source file: mills2.txt Date: Sat, 4 Nov 1995 11:53:34 -0800 From: "John H. Chalmers" From: mclaren Subject: Bach wars --- Many forum subscribers have added their 2 cents to the long-running "Bach wars." For my part, permit me to say that the posts by all concerned were absolutely superb. Full of detailed quotes, specific references, cogent reasoning. Paul Hahn, Gary Morrison, Manuel Op de Coul, Aleksander Frosztega, Johnny Reinhard and Helmut Wabnig did a marvellous job of distilling the references and citing competing sources. As to who is right or wrong, that is not nearly as interesting as the citations themselves. This controversy, raked over in admirable detail, gives *all* of us the references and direct quotes required to decide for ourselves. That should be the goal of scholarship...and in the "Bach wars" series of posts, all subscribers concerned have adhered to high standards of scholarship and logical reasoning. Unlike so many posts in which sarcasm, appeals to authority, or sheer naysaying substituted for a reasoned debate, the "Bach wars" have proven enormously enlightening. Reading this series of posts has taught me a good deal about an important question in the history of tuning. Congratulations to everyone who posted on the subject. You've all shown us how interesting and educational this forum can be at its best. --- As to the specific question of the "Bach wars" posts-- "What tuning did Bach use?"--it does not behoove me to speak directly, given the abysmal nature of my ignorance about the period and the people involved. However, some general observations seem in order: [1] "Statisticum radix scientiae malorum." It is my firm belief that misuse of stastistics is the root of all bad science. (As opposed to pseudo-science, like the N-rays which destroyed Rene Blondlot's reputation in 1906 and the abominable E-rays which constitute such a blot on the credibility of German science today. E-rays are nothing but dowsing performed on purported electromagnetic radiations, which radiations can neither be detected by any known instruments nor cut off by any known form of shielding. Yet they "cause cancer." What's the German word for "scam"?) One of the worst uses of statistics is what I call "stripmining the noise floor." When you've got too little data to form a reliable representation of a statistical universe, or when you've got dribs and drabs of data collected at time A, time B, time C, under wildly different conditions and with dubious controls...you're basically pushing linear parametric statistical methods beyond their useful limits. You're trying to statistically analyze noise...trying to make soup out of dishwater, mathematically speaking. The result? Hard numbers that look convincing but turn out to be "junk science." My best guess is that the "What tuning did Bach use?" controversy is undecidable because all participants concerned are stripmining the noise floor. --- Let me give some concrete examples: Statistical analysis of Bach's harpsichord compositions looks like a reasonable strategy at first glance. However, Bach's collected harpsichord compositions do not form a reliably complete representation of an underlying statistical universe for the following reasons: [1] Bach wrote his harpsichord compositions over a number of years. Some were penned in Cothen, some earlier, some later. If Bach's style of composition changed, this throws into doubt one of the underlying assumptions of a statistical analysis: namely, that all samples derive from the same statistical universe. To use an acoustics analogy, this is like taking half your measurements of reverberation time in a closet and half your measurements in Carnegie Hall. You've got a mixed set of data and you're lumping all the data points together willy-nilly. A guaranteed shortcut to "junk science." [2] Bach may have written some compositions for a harpsichord, others for clavichord. Does the statistical analysis take this possibility into account? Do scholars know for *certain* which compositions were written for which instrument? Did Bach (or his patron, the prince) use different tunings on different keyboard instruments? Are we *sure*? Are scholars *sure* that many of Bach's compositions weren't written to be played on *both* a harpsichord *and* a clavichord (whichever might have presented itself and been available) and might thus have represented Bach's attempt to compose music which sounded good *regardless* of the particular tuning used? For example, the clavichord might have used one well temperament, the harpsichord another--or the clavichord might have used, say, Kirnberger III, while the harpischord might have used equal temperament because harpsichord continuo often had to accompany an instrumental ensemble at Cothen. (Remember, Bach's harpsichord concerti were written at Cothen.) Did the statistical analysis take these issues into account? If not, why not? [3] Many assumptions are inevitably implicit in any linear parametric statistical analysis. In order to calculate r values, you have to fix parameters and make guesstimates about their influence and constancy. If you correlate verbal IQ test scores with length of stay in the US for new immigrants and assume