fatally small and short-sighted: ignoring all the minor-key pieces that are just as crucial to the problem, ignoring all the major-key fugues, and indeed ignoring all the rest of Bach's music outside the WTC. Pieces in G minor, C minor, and F minor are frequent in Bach's repertoire, and especially problematic for tuning; but Barnes hasn't addressed this. He's simply omitted those keys from his analysis!

----(3) If Charles had put his tempered fifths into D-A and A-E, instead of A-E and E-B, while slagging all the remaining garbage into F-C as he has it, he would have got an even better Barnes score as to lower deviations from a best-fit line. He even would have surpassed Barnes' own solution in that regard, while with his actual "Temperament IV" as proposed he has not.

----(4) An even simpler temperament fits the Barnes method much better than either Bach's solution or Charles' solution do: namely, the primitive circulating temperament with 1/5 Pythagorean comma fifths F-C-G-D-A-E and pure the rest of the way (basically, a simplified version of Vallotti, and one that I'd already used as a player 15 years ago just because I felt it sounds good...a pretty good reason for making musical choices). That temperament delivers a lower deviation than any others I know of, and I've run almost 30 of them through the Barnes pages of my spreadsheet to confirm this. That is to say: for whatever it is the Barnes method measures with its small sample set and subjective perceptions (quantified by Barnes), that temperament wins. And it, too, sounds better in Bach's music--in practice--than Charles' solution does; we don't need analysis by Barnes or anybody else to prove musical taste to such a degree! The proof is simple: set it up on a harpsichord and play Bach's music that way. Barnes himself missed that particular 1/5 comma layout, but so what?

If Charles had been intent on merely running with Barnes numbers (as a higher priority than listening to Bach's music itself) and not additionally on ripping off various comments of mine from the BCML/BRML, he might have found this much more elegant solution instead (either of the two I mention here as (3) and (4)) and found some Bach piece to pin it on (the same way he pinned his own concoction onto BWV 924). It would have been a lot less work than he put into his efforts. Either way, the pinning of any temperament from numerical calculations back onto a bizarre and inconsistent interpretation of a piece of music IS NOT RESEARCH; it's merely a creative outlet for people who put numbers ahead of music, and ahead of the historical record. Kellner did it, and Charles has followed suit.

I should add: that 1/5 comma temperament F-C-G-D-A-E is not Bach's, either, even though it happens to fit the Barnes experiment better thaBach's own does. All it shows is that the Barnes experiment is flawed, while it still has some useful predictive value. Bach's temperament (the one in my paper) outscores almost everything else (including Charles' "Temperament IV"), by Barnes' numbers...where the goal is to get the lowest deviation by least-squares from a linear fit, according to Barnes' own explanation. The satisfaction of a Barnes premise simply is not sufficient proof that a temperament has anything to do with Bach; the historical record is much
more complex than that!

=====

- Charles' defensive strategy of counter-accusing ME of being the plagiarist is a fallacious method of reasoning, trying to shift the burden of guilt to another person (me) and implicitly away from himself. The accusation was that he has lifted uncredited ideas of mine from BRML/BCML, and he hasn't presented an adequate defense to that; the ideas presented in his paper have an obvious similarity to my comments posted earlier on BRML/BCML. That, I suspect, is the reason why he never announced the paper here: because people on the BCML/BRML would recognize immediately that he's borrowed so many ideas (both analytical and musical) from my remarks.

- 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: http://launch.groups.yahoo.com/group/BachRecordings/message/14399
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 Charles' complaints that my remarks are allegedly "slanderous", he apparently does not realize that his own paper and the dissemination of it are even more insulting and caustic against musicians: frankly, it casts musicians (and especially Bach) as ignoramuses who cannot hear what sounds good and what does not, and it casts musicologists (through Charles' refusal to use any recent sources) as morons whose work is not worth taking into account. What "slander" is it on my part to point out this destructive subtext of his own paper, for discussion and to invite his defense of his methods? The paper's out there in a public place (two, now), and members of the public include experts who can see holes in the work, seeing beyond the numerical wizardry he's shoveled into the presentation. Why indeed DID he not use any input from current musicians or researchers to inform the material of his paper? That is a question that deserves a forthright response. His use of recent information, and his consultation with people who actually know the material, certainly would have helped him to avoid the gross errors in his premises and avoid the inconsistent use to which he puts his own data! My reactions have been to THE WORK as presented. If he takes that as "slanderous", it's because THE WORK as he's put it out there is unable to stand up to expert musicological scrutiny; there's no need to take that personally. If Charles is not prepared to play in the musicological Big-Leagues and defend his paper against a reasonable set of technical questions, perhaps he shouldn't have put it out there without getting everything checked out first.

