Review of "The Keyboard Temperament of J. S. Bach"
(c) Dr Bradley Lehman, 6/29/04, all rights reserved
by John Charles Francis
My questions are apropos of the paper "published" 6/25/04 at
and announced by the author in the internet group "alt.music.j-s-bach".
The paper, allegedly about Bach's system of tuning keyboard instruments, obviously has not gone through any
formal academic review by readers experienced in the field of keyboard tuning. The historical and practical problems
in Charles Francis' research (as presented in his paper) are glaring. I question both the academic and musical validity
of his results, and his research methods, as detailed below. I offer the following set of questions in that regard, as a level of
review that should have taken place before any publication.
Indeed, these are plenty of reasons why Francis' paper would not
even pass as satisfactory work as a university term paper in music theory or history:
inconsistent treatment of the evidence, disdain for historical research that has already been done,
unawareness of practical problems he proposes to solve,
and the use of graphs and tables that obfuscate rather than clarifying his results.
(That is: the presentation of impressive-looking data conceals the fact that he has not proven
what is proposed, giving the work a deceptive veneer of respectability.) In short, the paper shows that
Francis does not understand musicology as a science, such that any scientific methods should be
followed correctly in the research or presentation.
My objections here can be summarized: The unscholarly (even anti-scholarly) methodology
used here in Mr Francis' paper has yielded results that are absurd, both historically and musically.
Tune a harpsichord to Francis' recommended method here, and play Johann Sebastian Bach's music: the resulting
sound argues that Bach himself was incompetent as a musician and teacher!
Some of the specific problems:
1. Mr Francis claims a "PhD". What accredited university, year, and field, please? From the following questions about his serious historical omissions and musical inconsistencies, it appears that his degrees probably had nothing to do with music performance or musicology; in which case the citation of degrees does nothing but lend false weight to the authority of his research.
2. What precedent is there in the historical record that anyone (let alone Bach or anyone known to him) ever tried to fashion a circulating temperament from the inordinately tight amount of fifth-tempering of 1/3 comma? Kirnberger used the even tighter 1/2 comma, in the 1770s , but who if anyone used 1/3?
(See also question #23 below; for the moment, my complaint here is that Francis has not explained any historical use of
any 1/3 comma tempering. In his paper on its own, the point appears to come from nowhere.)
3. Has Francis ever listened closely to the sound of 1/3 comma fifths directly on harpsichords and clavichords, and the even narrower fifth he places on F-C? How is their rough sound reconciled with Bach's aesthetics?
4. Why is the leftover fifth in several of his methods referred to as an almost-equal-tempered fifth (only on the coincidence of its size, approximately 2 cents), instead of properly as a schisma? The mathematical explanation here needs to be made clearer, along with a discussion of the various types of commas used by theorists contemporary with Bach.
5. In the section that proposes to compare the new Francis temperaments with historical models: with the system of least-squares deviation that he has used to prepare his spiral graphs, he has merely proven (no more and no less) that his solutions are so "oddball" that no documented historical temperaments resemble them, other than equal temperament. (Such a task of inventing new temperaments, with that same property, is easy: simply choose the tempering such that abnormal keys are emphasized! Voila, equal temperament becomes the nearest fit ahead of comparisons with other historical temperaments!) And, in any case, they do not show sufficiently why Francis' solutions are in any way better for the keyboard repertoire by Bach or anyone else.
6. Also in that comparative section, what is the factual difference (if any) between "Silbermann" and "Telemann" temperaments? Specifics, please. Published articles by Bruce Haynes have suggested that Telemann and Silbermann both used similar schemes; Francis has not explicated the distinction in the formulation of his graphical analysis.
I suspect that Francis has merely collected his various historical temperaments from settings on an electronic tuning device, plus any cent tables he could find on the internet or elsewhere. For a meaningful comparison, and a historical overview, the paper needs much more detail as to the historical relevance and musical aims of these other tuning schemes.
7. All the remarks about distinctive tetrachords appear to come from nowhere and with insufficient explanation, as if Francis picked them up from some other source but did not credit them.  In any case, Francis' presentation does not tie the material together adequately, showing why the listener (or Bach) should care about distinctive tetrachords, especially in the context of discussing sharpened thirds. What is the explanation for this lack of relevance in the flow of the paper's logic, with no explanation where the notion or principle of tetrachords came from?
8. Indeed, it simply looks as if an assumption about distinctive tetrachords was read into the evidence, causing Francis to fashion Temperament IV deliberately as a contrived (forced) solution giving that outcome. What evidence in Bach's music or elsewhere suggests any use of 1/3 comma tempering to shift the notes' frequencies, at all, causing distinctive tetrachords?
Francis has used Bach's signed ornamentation to indicate some shift (i.e. tempering of fifths), but why 1/3?
9. As Francis proposes to use an ornament sign as a prescription to raise G#, and a similar but opposite ornament to lower B, what ornament explains the lowering of E by the same amount as B? If his application of his theory were consistent, E would have to be pure from A (as were the preceding notes that have the same ornament it does, proceeding by fifths).
10. What precedent is there, anywhere, that any tuning instructions by anyone have ever been based on the signed ornamentation (mordents, trills, etc) in music? Again, this is intriguing but looks contrived. Why would Bach's signed ornamentation not simply mean what it says, as to accentuation and grace in performance of the music?
11. What do any of Francis' temperament solutions tell us about Bach's music when played in any of these tuning schemes?
The paper does nothing to show the relevance to the music; all Francis has done is to explicate his own experiments and
assign to them his own interpretation of a single piece by Bach.
12. According to the New Bach Reader (Christoph Wolff, 1998) the Hopkins quote cited is actually from 1855,
not 1895 as Francis asserts. Why the discrepancy? Furthermore, the raising of the note G# (to the detriment of E
major) appears to be mostly a contrived attempt to satisfy this single quote, from more than 100 years after Bach's death,
to force A-flat major to sound more consonant; and this action creates two severely impure fifths (C#-G# and Ab-Eb)
that had already been tuned pure. Indeed, the musical improvement here is negligible anyway: by cranking the note Ab up by
1/3 of a comma to improve its relationship in the major third Ab-C, Francis has destroyed its relationship in the
fifth Ab-Eb, and the triad Ab-C-Eb is therefore (overall) still sour. Why would Bach do this, other than as a perverse
joke to improve the solitary sound of Ab-C, ignoring the melodic and harmonic functions of that note elsewhere in
his music? As the temperament--according to Francis--is based mostly on pure fifths, why would Bach raise G#/Ab with
the result that it creates two more impure fifths than had already been achieved? Francis' paper should explain Bach's
alleged motivations here, more thoroughly, to justify this bizarre step in the bearing plan.
13. Francis' bearing plan calls for the tuning and later retuning of the note F#. What in BWV 924 (allegedly the source of this unknown temperament) suggests or justifies such an activity? Francis first remarks that in his first derivation the interval B-F# is a wolf; then he reorganizes his tuning instructions to force F# to be pure to D (with no justification from BWV 924) and moves it again later (spreading this wolf among A-E, E-B, and eventually F-C!...plus a schisma). All this merely looks like a contrivance, an unwillingness to accept the information he has already derived from the piece at first reading. In short, he is forcing his evidence.
14. A "Handel" temperament is cited among the comparative choices. Where does it come from, except Owen Jorgensen's theoretical invention as published in 1991 from a vague set of tuning rules, ascribed back to Handel long after his death? This needs more explication from Francis.
15. He also has not explained why Silbermann's temperament "as expected" is far from his own derivations from Bach's music; the remark here needs to be connected more explicitly with the historical record.
16. How do any of Francis' temperaments solve or even address the outstanding performance-practice problems in 17th or 18th century repertoire? That is, why would Bach invent or teach anything like Francis' solutions to play his or anyone else's music?
17. What relevance, if any, do these Francis temperaments have to the organ and to fretted clavichords? It would seem that some discussion of that is in order, pedagogically or otherwise, especially as Wilhelm Friedemann likely played his lessons (including this piece) on a clavichord. Francis' bearing plan simply does not work on that instrument, as it would require tangents to be bent and then re-bent during the tuning process: a technique that is not only silly, but also destructive to the instrument.
18. Francis appears not to have considered the question of playability with other instruments, especially the strings (viola da gamba and violin) that have E strings. The strong tempering of 1/3 comma between A and E simply does not work at all when played with these instruments, as it makes the A-E interval too sour on them. What reason would Bach (a violinist himself) have to invent such a scheme for keyboards?
19. 18th century wind instruments, similarly, were not tuned to any system remotely resembling Francis' schemes. Again, why this discrepancy where such an impractical temperament is assigned to Bach, who composed music for winds?
20. What meaning, if any, is the listener to assign to charts full of cent values (up to sixths and sevenths), beyond amusement? The cent scale itself is an invention from long after Bach's death. The mere assignment of numerical values to phenomena does not give the research itself any more credence; it serves only to suggest an attempt to be nominally scientific. Meanwhile, any temperament scheme can be measured. Francis, to be believable, needs to show why this particular set of measurements from him mean anything to the music.