strong causality, you come to the bizarre conclusion that emigrating to the United States raises people's intelligence. You get this garbage answer out of linear parametric statistics because you put garbage *into* the equations: namely, garbage assumptions. Without basis, you assumed two parameters to be deeply causally connected for the wrong reason, and ran too far ahead of yourself with the results. This raises questions about the Bach statistical study. Questions of *both* causation *and* correlation. What are the *specific* r values by interval category for Bach's compositions? Do they imply causation? If so, what *kind* of causation? For a classic example of garbage science, see the r values buried in the appendix of Charles Murray's "The Bell Curve." You'll find r values between 0.4 and 0.6. As a rule, an r below about 0.75-0.8 is a sure-fire indicator of smoke & mirrors. The correlation is so weak that the researcher had better answer some *very* tough questions or risk being called slipshod, or worse, a fraud. So I for one want to know those r values on the Bach statistics. Did the Bach statistical analysis use linear regression? Quadratic? Cubic? Least-squares? What's the mean, median and the standard deviations for the r values of each interval broken down by year of composition? What do these profiles tell us about causation? Was multiple regression used on *different variables*? Were the results compared? What did *that* say about causation as opposed to correlation or even mere coincidence (AKA low r values)? Did the statistical analysis even bother to consider such issues? If not, I want to know why. Bach may in some compositions have been interested in exploring unusual dissonances: thus at certain points in his career his compositions might have *deliberately* used "bad" intervals in a given well temperament (if indeed he used a well temperament). But at other times in his career, he might have been more interested in exploring unusually perfect consonances in a given well temperament. This would change the intervals Bach tended to use over time: did the statistical analysis take this into account? We know for a fact that Bach's 7th chords were considered wildly dissonant and highly outre in his day. Therefore it seems reasonable to posit that he might have systematically explored sets of intervals unusual for composers of the period. Did the statistical analysis take this into account? Or did the statistical analysis arbitrarily assume that Bach would have used the most consonant (read: beatless) intervals in a given well temperament most often, and the least consonant intervals least often? More complexly, Bach (being the genius he was) might have switched his interests constantly, exploring one set of unusual dissonances in one composition, another set of exotic consonances (available only in a given well temperament) in another composition. Conflating all of the interval data into a single linear regression would destroy all of this information and produce *wildly* misleading answers. In this case, multivariate analysis would be called for. Was it applied? Was multidimensional statistical analysis used? Did the researcher test for correlation between (say) timbre *and* interval and interval, or only twixt interval and interval? [4] Bach might have preferred certain intervals (even if he used equal temperament) for numerological or ecclesiastical reasons. We know with surety that he considered C minor and D minor "special" keys. Only a few of his compositions use these keys: they are statistically underrepresented. Bach clearly invested these keys with some special significance, because he reserved these keys for his most ambitious works. The Chaconne (of which Bach wrote exactly ONE), for instance, uses d minor: so does the famous prelude and fugue. The passacaglia & fugue (again Bach wrote only ONE passacaglia) uses c minor...and so on. Does the statistical analysis take this into account? Depending on the well temperament (if such a tuning was indeed used), d minor and c minor might well have exhibited special intervallic properties. We can be reasonably certain from statistical analysis, for example, that a number of Buxtehude's later compositions use keys which when transposed down on the meantone Luneborg organ offer unusually consonant sets of intervals. Did the person who performed the statistical analysis take this possibility into account? Did s/he run a separate analysis on this assumption? Were the results compared with the straightforward statistical analysis? If not, why not? Bach could have had many reasons for using certain intervals. We know, for example, that Bach was numerologically inclined. In one of his chorales the melody enters 10 times, representing the 10 commandments: other examples abound. Does the statistical analysis of Bach's use of intervals take into account the possibility that he might well have used a given interval-set for reasons *other* than considerations of acoustic consonance and dissonance? This same objection applies to fugue subjects and counter-subjects. One fugue of the 48 deliberately uses all 12 tones of the chromatic scale in succession, for instance: does the statistical analysis