- The upside of this, from my perspective, is: because the Francis "Temperament IV" is so far off-base and makes such little sense musically, this is all nearly moot: whatever was stolen from me has been turned into unworkable results anyway (while noting that the process of plagiarism itself is deplorable and unforgiveable). The fact that his proposed temperament sounds silly is easily verifiable by anyone with a harpsichord and the skills to tune it following Charles' instructions: even five minutes of playing normal repertoire makes it obvious that something is seriously amiss. That's, after all, where things really matter most: musicians aren't going to use his solution in public performance BECAUSE IT MAKES THEM SOUND INCOMPETENT as musicians...being more swayed by number-wanking than by listening to the music. The alleged pinning of this back on Bach also makes Bach seem incompetent as a musician. Is that what Charles really meant to say?

=====

My additional comments are long enough and technical enough that they'll probably bore folks here further; so, I've moved them to an additional page at: http://www-personal.umich.edu/~bpl/francis-brml.htm
Again, these are more technical questions that deserve technical response from Charles, to explain the odd choices he's made in his paper to ignore musical and historical evidence, and to run roughshod over 17th/18th century music theory which is readily available in the tuning literature....

=====

Charles concluded his remarks at: http://launch.groups.yahoo.com/group/BachRecordings/message/15008
with the patronizing barb:
< As one who has authored many scores of referred scientific publications, let me add my congratulations to Bradley on achieving this first success with a journal article. >
Thank you. It's always good to write a paper in a field that one actually understands. I feel that I've achieved something important with mine. Musicians qualified to judge the musical and analytical aspects of the work have already confirmed that it's meaningful.

p.s. "Many scores"--what is that, 60, 80, 100? I know that a "score" is 20; what did "many" mean here? Any, if refereeing of scientific publications is obviously important, why Charles' choice to try to short-circuit all scientific review whatsoever before the distribution of his tuning paper, choosing to "publish" it at a web site (Eunomios) where the owners openly pride themselves on not doing any peer review?

p.p.s. I also got word today that the owners of a new pipe organ (currently in construction, to be finished in 2005) are interested in perhaps having Bach's temperament built into it, having seen a draft of my paper. That's exciting: a new organ for a new building, being the first in the world to be constructed from scratch with the correct tuning for Bach's music. I'm eager to hear and play it.

Bradley Lehman wrote (July 14, 2004):
Charles Francis wrote:
http://launch.groups.yahoo.com/group/BachRecordings/message/15008
(...)
< There are, I believe two main alternatives for you to consider:
1) Bradley was inspired to his rediscovery of the unique tetrachords in Bach's tuning system as a direct result of my directing him to BWV 924. Whether he used this as a spring board for some other solution or not is something we may find out, when his paper is eventually published.
2) I contrived an interpretation of BWV 924 that leads to unique tetrachords in all 24 keys (a property that does not occur in any other temperament of Bach's time, by the way). Moreover, this contrivance had the property exactly one fifth is tuned wide (an alledged discovery of Bradley). Moreover, I had to choose a piece that represented a communication within the family to demonstrate it as a trade secret of the Bach's (another supposed discovery of Bradley). Fortunately, according to this speculative line of thought suggested by Bradley, BWV 924 from Wilhelm Friedemann's Buechlein perfectly fitted all these requirements as it had exactly 14 trills (B=2, A=1, C= 3, H= 8 => BACH = 14), so providing a convenient framework to allegedly "reverse engineer" results supposedly "stolen".
If you make some effort to read the paper and try to understand it, you'll soon realise that the proposition of scenario 2, that an arbitrary piece of music can be so interpreted, is totally preposterous. >
As I've already explained in another posting which hasn't shown up yet, the correct explanation is quite a bit simpler than Charles' two suggestions:

