THE NEW FEDERALIST December 2, 1988 Pages 6-7

American Almanac

J.S. Bach's Campaign for an

Absolute System of Musical Tuning

by Renee Sigerson

Johann Sebastian Bach at the organ.

From the outset of his public life as an organist and composer, the great German Johann Sebastian Bach participated in a conspiracy to set an absolute system of values for musical tones, based on the pitch, Middle C = 256.

Recently, Socialist-linked European media outlets have issued slanders against the Schiller Institute, prompted by the institute's historic conference on the topic of musical pitch in April 1988. At the Milan, Italy conference, musicians and policymakers joined hands to call for the absolute standard of musical pitch of C = 256 to be legislatively adopted today. The recurrent theme of these slanders—which have cropped up in different corners of the world—is the characterization that a scientific standard for musical tones is "authoritarian," and thereby fascist. That was the assertion, for example of the Danish radio announcer last August who howled, "They are absolutists, up to the level of totalitarianism," in his broadcast report on the Schiller Institute campaign.

Johann Sebastian Bach was denounced in a similar fashion, both during his lifetime and after. Oligarchical and liberal academic circles ran witchhunts against Bach, even after he was dead, attempting to eradicate the very men-tion of his name from all accounts of history. Fortunately, the attempt to bury Bach's name was defeated. However, there is a direct link between the attacks launched by Bach's enemies, and the slanders circulated against LaRouche-associated musical-scientific efforts today.

As we show here, LaRouche's enemies believe, in part, that they just may be able to "get away" with their use of the labels "totalitarian" and "fascist" against the campaign C = 256, because of the existence of a voluminous amount of academic disinformation claiming that J.S. Bach was indifferent on the matter of musical tuning. All academic, conservatory sources argue either that Bach didn't care what pitch his compositions were performed at, or, that he arbitrarily "preferred" a pitch value nearly a half-tone below C = 256.

We begin here the process of ripping this academic fraud to pieces. The fraud is neatly summarized by such formulations as the following, published by Arthur Mendel, a leading falsifier in this field, in his recent book, Pitch in the Sixteenth and Early Seventeenth Centuries: "It is clear that absolute pitch could have relatively little importance to the musician before the late eighteenth century." This statement is a lie.

In materials soon to be released by associates of Lyndon LaRouche, a leading spokesman for the Schiller Institute's campaign for absolute musical pitch, it will be shown that C = 256 is a value at the center of the entire process of life within our universe. These materials further document why C = 256—and the associated major sixth in the scale, A = 432— are the only

pitch values which permit the proper development of the singing voice. Singing is the wellspring for musical thought.

As illustrated in Figure 1, when musical pitch is set at C = 256, the values of the musical scale coincide with the harmonic sectioning of the human voice. The line illustrating the soprano voice type shows what occurs when a child or adult soprano, starting on the tone C = 256, sings up the scale. As the child completes the tone F, in order to continue up the scale, he or she must now change the way in which the tone is produced. The voice will pass over an instability, called a register break, and the next tone, F-sharp, or G, will be the first tone in a new register.

The tones sung in the first, and then in the second, register form two groups, whose qualities differ in the same way that colors contrast in the visual spectrum. Proceed to the next voice type, the mezzo-soprano. This voice changes register on the tone E. Go through the six species of voice types in the human population. Each voice type has definite values where the register breaks occur. When the pitch is set at C = 256, the register breaks form a harmonic-geometric series, which establish the differences in the "keys" in the well-tempered system.

The value C = 256 also sets the musical scale as a continuation of the Earth's rotation around its axis, as illustrated in Figure 2. Scientific work defining music as the audible form of transformations in the geometric relations governing the universe began in ancient Greece. The name given to this work, since ancient times, was "Harmony of the Spheres." This term was then chosen by the German astronomer Johannes Kepler, in the 1620s, for his work on music and the planets. Bach's circles were familiar with this work.

The Cult of Helmholtz

All published academic material claiming that Bach was indifferent to pitch standards originates with the same source: the circles around Hermann Helmholtz, the nineteenth-century pseudo-scientist, who joined with British academia to crush continental European science and culture. In 1862, Helmholtz vowed, in print, to crush the tradition of the "Harmony of the Spheres" in classical music.