21. Taking Francis' recommended bearing plan for "Temperament IV" with due seriousness
I have tuned my Italian virginal to this method, and played pieces by Bach on it.
It simply does not work for the music, especially in F major (from both the unusually wide F-A third and flat fifth F-C),
or any employing the triads of F# or B major (so commonly used by Bach as dominants).
Francis' paper explains this away by asserting that Bach may have taught different schemes to different students.
But, what are the grounds for such an assertion, and why should any temperament
ascribed to Bach not work for his own music, most notably in the key of F? I suggest
that any interested in Francis' temperament should play the two F major preludes
(among that same group in the Wilhelm Friedemann Bach book) BWV 927-928, and the E minor
three-part sinfonia BWV 793: pieces Bach himself used to teach keyboard technique and
the principles of composition. Given that these simple pieces in common keys fail so egregiously,
Francis' conclusions about temperament were obviously not based on sufficient examination of Bach's music. 
22. Francis' section of References includes only one biography of Bach, no citations of work by performing musicians currently active, only three 17th or 18th century documents (other than the music), and only four 20th century articles. Nor is it evident that he has done any sort of literature review, to find out what has already been said in the field of tuning, beyond the cursory consultation of a few articles convenient to him. Most tellingly, all of his sources are more than 20 years old; no recent research in the field has been considered. Especially, the paper gives no indication that Francis has even glanced at the work of Lindley, Steblin, Jorgensen, Blackwood, or the full-length book by Barbour that came after his 1947 article.
Quite simply, Francis here shows no responsibility to know what's practical, what's normal, understand the role that scientific method plays in musicology, or even to know the nature of the problems that his temperaments are proposed to solve.
23. As shown through the questions above, Francis' technical command of the material is in question (as in, the presence
of so many basic errors that betray his superficial understanding of the topic). Apart from any accusations by me or anyone else that Francis
has lifted ideas from uncredited sources (which, after all, would matter only if he's come up with something valid...which
he has not!): Francis' tracks through the "research" process are crude and therefore easy to follow through the woods.
Like Herbert Kellner before him, Francis has
attempted to mine Werckmeister's writings for gold, although (unlike Kellner) Francis has neglected to explain why Bach would derive anything
Francis found the little-known "correct temperament #2" by Werckmeister,
which was a published attempt to convert organs from regular 1/6 comma meantone to something more circulating, with a minimum
of work. Werckmeister's formula there is as follows: Ab +1/3 Eb +1/3 Bb -1/3 F 0 C -1/3 G 0 D -1/3 A 0 E -1/3 B 0 F# -1/3 C# 0 G#.
That is: pure fifths alternate with 1/3-comma narrow fifths, except for the rough closing at the traditional meantone "wolf" point of Eb-G# where
Werckmeister has fudged with some wide 1/3-comma fifths. This temperament serves its original purpose well (i.e. as an easy conversion from
1/6 comma regular meantone, by straightening neighboring 1/6 comma fifths into pure ones) and indeed is quite usable for much of Bach's music.
With this idea that 1/3-comma fifths are workable,
Francis has simply taken to shuffling around the 1/3-comma and pure fifths willy-nilly until he has got something
especially with the forcing of the Ab-major triad to satisfy a 19th-century document (see above at question #12).
Then, he has forced it inconsistently (also, see above at #12-13) to look like an interpretation from a composition
by Bach. Crucially, he has not noticed himself (or, at least, has failed to explain adequately in the paper)
that he has switched from Werckmeister's use of 1/3 Pythagorean comma to his own use of syntonic comma.
That switch is the reason he has run into the surd of approximately 2 cents,
but he hasn't explained why this schisma is necessary at all, or why (from any tie to Bach) he has chosen to put it
into C-F...or why Bach would fool around with (or misunderstand) Werckmeister's ideas as he has done himself.
This appears to be just one more contrivance by him, among many as pointed out above.
The most obvious guess here to interpret this comma problem is: Francis himself when writing this paper did not
understand the two different commas himself, either technically or historically!
In any case, Francis has come up with the following scheme as his best: Ab -1/3 Eb 0 Bb 0 F -1/3** C 0 G 0 D 0 A -1/3 E -1/3 B 0 F# 0 C# +1/3 G#, where
he has dealt the schisma additionally into F-C (since he's splitting a different comma from Werckmeister's!).
OK, so what? There is no sufficient explanation given by Francis why his solution should be better for any of Bach's music (and, indeed, it does not sound better),
other than the forced improvement of the solitary triad Ab-C-Eb.
In short, why is Francis' recommendation in any way a musical improvement, and
why is this outcome thrust upon Bach except (crudely) by contriving BWV 924 as a source? Such a process of inventing
a new temperament is not research; it is simply a creative use of coincidences and contrivances.
Why does Francis show this disdain for the scientific fields of musicology and historical performance practice? Frankly, the overall impression I get from the paper is that it is an enormous (im)practical joke, a perhaps deliberate affront to serious work.
By putting up something that looks (only on the thinnest surface!) plausible enough to fool people who don't know better, by flashing a series of numbers that make his inquiry look scientific,
the implication is that real musicological research (elsewhere!) consists only of fooling people who don't know better, plus extensive marketing.
Francis' admonition to "musicians concerned with the historical informed performance practice of Bach's music"
that we should take his "findings" seriously must be some practical joke:
because the temperaments he presents here sound ludicrous in practice, the history he presents is superficial and selective, and the whole paper is a mockery of any process of serious research.
The only thing proved here by Francis is his own creativity, and his own lack of respect for musicians and musicologists.
To assign any of Francis' temperaments back to Bach is to assert that Bach himself didn't know what he was doing.
 For explication, see Rita Steblin's dissertation: reprinted most recently as A History of Key Characteristics in the Eighteenth and Early Nineteenth Centuries, 2nd edition (2002); the first edition was 1983. Her chapter "Marpurg vs Kirnberger: The Tuning Controversy in Germany" (as does her entire book) presents vital information in the historical background of this topic.
 Indeed, I do not know of their use anywhere in the tuning literature, other than in a paper of my own: one which was already submitted as a candidate for publication through an established journal, earlier in June 2004. The melodic study of tetrachords is my own development,
as a method (among several others) to assess the musical properties of historical temperaments.
It appears that Francis has scooped my own observations from remarks I made in May in an internet discussion group,
sharing one of several preliminary results from my own paper (from my analysis of some other temperaments).
Frankly, it simply appears to me that this paper by Francis is an attempt by him to scoop my own findings
(whatever they might be) and be the first to present anything, using any ancillary clues he could gain from my
remarks in the discussion...without even so much as a footnote of acknowledgment to me as a source.
Also tellingly, Francis has not announced his findings in the other discussion group where I had mentioned
small pieces of my own preliminary work during May and June; members there would certainly notice and recognize
the parts he has derived from my analyses and methods! Quite simply: the use of "distinctive tetrachords" comes
directly from several messages I posted on May 21st in response to another member in the discussion. Francis has
recycled this idea into his own paper, without attribution.
 This point, again, reinforces my belief that Francis simply took some of my own remarks about other temperaments
from an internet discussion group, and "ran with them" trying to guess my own findings and publish them ahead of me
(while my own work is going through a formal review process). Indeed, on May 2nd during that discussion Mr Francis
asked me directly to give him the cent values from my own research, with his request: "If you post the 12 deltas from ET in cents,
I'll try it out (I presume no octave stretching is required)." I of course refused to post those.
That request by him is (I believe) clear evidence he was trying to pump me for free information,
and preparing to run with whatever I might divulge...claiming it as his own work.
For what it's worth: (see also my question #5, above) Francis' results sound vastly different from any
historically documented temperaments (including some previously unknown ones, of my own recent discovery),
and BWV 924 is not the source of any musically or historically valid "Bach" temperament!
I believe, axiomatically, that any temperament ascribed to Bach should sound plausible playing his music,
especially the music closest to any alleged source (in Francis' case, the preludes for Wilhelm Friedemann).
Apart from all the problems with Francis' methods of research and divination, as pointed out above,
his musical results are simply so bizarre that I cannot believe he even takes them seriously himself. His project
is a grand hoax, given that it does not bring to Bach or his music a convincing sound in performance. With
publication comes the responsibility of checking out the musical results first, and getting opinions
from musicians and scholars who understand the material, to make sure it makes any sense before it is presented
to the public. As I remarked above: this paper shows that Francis does not understand musicology as a science,
such that any scientific methods should be followed correctly in the research or presentation. This hoax
by him is an affront to (and a mockery of) those of us who do serious work in this field.
Dr Bradley Lehman
B.A., Goshen College, 1986 (music and mathematics)
M.M., University of Michigan, 1992 (early keyboard instruments)
A.M., University of Michigan, 1992 (historical musicology)
A.Mus.D., University of Michigan, 1994 (harpsichord)
One of my own doctoral projects (in 1993-4) was on the topic of harpsichord tuning,
and I offer also the temperament-analysis spreadsheet that has been available
here on the web since 1997.
Furthermore, I am a harpsichordist and organist with 22 years of professional performance experience as
such: therefore I have particular practical interest in any findings in this field.