3) Bradley actually understands the material (from 20 YEARS of working on the problem and its background!) and has written a paper that has nothing directly to do with BWV 924 one way or another. BWV 924 is meaningless! Charles, to try to get a piece of the action here, is merely alleging that he himself has had some role in this, when in fact he has not...other than wasting huge quantities of Bradley's time and expertise, and trying to scoop the findings for himself. His contrivances are actually quite a bit more extensive than he has explained in (2) above, as I've already reviewed, but to which Charles has fashioned no response whatsoever--except to try to mock and belittle Bradley's abilities as a musicologist and musician, and to try to misdirect all guilt away from himself. Charles' choice of BWV 924 as a source is merely a red-herring created by himself, twisted by himself to look (at least in his own estimation) as if it's meaningful in ANY way!

As for Charles' assertion here in (2) that "unique tetrachords" is "a property that does not occur in any other temperament of Bach's time, by the way"...he's completely wrong about it, probably from not understanding the material or knowing whether "unique tetrachords" are important. Want one that has unique tetrachords across all 24 keys? Happy to oblige. How about Werckmeister's "Septenarium Temperament" based on a 1/7 division of the comma, as described on page 166 (new edition) of Barbour's book? It was published in 1690, which is clearly within "Bach's time". It achieves that uniqueness of tetrachords through the extraordinarily wacky use of a 4/7 comma fifth in the interval G-D, and various 1/7 and 2/7 pieces elsewhere making some fifths wide and others narrow. The tones range from 187 to 207 cents, and the semitones from 90 to 110, scattered all over the place. This temperament has the musical subtlety of a Mack Truck screeching around a corner; but yes indeed, all those tetrachords in it sound different from one another. So what? THE MERE PRESENCE OF UNIQUE TETRACHORDS IS NOT SUFFICIENT PROOF OF A BACH (OR ANY OTHER) TEMPERAMENT! Anybody can make up a temperament that has unique tetrachords in it, merely by putting three or four of the notes in exceedingly strange places (as Charles, indeed, has done). Whenever each tetrachord encounters one or more of those notes, voila, the note is so grossly out of tune in that context that the tetrachord becomes unique when compared with all the others. SO WHAT?

Another temperament with "unique tetrachords" is the "Handel" one that Charles cites in his paper, but which is really a 20th century invention of Owen Jorgensen (published 1991), reading theoretical strictness back into a document late in the 18th century which probably was not by Handel at all, but only attributed to him. That one achieves its unique tetrachords by having six different sizes of fifths in it, playing havoc with all the scales but in a nicely orderly way, and very subtly. It's a very nicely balanced nice temperament, although it can be done with Jorgensen's prescribed strictness only through the use of an electronic tuning device, not by ear. Whether one follows Jorgensen's prescriptions with an electronic device, or tunes more freely by ear from the 18th century instructions as he presents them, the result is a setup with unique tetrachords in it...from having so many different types of fifths. Want to hear "Handel/Jorgensen" in action? That's easy; listen to Robert Hill's Hänssler recording of the Art of Fugue. It's a beautiful-sounding temperament all around, although it's measurably very different from Bach's temperament, and therefore also different from Bach's expectations. Its adoption by fine musicians (including Dr Hill) speaks well for its general usefulness, anyway; it gives good musical results. That's a recording that I enjoy very much, personally.

The musical coup here, as Bach's temperament does, is to set up a temperament where everything sounds harmonious (no odd crap sticking out anywhere, with notes sounding randomly too sharp or flat in any context), with the additional outcome (not sufficient proof in itself!) that all the keys happen to sound objectively distinct from one another. The points in my paper about unique tetrachords are not even part of the proof, but indeed an ancillary remark about the musical outcomes of the system. The system itself is proven by many other pieces of the paper.

Charles, obviously, has simply taken my remarks about this outcome (i.e. its unusual but by no means unique musical property here) and misread them back as supposedly sufficient proof on which to base his own paper...as if all he had to do was discover some temperament that has unique tetrachords, and voila, he's convinced himself that he's scooped all the goods for himself! Again, this citation in his email today merely shows his misunderstanding of the material, and the superficial level of his "research"...preferring to lift uncredited observations from an expert as a shortcut, instead of learning the material adequately before writing his paper. The misuse of the stolen material is just more of the same: the failure to recognize where and how it fits in appropriately. That's why his paper does not explain at all why the reader should care about unique tetrachords; Charles himself doesn't really understand why it would matter, except that Dr Bradley Lehman has said so in various remarks on the BRML/BCML (including these here today).

Notice how, instead of directly denying that he's "reverse engineered" his paper from my work, he's merely tried to make it look unlikely?

Charles Francis wrote (July 15, 2004):
Bradley Lehman wrote:
< - 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: http://launch.groups.yahoo.com/group/BachRecordings/message/14399
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 shouldcare 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 4:3 interval, outlining many new intonations), or perhaps to earlier works such as Ptolemy's Harmonika and the treatise of Aristoxenus.

John Pike wrote (July 15, 2004):
Bradley Lehman wrote:
< Pieces in G minor, C minor, and F minor are frequent in Bach's repertoire, and especially problematic for tuning; but Barnes hasn't addressed this. He's simply omitted those keys from his analysis! >
Two pieces which quickly come to mind, (bearing in mind Brad's comments about the fifths in Charles' temperament and the problems of tuning with violinists), are the sonatas for violin and harpsichord in Cminor (no. 4) and F minor (No. 5)....beautiful works. The C minor starts with a beautiful sicillienne, reminiscent of the "Ebarme dich" and the F minor starts with a wonderful unmarked movement (but headed "Lamento" in a later copy, not in Bach's hand).

I am amazed that Brad has put so much time and effort into commenting on Charles' work, which I have read. I know almost nothing about this topic but the whole thing struck me as being too far-fetched for words.
[rest of the message was removed]

Jan Hanford wrote (July 15, 2004):
[this part of the message was removed]
I also know almost nothing about this topic and I like it that way. I play the harpsichord every day and I tune my harpsichord nearly as often; it sounds just fine to me.
[this part of the message was removed]

Johan van Veen wrote (July 15, 2004):
[To Jan Hanford] [the message was removed]

Charles Francis wrote (July 15, 2004):
[To Jan Hanford] Please note, I at no time mentioned my theory of Bach's tuning on this particular forum. But since another member did reference my published paper, I have made available some illustrative Bach recordings. At the specific request of a long-standing member of this group, I also addressed certain unsubstantiated allegations; this was done with the prior permission and clearance of the text by the group moderator.

Bradley Lehman wrote (July 16, 2004):
Bradley Lehman wrote:
<< Pieces in G minor, C minor, and F minor are frequent in Bach's repertoire, and especially problematic for tuning; but Barnes hasn't addressed this. He's simply omitted those keys from his analysis! >>
John Pike wrote:
< Two pieces which quickly come to mind, (bearing in mind Brad's comments about the fifths in Charles' temperament and the problems of tuning with violinists), are the sonatas for violin and harpsichord in Cminor (no. 4) and F minor (No. 5)....beautiful works. The C minor starts with a beautiful sicillienne, reminiscent of the "Ebarme dich" and the F minor starts with a wonderful unmarked movement (but headed "Lamento" in a later copy, not in Bach's hand). >
I love those two sonatas. I played both of them in a concert with Jaap Schroeder, on the same day that I met my wife. (She and I had corresponded by e-mail and telephone for some months before actually meeting, and then she came to meet me on the weekend of this concert.) I played through those two sonatas (indeed, all six: in b, A, E, c, f, and G) last month with another friend, one evening here at the house, to confirm how they work in Bach's tuning: it worked even better than the tuning I had used back then. That's simply more confirmation, among many other pieces, that the findings have nothing to do with idle number-crunching but are of immediate practical value: letting the music be beautiful. Obviously, part of the problem to be solved in the first place was to find a tuning that works well in these six violin sonatas, as they are notoriously difficult in terms of intonation for both instruments! As we played here, the violinist remarked how the usual problems simply are not present anymore; the pieces seemed easier to play. My paper mentions that problem and experiment....

[this part of the message was removed]

=====

p.s. to Jan and others here who have harpsichords, or other keyboards: here's a simple practical test to run. Tune Charles' temperament as described, and play for a while in it. Then, tune with the following c1690 temperament by Bendeler (a schoolteacher and the cantor in Quedlinburg, at the same time that Werckmeister was the organist there: his professional colleague), and play the same music. This method was republished in Leipzig in 1739, after Bendeler's death...obviously at the time and place where Bach was. It happens to have only two sizes of major thirds in it: both pretty close to equal temperament, but favoring the four of Bb-D, F-A, C-E, and G-B (i.e. the most common keys). Which way does your harpsichord sound better to you: this way with the smooth organization of common keys, or Charles' way? Which one do you think Bach would prefer, musically, of only these two choices: Bendeler's or Charles'?

Splitting the Pythagorean comma:
Ab -1/4 Eb 0 Bb 0 F 0 C -1/4 G -1/4 D 0 A 0 E...
E -1/4 B 0 F# 0 C# 0 G#

With an electronic tuning device, the cent values are:
C 0
C# 96
D 192
Eb 294
E 396
F 498
F# 594
G 696
G# 798
A 894
Bb 996
B 1092

No, Bendeler's isn't Bach's temperament either, but IMO it's a very good one, and it's verifiably less bumpy and less harsh than the various Werckmeister layouts! This temperament has been readily available since 1951 in Murray Barbour's book, and of course published on its own in Germany in the 18th century. I ran it through the Barnes experiment last night just to see what it does, and it gives the lowest deviations I've ever seen (by that measurement system): doing even better than the 1/5 PC temperament I mentioned yesterday. That is: whatever the Barnes method measures (because it happens to favor flat keys a bit), this one's now the winner. That's not proof that it's Bach's, in any way; it's just one that happens to sound very good in the major-key preludes of the Well-Tempered Clavier, which was what Barnes' method proposes to measure.

And as John and other string players here will notice, this Bendeler temperament has nice pure fifths on D-A-E where string tuning is most noticeable; and, as I mentioned, overall there are only the two different sizes of major thirds to match. That is, this one should be really easy to play with.

By contrast, Charles' proposed solution has five sizes of major thirds, zigzagging in a weird way: Ab-C best, then G-B and D-F# and A-C#, then Eb-G and Bb-D and F-A, then C-E, and lastly the others. Is there any hope of playing strings and winds with that? Why should harmonic resolutions into C major run into one of the most unsettled tonic triads? What's up with the dominant-tonic cadence into Db major having the sweetest third (in the dominant) resolving into the most discordant (in the tonic)? What about the tonic triad of F major, with an unusually high third and the worst fifth anywhere in the temperament? These are the types of basic musical questions that simply have not been addressed by Charles, but need to be if musicians are to be convinced...because those were high priorities among 18th-century musicians!

John Pike wrote (July 16, 2004):
[To Bradley Lehman] Many thanks, Brad, for sharing your moving experiences of these wonderful sonatas.

Regarding Charles' paper. I have read it and Brad's formal response on his website. I have also read the numerous e mail messages on the subject. Brad's allegation, that Charles had plagiarised his paper was a serious one, which warranted a close examination of the arguments on both sides. I know that I have sided with Brad in the past when there have been controversies but I wanted to look at this issue impartially. Having reviewed all the material available, I am convinced that Brad's allegation was well founded. I say this not because I want to take sides but because I strongly feel that Brad was RIGHT, both about the plagiarism and about the lof value of Charles' paper.

Charles feels that he initiated things by telling Brad about a piece by Sting which resembled a minor piece by Bach. When Brad later says that he has found the true Bach temperament, Charles makes some sort of connection between this piece and the Bach temperament, which he discusses in his paper. I am at a loss to understand the thought processes that may have been involved. Frankly, I found the whole paper bizarre. If Bach had wanted to communicate his ideal temperament to WFB, he would surely have done it in a direct and clear way, rather than in some special code in the music. It is hard to imagine that a serious musician like Bach could allow considerations such as coding a temperament or the number of trills needed to make up a symbolic representation of his name get in the way of his musical expression. Far too many assumptions are made in the paper and it just doesn't stand up to even the most cursory scrutiny, although I read it all.

By contrast, it seems clear to me that Brad was working along a completely different line of investigation using reliable sources and having his work peer reviewed at every stage. He checked very carefully that his results worked in practice.

It is also clear to me that Charles was trying to extract little snip bits of information from Brad in an attempt to come up with a rival publication which he was keeping secret. He wanted to beat Brad to the mark. I find his behaviour devious and unbecoming of real professionals who would not behave in such a manner.

Finally, Charles seems to think that he can quote his admirable qualifiactions at the head of the manuscript and deceive people into thinking that they are relevant to the publication. So far as I am aware they are not. He behaves as if a bizarre idea without any substance and a amateur degree of experience, expertise and research of the relevant material is an adequate stand-in for serious study, experience and research. This will not wash and I think that an urgent apology to Brad is warranted. I also hope that Charles will not be tempted again into this type of pseudo-science and research.

Charles Francis wrote (July 16, 2004):
Bendeler temperament as recommended by Bradley Lehman

Two musical examples using the Bendeler temperament as recommended by Bradley Lehman, the 6-Part Ricercare and Contrapuctus XIV are available at: www.bach-cantatas.com/Articles/Keyboard-Temperament[Francis]-Music.htm

To facilitate aesthetic benchmarking against Temperament IV, the same registration, same tempo, same bitrate, and indeed same everything, has been used, only this time it is the Bendeler temperament according to the cent values Bradley Lehman put out. The examples 2-28 are arranged in order of size, the 6-Part Ricercare and Contrapuctus XIV are the two longest examples and, of course, both masterworks.


Bradley Lehman wrote (July 16, 2004):
[To Charles Francis] The details about that Bendeler temperament are in this section, reproduced from my message to BachRecordings yesterday:

p.s. to Jan and others here who have harpsichords, or other keyboards: here's a simple practical test to run. Tune Charles' temperament as described, and play for a while in it. Then, tune with the following c1690 temperament by Bendeler (a schoolteacher and the cantor in Quedlinburg, at the same time that Werckmeister was the organist there: his professional colleague), and play the same music. This method was republished in Leipzig in 1739, after Bendeler's death...obviously at the time and place where Bach was. It happens to have only two sizes of major thirds in it: both pretty close to equal temperament, but favoring the four of Bb-D, F-A, C-E, and G-B (i.e. the most common keys). Which way does your harpsichord sound better to you: this way with the smooth organization of common keys, or Charles' way? Which one do you think Bach would prefer, musically, of only these two choices: Bendeler's or Charles'?

Splitting the Pythagorean comma:
Ab -1/4 Eb 0 Bb 0 F 0 C -1/4 G -1/4 D 0 A 0 E...
E -1/4 B 0 F# 0 C# 0 G#

With an electronic tuning device, the cent values are:
C 0
C# 96
D 192
Eb 294
E 396
F 498
F# 594
G 696
G# 798
A 894
Bb 996
B 1092

No, Bendeler's isn't Bach's temperament either, but IMO it's a very good one, and it's verifiably less bumpy and less harsh than the various Werckmeister layouts! This temperament has been readily available since 1951 in Murray Barbour's book, and of course published on its own in Germany in the 18th century. I ran it through the Barnes experiment last night just to see what it does, and it gives the lowest deviations I've ever seen (by that measurement system): doing even better than the 1/5 PC temperament I mentioned yesterday. That is: whatever the Barnes method measures (because it happens to favor flat keys a bit), this one's now the winner. That's not proof that it's Bach's, in any way; it's just one that happens to sound very good in the major-key preludes of the Well-Tempered Clavier, which was what Barnes' method proposes to measure.

And as John and other string players here will notice, this Bendeler temperament has nice pure fifths on D-A-E where string tuning is most noticeable; and, as I mentioned, overall there are only the two different sizes of major thirds to match. That is, this one should be really easy to play with.

By contrast, Charles' proposed solution has five sizes of major thirds, zigzagging in a weird way: Ab-C best, then G-B and D-F# and A-C#, then Eb-G and Bb-D and F-A, then C-E, and lastly the others. Is there any hope of playing strings and winds with that? Why should harmonic resolutions into C major run into one of the most unsettled tonic triads? What's up with the dominant-tonic cadence into Db major having the sweetest third (in the dominant) resolving into the most discordant (in the tonic)? What about the tonic triad of F major, with an unusually high third and the worst fifth anywhere in the temperament? These are the types of basic musical questions that simply have not been addressed by Charles, but need to be if musicians are to be convinced...because those were high priorities among 18th-century musicians!

 

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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
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