His declaration appeared in a tome entitled Sensations of Tones. There, Helmholtz wrote:

The relation of whole numbers to consonance became in ancient times, in the Middle Ages, and especially among Oriental nations, the foundation of extravagant and fanciful speculation. "Everything is Number and Harmony," was the characteristic principle of the Pythagorean doctrine. The same numerical ratios which exist between the seven tones of the diatonic scale, were thought to be found again in the distances of the celestial bodies from the central fire. Hence the harmony of the spheres, which was heard by Pythagoras alone among mortal men, as his disciples asserted. The numerical specula-tions of the Chinese in primitive times reach as far. . . . The whole numbers 1,2,3, and 4 were described as the source of all perfection . . . references of musical tones to the elements, the temperaments, and the constellations are found abundantly scattered among the musical writings of the Arabs. The har-mony of the spheres plays a great part throughout the Middle Ages. . . . Even Keppler [sic], a man of the deepest scientific spirit, could not keep himself free from imaginations of this kind. Nay, even in the most recent times, theorising friends of music may be found who will rather feast on arithmetical mysticism than endeavor to hear upper partial tones.

Helmholtz's reference to Kepler assumes that anyone reading Sensations of Tones was either already illiterate—or would certainly soon become so. The giveaway that Helmholtz never hesitated to put forward a lie for evil pur-poses is his lumping of Kepler into the phrase "arithmetical mysticism." As Helmholtz's circle fumed, it was precisely due to the fact that Kepler never had anything to do with corrupt "arithmetical" approaches which drove them to fiercely hate Kepler and his legacy—for which Bach was a leading repre-sentative.

The method of Kepler, Bach and all others associated with the humanist current in European history, was that of constructive geometry, in which the only self-evident basis for knowledge of the universe is the least action of conical rotation. The astonishing fraud of Helmholtz's construct will best be appreciated after one has read Kepler's works; for this situation, the follow-ing comment from Kepler's own Harmony of the Spheres will simply set the record straight.

In the appendix, Kepler compares his great work to the three books on harmony of the astronomer Ptolemy. Kepler states:

Since Ptolemy, along with the ancients, seeks the foundations of harmony in abstract numbers, whereas I deny the significance of the pure numbers; and I, in place of their named numbers, i.e., things which are governed by those numbers, pose the regular plane figures and the divisions of the circle which serve for their construction as the principle of harmony; so did I have to organize this book differently than Ptolemy organized his.

Similarly, in an earlier location, Kepler states,

Numbers have nothing in themselves, which they would not have received from quantities, or from other actual and real essences, or from actions of the mind.

Soon after release of the disinforming Sensations of Tones, the British Museum hired a tone-deaf linguistician named Alexander Ellis, to translate Helmholtz's tract. As part of his assignment, Ellis was paid by the British Museum to codify a vast amount of historical "evidence" on tuning practices since the beginning of European history. Ellis's data on this subject, estab-lishing a "historical" school of musical practice, in opposition to the method of constructive geometry associated with Kepler, is the source of the massive confusion on this subject today.

Helmholtz also disagreed with Kepler's conviction that human hearing perfectly conformed to the geometrically provable well-tempered system. Helmholtz argued that the human ear is very imperfect—and that music theory should be directed toward dissecting how tones "really work," since man can't hear them. This section of Sensations of Tones so disgusted the great mathematical physicist Bernhard Riemann, that he told his friends that disproving Helmholtz's theory of the ear was the most important work he had to complete in the final months of his life.

Helmholtz first voiced the doctrine later seized upon by anti-Semite Richard Wagner, that music is hermetically sealed off from all other human activity: "Music alone," he scrawled, "finds an infinitely rich but totally shapeless plastic material in the tones of the human voice and artificial musical instruments, which must be shaped on purely artistic principles, unfettered by any reference to utility as in architecture, or to the imitation of nature as in the fine arts, or to the existing symbolical meaning of sounds as in poetry. There is a greater and more absolute freedom in the use of the material for music than for any other of the arts."

Like Wagner, Helmholtz was a racist: "What is the smallest interval admis-sible in a scale," he wrote, "is a question which different nations have answered differently according to the different direction of their taste, and perhaps also according to the different delicacy of their ear." The wretched view, that musical "taste" is biologically transmissible, was later enthusiasti-cally endorsed by the Nazis and by the Russian Empire.

Today, in academic circles, Alexander Ellis is the godfather overshadowing most work on the history of pitch standards. Arthur Mendel, cited above, is considered his leading protege.

It is this Helmholtz circle which has invented the tale that Bach was a proponent of a system which set the relative distances between pitches, but that he didn't care on what central value the whole system was based. In the minds of these liberal academics, the belief that relative values are admissi-ble, but absolute values are "totalitarian" is a form of brainwashing, com-pletely contrary to the outlook of a J.S. Bach.

It is time to burst the credibility of this tale, and to make clear that any journalist who hurls the label pro-Nazi against those dedicated to an absolute standard of pitch, is probably a simple lunatic. It is time for the evidence to be assembled showing that Bach fought for a pitch standard; and that moreover, this standard was based on the same geometric principle as the standard adopted by Mozart, Beethoven, and called for by LaRouche and the Schiller Institute today. A mere sample of the type of evidence readily available is summarized below.

Bach's Mission

Johann Sebastian Bach was a scientist whose work was shaped by the same effort that produced the "continental science," against which Helmholtz pitted himself in the nineteenth century. Bach's life is a testimonial to the way a man can adhere, fiercely, to scientific principles he shares with God, even when there exists tremendous "everyday" pressure to let those principles go.

Figure 1: The Six Species of the Human Singing Voice

All great music is based on the principles of register shift, as they occur in the soprano voice.

Throughout his life, Bach wrote music to be played at the classical pitch of A = 432, and worked with instrument specialists to produce instruments at that pitch. Of specimens of instruments used by Bach that survive today, many appear to have been built in the range of A = 422; in many cases, when their temperatures rise after being played for awhile, the pitches come up to a level A = 427-432, which is the largest acceptable range of variation for a fixed system of tuning.

Furthermore, according to Bach's son Carl Phillip Emanuel, and to other contemporaries, whenever Bach played on an organ whose the pitch diverged from this range, he would instantly transpose the score.

The view that musical instruments should be constructed to imitate an idealized choir of singing children and adults had been introduced in Germany decades before Bach was even born. Nonetheless, in Bach's time, chaos hung over Europe in respect to practices of tuning. A tone sung in Venice, and called there an "A," would be named by many Germans as a "B-flat," and by a Frenchman as a "C." The problem, moreover, did not merely exist from country to country. Wide divergences in tuning existed from town to town, and in many towns of Germany, the church organs were tuned close to the high pitch of Venice, while the wind instruments, imported from France, were tuned low!

Bach and his closest circle of friends never accepted this status quo as their starting point for practice. Over a period of decades, they fought for a tuning based on scientific and moral principles, and Bach, personally, played the most critical role in getting the job done.

One of the testimonials to Bach's effort in this direction appeared in 1752, two years after his death. Johann Joachim Quantz, the most influential representative for music policy at the court of Frederick the Great, called for the establishment of a fixed system of tuning, in a widely circulated manual on how to play the flute. There is little question that Quantz's call was a result of an historic visit made by Bach to the Berlin court in 1747, an event that has been immortalized by Bach's composing of a six-part fugue and canons for the King, as a "Musical Offering." The King talked about the visit for decades.

In his flute manual, Quantz writes:

The diversity of pitches used for tuning is most detrimental to music in general. In vocal music, it produces the inconvenience

that singers performing in a place where low tuning is used are hardly able to make use of arias that were written for them in a place where a high pitch was employed, or vice-versa. For this reason it is much to be hoped that a single pitch for tuning may be introduced at all places.

Similarly, six years after Bach's death, the town of Leipzig installed a new organ at St. Thomas's Church, where Bach had been cantor for twenty-seven years; for the first time in Leipzig, the pitch of the organ was the same as that for which Bach composed for human voice.

The Task Defined: The Role of Gottfried Leibniz

Bach's conviction that musical practice had to be made scientific was instilled during his youth, by the towering scientist-statesman Gottfried Wilhelm Leibniz. As a youth, Bach was brought to study and sing at the St. Michaelis school, in the kingdom of Hanover, where Leibniz was the director of education. Leibniz continued the work of Kepler, and inspired every political and scientific breakthrough over the following century and a half that was hated and fought against by the circles of Helmholtz.

In his library, Bach had a pamphlet written by Leibniz in 1707, entitled "On Wisdom." Usually, Leibniz wrote in French or Latin, but this pamphlet was part of a series addressed, in a very personal way, to the German nation. It included a challenge to the musicians of Germany, to help bring true happi-ness to the men and women of their nation; it urged that such happiness depended on showing them how to perfect themselves, with the example of beautiful music. The power of musicians to accomplish this, Leibniz warned, could only develop if musical practice were made more scientific.

The pamphlet stated, in part:

Wisdom is nothing other, than the science of happiness itself, thus teaching us how happiness is to be achieved.

Happiness is a condition of a continuous joy— Joy is a desire, which the soul feels as part of itself. The desire is a feeling of a perfection, or an excellence, be it within ourselves, or in something other; . . .

Figure 2: Astronomical Definition of C=256

The pitch of Middle C at 256 cycles per second has a uniquely defined astronomical value. The period of one cycle (l/256th of a second) can be constructed as follows: Take the period of one rotation of the Earth. Divide this period by 24 ( = 2 x 3 x 4), to get one hour. Divide this by 60 ( = 3 x 4 x 5) to get one minute and again by 60 to obtain one second. Now divide that second by 256 ( = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2). These divisions are all derived by circular action.

The image of such perfection, impressed upon us, makes it so that something of that is also implanted within us and awak-ened. . . .

We do not always take notice, wherein the perfection of pleas-ing things rests, or on behalf of what perfection within us things serve, even as our mental processes—though not our under-standing—has feeling of them. We say in general: It is, I know not what, which pleases in this matter, we name that Sympathy; but they who research the causes of things, find the reason more often than not, and grasp, that something lies behind that, admittedly unnoticed by us, but nevertheless to our benefit.

Music gives a beauteous example of this. Everything which rings, has a tremor, or a back-and-forth-going motion in it, as we see in the case of strings; and thus, what rings, makes invisible beats; when such proceed not unnoticed, but in an orderly fashion, and with a certain interchange, they are pleasant, as we observe also otherwise a certain interchange of long and short syllables and the coming together of rhyming in verses, which possess a certain silent music in themselves. The beats upon a drum, the pulse and the cadence in dances, and similar other motions according to measure and rule, receive their pleasureableness from an ordering, for all ordering appeals to mental processes, and an even-measured, though invisible ordering is discoverable also in the beats, or motions of trembl-ing of strings, pipes, or bells, caused artistically, yes, even of the air, which thereby is made to excite evenly, and which then also creates within us, by means of the hearing apparatus, an echo agreeing in tone, according to which also our living soul excites. Thus is music so suited to move our mental processes, though in general such a primary goal has been insufficiently observed and examined.

Leibniz's correspondence shows that Leibniz viewed musical science as a political organizing tool. In a letter to Conrad Henfling, a scientific co-thinker and friend, he wrote:

Our understanding seeks the simplest measurable thing, and we find this in music, even if those who do not know this, do not realize [it is there.] I have noticed an entire series of typical passages, and so to speak, phrases, in music, which are able to be the most obvious cause for the excitement of the passions. . .

As you, so I, believe, that this science is not yet sufficiently grounded and cultivated, particularly the science of its practice, in respect to the art, by means of music to move even the world of feelings of the most rough-hewn person. We can proceed with music in two fashions. One way is like with physics, mathematically provisioned through a geometry which explains the laws of force, and thereby strives to draw out what the figures, the magnitudes and the motions of the portions might mean. The chemist does not go so far, because he is all too limited, as he must conclude everything a priori, and take what

nature offers as a given, and use it the way one uses acid for engraving. It is in this way that the practical musician uses the phrases, about which I spoke, which are similar to the more sensitive [physical] components. . . .

Theory must explain, how these elements are composed and wherein the effect of these sensitive elements exists in practice. Theory must show the pathway, where it is otherwise formed from instinct.

Saint Thomas's Square in Leipzig, with St. Thomas's Church in the right foreground. Here, Bach was cantor for nearly three decades in the first half of the eighteenth century; Mozart visited here to study Bach's manuscripts; here, Beethoven's teacher, Christian Neefe, was trained by Bach's successor as cantor.

Bach and Kuhnau

Although he was employed as a practical musician, Bach's work was never tainted with the flaw of treating music like a known chemical compound. He dedicated himself to examining "the causes of things," which is why he and his associates resolved upon their efforts to establish an absolute system of pitch.

One of the people with whom Bach collaborated, starting early in his life, was Johann Kuhnau, cantor of the St. Thomas School in Leipzig. When Kuhnau had assumed direction of St. Thomas School in 1702, the situation he found was typical for much of Germany. The organ was tuned close to Venetian pitch, somewhere between A = 460 and 466. This pitch was called "choir pitch" or "cornet pitch," and it was widely recognized that it was impossible for humans to sing well at this pitch. Johann Mattheson, the Hamburg-based organist who was a bitter rival of Bach's, but who was privy to the debates of the age, wrote in the 1720s:

Choir tone . . . is so . . . difficult for singers and unsuitable for oboes, flutes, and other new instruments.

Georg Muffat, a leading woodwind player and composer from the late 1600s, who had worked in France, described the turn of the century situation as follows:

The pitch to which the French tune their instruments is usually a whole tone lower than our German one, and in operas, even one and half tones lower. They find the German pitch too high, too screechy, and too forced. If it were up to me to choose a pitch, and there were no other considerations, I would choose the former. . . . This [lower] pitch lacks nothing in liveliness along with its sweetness.

The problem which Kuhnau faced, of course, was that simply choosing French or Venetian pitch, did not answer what the correct criteria were upon which that decision had to be made.

Kuhnau was not only a musician: he was a thorough scholar of ancient languages and a mathematician. The problem he faced was not new, and the solution he chose had actually been first tried in Germany in the early part of the previous century.

In part, the wide divergence of tuning across Europe was one outcome of the split between Catholicism and Protestantism. Catholic Rome and France had, generally, the lowest pitches, while the German Protestants tuned their organs high to symbolize the importance of the church. In the early 1600s, the Protestant composer Michael Praetorius intervened to correct the damage this was doing to singing, by introducing a practice already in use at Catholic chapels around Prague and Bohemia.

Both for reasons of cost and political pressure, it was generally not possible to alter the organ pitch. What Praetorius did was to "transpose" the parts. To perform a piece in the key of C, for example, he would have the organ play a whole step lower, in B-flat or even a third lower, at A. Praetorius viewed human singing as the standard for musical practice. This was consistent with the handbook he wrote on musical instruments. Returning to a practice started during the Italian Renaissance, Praetorius grouped musical instruments in "families," composed of recorders, cornets, viols, etc., in which each member of the family was intended to imitate one human voice type, such as the tenor, soprano, or bass. For Praetorius, the first criterion for setting the pitch for performance of a piece was the physiology of human singing, not the structure of instruments.

Kuhnau, who knew of Praetorius's work, wrote in 1717:

Almost from the moment I took over the direction of church music [in 1702], I eliminated the use of cornet pitch [A = 460-466] and introduced Cammerton, which is a second or a minor third lower, depending on the circumstances.

The primary constraint which caused the pitch to be varied at that time was that the woodwinds, imported from France, were built at the French-Roman standard. In 1714, Bach, who lived in Weimar, but who worked with Kuhnau on repairing organs, came to Leipzig to perform a cantata, Nun komm der Heiden Heiland. Up to this point, Bach, just like Kuhnau, always wrote his cantatas in two keys, either a whole step or third below the organ pitch. In 1714, when they entered into more intensive collaboration, Bach wrote five cantatas featuring oboe "obbligato" accompaniments to soprano solos, in which for the first time, the oboe part is only one whole step above the organ part. The oboe was manufactured in Germany, not in France.

One modern-day historian who has succeeded in gathering useful informa-tion on this collaboration between Bach and Kuhnau states that the events of 1714 "all suggest the possibility that a pitch standard was consciously agreed upon among German musicians, beginning the second decade of the eighteenth century."

Later, Quantz provided a very clear indication of the preferred pitch of the German composers, when faced with the choice of Venetian or Roman pitch. He wrote:

I do not wish to argue for the very low French chamber pitch, although it is the most advantageous for the transverse flute, the oboe, the bassoon, and some other instruments; but neither can I approve of the very high Venetian pitch, since in it the wind instruments sound much too disagreeable. Therefore I consider the best pitch to be the so-called [German] A-chamber pitch, which is a minor third lower than the old choir pitch. It is neither too low nor too high, but the mean between the French and the Venetian; and in it both the stringed and the wind instruments can produce their proper effect.

The mean between the French and Venetian pitch is A = 429.

Further evidence that Bach's circle was associated with a broad effort to adopt the C = 256 standard comes from France. In 1713, parallel to Kuhnau's efforts, the French scientist Joseph Sauveur completed more than a decade of experiments in waves, establishing the field of acoustics. Sauveur concluded that C = 256 was the only correct pitch, revising an earlier view that C should be tuned to 100 cycles per second, and presented the work to circles with whom Leibniz would have had access.

Elementary Principles

Above all, Bach's music is the best proof that his criteria for tuning were the same as Mozart and Beethoven's. There are two features to his compositions which show that C = 256 was the pitch standard from which he composed: first, the placement of the registral shifts in the musical lines; second, the highest and lowest notes which he wrote for the vocal sections (that is, so-prano, alto, tenor, bass) in his choral works. This span between the highest and lowest note for each voice is called the vocal range.

There is an unlimited number of musical examples that illustrate this principle. We take three examples here.

The first example, shown in Figure 3, is from an instrumental composition, the Well-Tempered Clavier, written for keyboard. Even though it is written for keyboard, the piece is a very transparent illustration, (in idealized, instrumental form) of vocal species characterized by unique register passages.

Figure 3: From Prelude I, of Bach's Well-Tempered Clavier

This phrase illustrates the vocal principles in composition. The highest note in the soprano line, A, is "answered" by introducing F-sharp, the note at which the shift occurs from the first to the second register for the soprano voice.

The piece opens with three voices, beginning on C (male voice), E (mezzo-soprano) and G (soprano). The soprano voice moves the fastest, (has the most number of notes). Each voice begins in the second-register position. The composition opens with an elementary four-measure statement, in which the two lower voices each get the chance to move, momentarily, to their first register. The second four measures "answer" the first four.

To create this apposition, the soprano must do something new: the soprano rises to A, a third-register position, and then "answers" itself by introducing the singularity F-sharp. This tone is a singularity, because it is not part of the "family" of tones in which the piece began, which was the "key" of C-major, a grouping which has no sharps or flats. However, the F-sharp must be in the second register to be heard in respect to the first four measures. If the tuning is below C = 256, this tone falls over, into the first register, and is not part of the first four-measure statement. The interconnected action

between registral and harmonic change is a fundamental feature of Bach's method of composition; this phrase has to be "sung" at C = 256, or it would not have been written this way.

Figure 4: From Bach's Mass in B-Minor

The bass voice ascends, on the word "ascends," to the high note E. At current high levels of tuning, a chorister would strain his voice attempting to sing this note.

Not only the lowest limits for tuning, but also the highest limits for tuning are shown by Bach's choral works. In Figure 4, an excerpt from Bach's Mass in B-Minor, the bass section of the chorus, singing on the words "ascends to heaven," rises to an E, a third-register pitch for the bass. Bach expects all bass singers, not just highly trained virtuosi, to be able to sing this tone.

Such writing shows that Bach would never have composed at the value A = 440, (the pitch endorsed by Helmholtz), or at the even higher pitches fashionable today. At such values, the bass voice is horribly strained and cannot properly phrase.

How low did Bach expect his chorus to sing? In his four-part writing for chorus, the second voice, alto, was sung by boys and, in some cases, women. In earlier times, this voice part had been sung by men (with higher "tenor" voices), and would descend even lower than the pitches indicated in Figure 5, an example taken from Bach's St. Matthew Passion. The voices are descending deeply here to create suspense on the text, "the murdering blood." The F-sharp in the second measure, alto part, is near the absolute limit where this voice part, executed by boys, not men, could be expected to produce a tone. The same is true of the final E in the last measure, bass part.

Figure 5: From Bach's St. Matthew Passion

As the chorus sings the text, "the murdering blood" (mördrische Blut), the alto and bass voices descend to the lowest tones of their vocal range. At a pitch below Middle C = 256, only the best of professional singers could properly produce these notes.

Bach's Legacy

It was Bach's campaign on behalf of scientific criteria for musical composi-tion, including a fixed standard of pitch, which laid the groundwork for momentous achievements by a subsequent generation of composers. In 1722, Kuhnau passed away, and one year later, Bach was chosen as his successor as cantor of the Leipzig St. Thomas School. His work established the school as a wellspring for scientific work for all posterity.

Bach's successor at the St. Thomas School, Adam Hiller, for example, educated Christian Neefe, the musician and philosopher who educated the child Ludwig van Beethoven. In 1787, Wolfgang Amadeus Mozart visited the St. Thomas School, and joyously peered over the manuscripts and parts stored there. It was one of the only places where Bach's works could be found.

One of the testimonials to Bach's efforts were the organs built during his lifetime. From time to time, Bach was invited to give organ concerts in Dresden, events which became famous. Some of these concerts were performed on organs built by Gottfried Silbermann, a proud and meticulous craftsman with whom Bach had good-natured feuds on the principles of tuning. Silbermann would build a keyboard, Bach would try it out; Bach

would criticize the instrument, Silbermann would bristle—and then adopt Bach's ideas. As a result of this back and forth, Silbermann built two organs in Dresden during Bach's lifetime, both of which were set at the Cammerton pitch adopted by Bach and Kuhnau, and for which no transpositions were required.

Let the Helmholtzians rant and rave. The lid is being ripped off their frauds, and the method of scientific inquiry is rightfully being established as the basis for beauty in musical form.