take into account the effects of such part-writing? [5] Some of Bach's klavier compositions were originally written for organ, some are alterations or emendations of works written for instrumental ensemble, and some are greatly modified versions of other composer's works--specifically, the "transcriptions" of pieces by Vivaldi, which are very much more than mere transcriptions. Does the statistical analysis take this into account? If not, why not? --- Statistical arguments for or against this or that historical trend fill me with foreboding. They're a fertile breeding ground for "junk science" (without the researcher *intending* to do junk science, of course--or even realizing it). So many assumptions and presuppositions are implicit in any linear parametric statistical analysis of historical data as almost to force me to proclaim: "a pox on all historical statistical studies!" Classic examples of "junk science" from statistics abound in economics. For instance, those bogus United States GNP charts going back to 1876--charts which completely ignore the fact that the U.S. switched from an agrarian economy in the early 19th century to a steam-driven Bessemer-furnace economy in the late 19th century to an oil-and-steel-driven machine-tool economy in the early 20th century to an information-driven service economy in the late 20th century. What's the net discounted dollar value of a bushel of tobacco in 1876 compared to the net discounted dollar value of a megabyte of computer code in 1996? The question is unanswerable. You're not just comparing apples and oranges, you're comparing apples and *mu-mesons.* The question doesn't even make *sense.* Again, sociological historical studies purporting to show improvements in "quality of life" as the century progressed are equally flawed. While in 1880 there were no antibiotics, it was also standard for a middle-class family to have 2 or 3 live-in servants. If you're a healthy person, would you be willing to trade lack of antibiotics for being waited on hand and foot and having your meals cooked for you and your washing done by a crew of servants? Would this be an overall improvement or decline in your standard of living, as opposed to today? The answer isn't obvious to me. Again, apples compared with oranges. Again, garbage science produced by a misuse of statistics. All told, the value of historical statistical studies of Bach's interval-usage seems at best right on the borderline of junk science, and at worst little more use than examining bird entrails. --- This leaves us with the written historical record. Does any specific numerical record exist of the frequencies to which Bach tuned each of the keys on his harpsichord? Clearly not. Thus we are left with inadequate data. *Grossly* inadequate data. Regardless of what tuning you think Bach used, the fact remains that (unless we want to swim in the VERY murky waters of statistical historical numerology) we must fall back on vaguely-worded hearsay testimony about Bach's tuning. My standard for this kind of historical hearsay is: would you convict someone of murder on the basis of this stuff? In this case, no way. You don't need O.J.'s Dream Team on this one. The testimony is so weak and so open to interpretation that even a grand jury would no-bill the defendant. It wouldn't even get to trial. Thus my sense here (reading the "Bach wars" posts) is again that the question is undecidable on the basis of the hearsay testimony from Bach's relatives and acquaintances. Many of the quotes supposedly come from "eyewitness" accounts--but can we be *sure* it was *actually* an eyewitness account, or was Forkel remembering long after the event? Or did Forkel miss the incident entirely, and perhaps have to rely on C.P.E. Bach's recollection? Or was it one of those "a friend of my cousin's brother told me he heard someone say..." things, gussied up in first-person narrative form? What's that? Did someone mention "false memory syndrom"...? Meaning: people tend *not* to remember the event itself, but what someone else *told* them about it...? We know *some* generalities with reasonable certainty: Bach was considered "old-fashioned" during his lifetime, and his style was out of date long before he reached middle age. The homophonic, racier, faster-paced "Italian style" was much more in vogue by the 1720s than Bach's almost quattrocentric polyphony. Did this influence what friends and acquaintances remembered about Bach's tuning? Did they unconsciously exaggerate the "meantone" quality of Bach's music because of the old-fashioned nature of his polyphony? Or did they instead unconsciously redact their memories of his tuning procedures so as to "modernize" Bach and unwittingly make his music more fashionable to fit in with the new music everyone was used to? I don't know the answer to these questions. Before making up my mind about "what tuning did Bach use?" I'd sure like to. --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 5 Nov 1995 04:39 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id SAA29690; Sat, 4 Nov 1995 18:39:15 -0800 Date: Sat, 4 Nov 1995 18:39:15 -0800 Message-Id: <951105023715_71670.2576_HHB54-5@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu