Number Symbolism in Bach's Vocal Works
Discussions - Part 2

Continue from Part 1

Golden ratio
Bach and the Golden Section: Clarification

Rémi Schulz wrote (December 19, 2003):
That's Remi from France.

I wondered if this group had discussed the thesis and the recent book (both in French I'm afraid) by Canadian lute-player Guy Marchand, about Bach having used golden ratio in Church Cantatas.

I would find his argumentation convincing if I didn't know my own work about Bach numerology and golden ratio, which might bring something to the subject, so I tried to translate (poorly) a bit of it: http://perso.club-internet.fr/remi.schulz/bach/GV.htm
Shortly it states that there are numeric patterns that are so perfect they could be neither intentional nor coincidental.

Sorry if this is not the right place to refer to, and thanks to anyone that would indicate me some group more devoted to Bach numerology.

Dale Gedcke wrote (December 19, 2003):
[To Rémi Schulz] I am not an expert on numerology in Bach's compositions. But, your inquiry about the golden rule caused me to recall something I had read.

I was researching the origin of the fanfare "Abblasen", originally ascribed to Gottfried Reiche, because of a painting of him on his birthday. The portrait showed him with his trumpet under one arm and a copy of the score of Abblasen in one hand. His thumb obscures the name of the composer of the fanfare.

In the research referenced below, the author points to J.S. Bach as the composer of Abblasen. One of the reasons mentioned is based on numerology and "personal signatures" that have been found to be common in the compositions by J.S. Bach. The author notes that Gottfried Reiche was a favorite trumpeter employed by Bach, and conjectures that Abblasen may have been a birthday present from Bach to Gottfried. In the USA, Abblasen can be heard each week on "Sunday Morning (CBS News)". The musical introduction is played by Doc Severenson on a piccolo A trumpet.

The link to this researcher's work may expose other sources of information on numerology in Bach's compositions to you: http://ucsdnews.ucsd.edu/newsrel/arts/dbachfanfare.htm.

Here is the relevant quote from that site:

"Bach was also well known for his use of various self-referential word and number games within his pieces. For example, the last subject of the final fugue of the Art of the Fugue has as its four-note theme BACH (in old style German notation "B" stood for b-flat and "H" for b natural). Bach used the BACH theme in other pieces as well. Among his favorite numbers were 14 (=BACH with B=2, A=1, C=3, H=8) and 41 (=JS BACH -in old German notation, as in Latin, "I" and "J" were the same letter)."

Good luck on your research into Bach's numerology!

Dale Gedcke
(Amateur classical and modern trumpeter)

Santu de Silva wrote (December 22, 2003):
My humble opinion about the golden ratio is that it really isn't relevant to Bach's numeralogy.

As you might know, the Golden ratio is what is called an irrational algebraic number, that is, it is not the ratio of two integers. You cannot represent it as a fraction, such as 7/13, or whatever.

You can, however, represent it arbitrarily closely --this is called approximation-- as a fraction. What does this mean? It means, you can find fractions as close as you like to the GR, but not exctly equal to it.

If ANYONE wanted to consciously represent the golden ratio in their compositions, it is impossible. If they want to represent it approximately, it is very easy, but then, how would we know it was the golden ratio, and not the square-root of three, or whatever? Approximation has no place in numerology/numeralogy.

There is statistical evidence that many sonatas, etc, when you divide the duration --in some units, e.g. half-notes-- of one movement by that of another, you often get ratios roughly equal to the g.r. VERY roughly. But then, if you divide actual time duration, taking into account the tempi, the ratio of the two movements will be quite different (unless they are performed at the same tempo, which, of course, will vary from performer to performer). In addition, unfortunately, 25% of the numbers between 1 and 2 are close to the G.R. in the eyes of many beholders. So there you are: it's not worth worrying about. The golden ratio is all about taste and proportion, not about numerology.

It's like asking: what is the most central spot on the surface of the Earth? Answer: there isn't one.

Matthew Neugebauer wrote (December 23, 2003):
[To Santu de Silva] I'm no mathemetician, but I've always wondered about the gr-how on earth can a composer use it when he/she has only a vague idea of how long the movement/piece will be? I think it just boils down to the typical dramatic curve, where the climax occurs about 2/3 into the work. Does this have to do with the gr? My theory teacher (who'll be off researching Bruckner all 2^nd term) mentioned the gr in class, so maybe it has some weight. Although I don't hang on his words blindly just cause he has a PhD. Oh well...

Satofumi wrote (December 23, 2003):
[To Rémi Schulz] Math principles are prevalent all over the phenomena we experience, with or without human intention. Saying like this is not denying the significance of studying the golden ratio or math principles in Bach's music, as the study of quantum mechanics is, as a typical instance, meaningful for understanding the world, the relation of phenomena with human consciousness being unclear in physics. Thanks for the very interesting link.

J.B. (Schwesteringeborg) wrote (December 25, 2003):
Bach and the Golden Section: Clarification

In order to clarify such discussions, allow me to note that the GS, although expressed in number, and illustrated arithmetically or geometrically is NOT an aspect of number symbolism, wherein numbers are assigned an extra-referential significance. Certainly, the nominally absolute GS can only be approximated by a fraction, which is itself a ratio. "Ratio" is the quantitative comparison of two things. "Proportion" is the equality of two or more ratios (Euclid). When in a given ratio, where the larger number's correspondence to the pair combined approximates the lesser's correspondence to the larger, a singular "poportion" is approximated: the GS.

The modernistic tendency to lump all matters concerned with "number" together is misleading, disingenuous and may betray a poor education. Symbolism, numerology, gematria (or alpha-numerical cryptography)are distinct and discrete topics. The GS, Divine Proportion, and Euclid's "Division in Mean & Extreme Ratio" belong to a field of study far removed from matters of purported numerology and supposed symbolism. Certainly, some studies in each field are more credible than others are should be judged on their own merits. Apart from the Guy Marchand study mentioned earlier, I recommend Dr. Tushaar Power's dissertation "J.S. Bach and the Divine Proportion," Duke University: 2001, (ISBN # 0-493-54647-2) for those who wish to pursue the latest scholarship.

Rémi Schulz wrote (December 25, 2003):
Thanks for all the answers.

There are architects, like Le Corbusier, directors like Eisenstein, composers like Bartok, who claimed they used the golden ratio in their works. It's up to anyone to like these works or not, to judge if their success has anything to do with the gr, but the reality of these works is doubtless.

For other artists like Bach who didn't claim anything but where some clues might make one think he could have used the gr, I think there will never be any certainty about it, unless some new documents were found, and that nothing is forbidden a priori.

My humble opinion is too that Bach had nothing to do with the gr, but I'm troubled by some relations found by Marchand, others (over 90 entries for "Golden section" in the Bach bibliography), and myself.

I don't think either that the rosicrucian thesis of Van Houten is rel, but some of his readings are obviously not only wishful thinkings. I'll try another example, the Symbolum Nicenum of B minor Mass (BWV 232), composed of five great parts :
choirs of Credo in 129 bars (45+84)
duet in 80 bars
choirs of Crucifixus in 233 bars (49+53+131)
aria in 144 bars
choirs of Confiteor in 251 bars (141+110)

Marchand finds significant that the pieces in 49 and 131 bars framing the climax of Crucifixus give perfect golden sections, and that sure might be, but, looking only for relations in single pieces, he forbids himself to see that 129 and 80 are in perfect gr, as well as 233 and 144. More, 144 and 233 are Fibonacci numbers, that means they offer the most perfect approximated gr for numbers in this range, and their sum 377 is the 14th Fibonacci number.

Besides of gr, Van Houten states that 80 with 129 alludes to Bach's birth and death (the 80th and the 209th days of the year).

For others, 129 is 3 times 43, gematria of CREDO, of which there is 43 single entries of the word, and 6 multiple entries giving 15 other CREDO sung, number of letters of "Credo in unum deum".

And the 84 bars of "Pater omnipotentem" fit with the 84 letters of the 14 words sung.
Etc., etc.
http://perso.club-internet.fr/remi.schulz/bach/GV.htm

Jason Marmaras wrote (December 26, 2003):
The Golden Section (or "cut", that is the exact greek translation) was used in antiquity to enhance buildings, shapes, sculptures et c. with harmony; that is, to make the proportions seem 'correct', comfortable and pleasant to the beholder's eye.

[I even watched a documentary about beauty and the GS, that showed that, statistically, the prettier women had their proportions (chin and cheek, nose and mouth[width], leg and torso etc.) closer to the SR than the others ]

It is my speculation (and I think not mine alone) that the use of such a ratio (as defined by J.B., a section "where the larger number's correspondence to the pair combined approximates the lesser's correspondence to the larger") should be - in a music where every note is placed harmonically and dependently among the others - to give harmony to the whole an inner harmony that can just be felt or guessed...

Anyways, the main point today(*) (or what it should be):
MERRY CHRISTMAS ALL!!!
Have a merry Christmas, close to the ones you love (including Johann, I guess ; ) ) ! ! !
[Enemies embrace]

Bradley Lehman wrote (December 26, 2003):
[To Rémi Schulz] In Why People Believe Weird Things Michael Shermer explains an example where mathematician Martin Gardner analyzed the Washington Monument and found it to be based heavily on the number 5. The exercise was simply to show that from any sufficiently large amount of undigested data, and with a sufficiently creative person analyzing it, it is not surprising at all that patterns can be demonstrated. That ease does not prove (or disprove) that other patterns are present anywhere deliberately...it just suggests that anything argued "after the fact" should be greeted with plenty of skepticism.

Yes, I'm familiar with some of the Bartok examples; we went through them in music theory classes to see where he did set things up deliberately with the golden ratio. That doesn't prove that any other composer did, or did not; only that such proportions (being observable in many natural phenomena) furnish a useful structure for music, if a composer chooses to use them.

As a kid, one of my favorite films was "Donald Duck in Mathmagic Land" where the golden ratio (and Fibonacci spiral etc) was shown to apply to anything from plants to architecture to the human body to music to pentagrams to the game of billiards.
http://us.imdb.com/title/tt0052751/

Thomas Braatz wrote (December 27, 2003):
Ruth Tatlow, who investigated the role of numbers in music thoroughly, wrote the article on ‘Number Symbolism,’ in the “Oxford Composer Companions: J.S. Bach [Boyd, Oxford, 1999] and also has published the book, “Bach and the Riddle of the Number Alphabet” (Cambridge, 1991.) She, along with others (such as Brad Lehman,) advise correctly that a very healthy dose of skepticism is required when working with any number-related concept when applied to Bach’s music. This does not mean that out of fear of repeating the conclusion such as that of the ‘Washington Monument’ being based heavily on the number 5, all intellectually astute individuals must avoid investigating Bach’s possible use of numbers (whether deliberate or not) to their own satisfaction. The following excerpts taken from Tatlow’s article on numbers in music in the New Grove (Oxford University Press, 2003) will bear out the point that there are still some open avenues to be explored despite the fact that some Bach scholars such as Smend tended to carry their investigations to extremes at times:

>>In the past 50 years some startling claims have been made about how Renaissance and Baroque composers might have used numbers in their music. The numbers are generated from the score by counting, for example, how many breves, bars, pulses or notes there are, or how many times a word is repeated, in a phrase, section, complete voice or movement. Characteristic of this so-called ‘numerological’ approach is the swift move from counting to interpreting. When a number recurs or is deemed significant it is treated as symbolic and interpreted either by traditional symbols or through the use of a number alphabet.

The number alphabet was first introduced to musicology by Friedrich Smend Smend and his colleague Martin Jansen spent many years trying to discover the meanings of numbers that recur in the works of J.S. Bach. They began from the premise that every numerical relationship in the score was consciously placed there by the composer and could therefore be considered symbolic. In 1943 Smend added the use of the natural-order number alphabet (A = 1, B = 2, C = 3 etc.; IJ = 9, UV = 20, Z = 24) to their growing list of interpretative methods. Jansen was alarmed by this, arguing that the method could make any number mean many things, but his early death in 1944 cut short his moderating influence.

In 1947 Smend wrote publicly about the number alphabet in the third and fourth of six booklets of programme notes for a series of performances of Bach’s church cantatas in Berlin. He unwittingly introduced several factual errors, however, which in turn misled him as he interpreted the numbers: he gave examples of only two number alphabets, whereas over 40 may be found in various printed German sources of the 17th and 18th centuries, and he confused two distinct number alphabet traditions, the cabalistic gematria, which is a means of interpreting the Bible, and the poetical paragram, which is a means of generating ideas used by poets. Since 1947 other musicologists have experimented with Smend’s theory, with varying degrees of credibility. Some fundamental errors have been perpetuated, including the inaccurate use of the term ‘cabalistic gematria’, indiscriminate use of the natural-order number alphabet and historically incongruous interpretations of numbers.

There is value in Smend’s work, however. It has recently been shown that, since at least the 1630s, the poetical paragram had been a widely known technique for generating ideas before writing a poem (Tatlow, 1991). In Bach’s day it was one of the techniques listed among the “loci topici” in poetry textbooks. Although the paragram technique does not appear in books on music theory, it is possible that musicians may have applied it to music.

Musicology is left with a dilemma. Counting notes and pulses frequently reveals a numerical correlation between the sections of a musical work. This could imply that the composition was organized numerically at an early stage, and the temptation for the modern analyst is to assert that the numerical relationships were devised by the composer. Yet there is slender historical evidence to support this: little is known from music theory or surviving sketchbooks about the pre-compositional processes ocomposers before Beethoven. Without a firm historical basis it is both premature and irresponsible to draw conclusions about compositional procedure from numbers in the score. A separation must be maintained between numerical analysis, comment upon the compositional process and speculative interpretation of the numbers. There is also a need to consider whether there is any historical justification for the analytical techniques used to generate the numbers; and if so, whether the numbers in the score were created consciously by the composer and whether the numbers are wholly structural or have some further significance.<<

And

>>The lack of historical evidence of the use of compositional numbers seems extraordinary in view of the quantity of writing on Bach and number symbolism. A series of number techniques based on Smend’s work has evolved and become accepted by dint of repetition. [My comment: this sounds a bit like the ‘shortened declamation or accompaniment’ theory for performing Bach’s secco recitatives!] Yet in treatises of this period there is virtually no discussion of the use of numbers in the construction of a composition, either proportionally or symbolically, nor any description of numbers used as a pre-compositional aid to invention.

A popular way of generating ideas at this time was through the “ars combinatoria.” In his dissertation “De arte combinatoria” (1666) the mathematician and philosopher G.W. Leibniz described the principle of a universal language, and 12 years later he produced a fully developed artificial language which he believed could be translated into music by using intervals instead of consonants and vowels.

The “loci topici” or “loci dialectici” (which despite their classical-sounding title, were not known to the ancient Greeks) became popular as devices for generating philosophical and rhetorical arguments in the early 16th century, and were also applied to poetry and music. The classification of “loci” species varied from author to author. In a lecture given at Leipzig University in 1695 the poet Erdmann Neumeister described 15 species: “locus” (i) “notationis,” (ii) “definitionis,” (iii) “generis & specierum,” (iv) “totius & partium,” (v) “causa efficientis,” (vi) “causae materialis,” (vii) “causae formalis,” (viii) “causae finalis,” (ix) “effectorum,” (x) “adjunctorum,” (xi) “circumstantiarum,” (xii) “comparatorum,” (xiii) “oppositorum,” (xiv) “exemplorum” and (xv) “testimoniorum.” The “locus notationis” itself was subdivided into (i) “derivation,” ii) “aequivocation,” iii) “synonyma,” iv) “anagramma” and v) “artificium cabalae.” Under “locus notationis” (v) “artificium cabalae” five different number alphabets are listed, each of which could be used in several ways to generate ideas in poetry. Among these is the poetical paragram, a technique adapted from cabalism simply to stimulate the imagination. For example: …As the words ‘Margaretha’ and ‘Meine Seele’ have the same numerical value using the natural-order number alphabet, the poet could use them as the starting point of his poem. Neumeister’s work was published in 1707 by the poet and librettist ‘Menantes’ (C.F. Hunold). Both men were known to J.S. Bach, who was probably familiar with this publication but there is no proof that he adapted the paragram technique to musical invention.

Several German theorists, from Burmeister (“Musica poetica,” 1606) to Spiess (“Tractatus musicus compositorio-practicus,” 1745), used rhetorical models and the “loci topici,” in their discussions of music). Mattheson used the terms “inventio,” “dispositio,” “elaboratio” and “decoratio” to structure his discussion of compositional procedure in “Der vollkommene Capellmeister” (1739). In the section on “Inventio” he applied Neumeister’s 15 “loci” to musical composition, but included neither number alphabets nor any adaptation of the poetical paragram to music in his illustration of the “locus notationis.”

Following the many experiments in using the “ars combinatoria” for musical invention (notably by Leibniz, Euler, Riepel, Christian Wolff and Gottsched), Lorenz Mizler von Kolof produced his own theoretical explanation of music. An important debate between Mizler and Mattheson about numbers in music is documented in Mizler’s journal the “Neu eröffnete musikalische Bibliothek” (founded in 1737) and Mattheson’s treatise “Plus ultra” (1754–6). In response to Mattheson’s assertion that mathematics is not the basis of music (Harriss, 1981, p.46), Mizler wrote:

Mathematics is the heart and soul of music … Without question the bar, the rhythm, the proportion of the parts of a musical work and so on must all be measured … Notes and other signs are only tools in music, the heart and soul is the good proportion of melody and harmony. It is ridiculous to say that mathematics is not the heart and soul of music [“Neu eröffnete musikalische Bibliothek,” ii, 1743, p.54]

It is highly likely that Bach was aware of these discussions, as he knew both men and in 1747 became the 14th member of the society founded by Mizler in 1738 in order to stimulate discussion about music among composers (numerologists have made great play of this since BACH = 2+1+3+8 = 14 in the natural-order number alphabet). But the analyst must be cautious: documentary evidence that Bach’s sympathies lay with Mizler rather than Mattheson may not necessarily be a sufficiently firm foundation on which to build a theory of Bach’s pre-compositional numerical method.

The evidence that comes closest to implying the use of number in the pre-compositional organisation of a work comes not from Mattheson’s section on “Inventio,” but from his section entitled “Dispositio.” Again combining artistic forms, he likened compositional construction to architecture:

DISPOSITIO is a neat ordering of all the parts and details in the melody, or in an entire musical work, almost in the manner in which one arranges or draws a building, makes a plan or sketch, a ground plan, to show where e.g. an assembly room, an apartment, a bedroom etc. should be situated. [Harriss, 469]

Although numbers are not specified, one could argue that Mattheson strongly implied their use since architectural plans at that time were ordered numerically. Mattheson’s clearest articulation of pre-compositional planning can be read in paragraph 30:

§30 [the composer] should outline his complete project on a sheet, sketch it roughly and arrange it in an orderly manner before he proceeds to the elaboration. In my humble opinion this is the best way of all through which a work obtains its proper fitness, and each part thus can be measured to determine if it would demonstrate a certain relationship, similarity, and concurrence with the rest: in as much as nothing in the world is more pleasing to the hearing than that. [Harriss, 478]

Again Mattheson does not specify numbers, but a recommendation that could easily be a practical demonstration of Mattheson’s principles appears in volume iv (1754) of Mizler’s “Bibliothek” (pt 1, p.108). In a section that directly follows the announcement of Bach’s presentation to the society of canon bwv 1076, the anonymous author writes:

In the winter the cantata should be somewhat shorter than in summer … From experience one can specify the duration, namely that a cantata 350 bars long of varying mensuration takes roughly 25 minutes to perform, which in winter is long enough, whereas in summer it can be 8 to 10 minutes longer and so give a cantata of roughly 400 bars.

Although Bach may not have devised these guidelines, he , as a society member, have been involved in the discussions and endorsed the recommendations. In 1619 Michael Praetorius had made a similar recommendation for measuring the duration of a composition:

80 tempora take half of a quarter of an hour, 160 tempora take a quarter of an hour, 320 tempora half an hour, 640 tempora an hour. In this way one can so much better judge how long the song or work is so that the sermon may begin at the correct time and the other church ceremonies adapted accordingly.

In both of these examples numbers are used as a tool to measure the length of a church cantata in bars and in minutes. It is an indication that in this period there was an increasingly pragmatic approach towards composition.<<

For more information on how the proportions in architecture have been related to specific pieces of music in the Renaissance, check out those portions of Tatlow’s extensive article on numbers in music in the New Grove. Do read Tatlow’s article in the “Oxford Composer Companions: J.S. Bach” that many of you have available. It gives more detailed information on Friedrich Smend’s research.

Eidam spikes gematria

Bradley Lehman wrote (November 10, 2005):
While looking up some things about the Well-Tempered Clavier and Art of Fugue, in Klaus Eidam's biography of Bach, I ran across Eidam's humorous skewering of cabalistic/gematric symbolism:
http://tinyurl.com/8c2c7 (pp138-40) and
http://tinyurl.com/8b598 (pp339-40).

Eidam's writing gets giddy-silly to make his point, and some of it made me laugh out loud. I especially like his wry comment, after he has presented some outlandish but typical dogma about sharps and naturals, "It is deeply regrettable that to this day musicology still has not deciphered the theological meaning of the accidental musical flat symbol b."

The links go to Google Print -- create an account if necessary, to see those pages.

"People who believe in the significance of such numeric relationships in music are victims of a fundamental error: that written notes and music are identical. But music obeys a simple formula: What we do not hear is not music." - Eidam, p340

Tom Dent wrote (November 11, 2005):
[To Bradley Lehman] I thought the 3 flat signs of the Clavierubung Part III were supposed to refer to the 3 persons of the Trinity. Eidam, to judge by your quotation, is a vigorous thrower of bathwater, but may not have the subtle perception to see an infant therein.

Music's message to the audience is, indeed, sound; but the composer's message to the player(s) is inescapably graphical - whether or not the composer consciously intends to use visual properties of a score. Is the well-publicised business of the 'Kreuz' motif (cross-shaped patterns of 4 notes) pure coincidence in all cases?

The tinyurls don't seem to yield anything.

Setting aside gematrian and suchlike debates, how accurate do list members who have read him believe Eidam to be? Does he provide source references? Tomita says not.
http://www.music.qub.ac.uk/tomita/bachbib/review/bb-review_Eidam-TLJSB.html

The book's apparent features - claims contradicting most current scholarship, plus lack of verifiable references - are not particularly encouraging. Is he, in fact, a polemicist like Mattheson? (cue gasps of horror...)

To be sure, the fact that he may have had access to previously-not-considered east German materials makes it conceivable that he could get somewhere.

Bradley Lehman wrote (November 12, 2005):
< I thought the 3 flat signs of the Clavierubung Part III were supposed to refer to the 3 persons of the Trinity. Eidam, to judge by your quotation, is a vigorous thrower of bathwater, but may not have the subtle perception to see an infant therein. >

[The True Life of Johann Sebastian Bach by Klaus Eidam, 1999 German, 2001 English]

At the beginning of chapter 24, p291, Eidam treats that same alleged "Trinity" fugue. "The fugue, in E-flat major, has become known as the St. Anne or the Trinity Fugue, in allusion to its triple character---three themes are separately introduced and then interwoven with each other. Since there are three themes, Schweitzer posited the reference to the divine Trinity, not without carefully distancing himself from the idea: He states that an organist (unnamed) drew his attention to the correlation. Rueger then expands on the insinuation in his Bach biography, pointing out that not only the fugue but also the prelude is tripartite. The structural observations are correct, but identifying the work as a detailed portrayal of the central Christian belief undoubtedly goes too far. With complete impartiality, we might conceivably recognize the first fugal theme as the ascent of God's spirit from the depths. But if the second theme depicts Jesus Christ, we have him speeding by on roller-skates, and the third evokes a Holy Ghost who clanks along like a knight in armor."

He then goes on, a couple pages later, into the question why Bach wrote so many cantatas.

Eidam's procedure that I've seen so far is that he puts up romanticized legends, and other biographers by name, like a row of straw-men, and then he knocks them all off with irreverent jokiness...instead of providing references.

Bradley Lehman wrote (November 12, 2005):
Tom Dent wrote:
< I thought the 3 flat signs of the Clavierubung Part III were supposed to refer to the 3 persons of the Trinity. >
Maybe, maybe not, but why flats? Why not 3 of anything that's convenient? I don't think it's a very important point.

< Eidam, to judge by your quotation, is a vigorous thrower of bathwater, but may not have the subtle perception to see an infant therein. >
I read some other parts of the book, months ago, and wasn't terribly impressed; but I still found his gematria-spiking humorous and entertaining a few days ago, exactly as I said. It's not fair to judge the whole thing by just a handful of quotations anyway. I still want to read the rest of it.

< Music's message to the audience is, indeed, sound; but the composer's message to the player(s) is inescapably graphical - whether or not the composer consciously intends to use visual properties of a score. Is the well-publicised business of the 'Kreuz' motif (cross-shaped patterns of 4 notes) pure coincidence in all cases? >
Well, what do you think about its putative use all through the keyboard partita #6 in E minor? Why would anything allegedly symbolic be there? Or in Herrmann Keller's analysis of WTC 1 C# minor fugue, harking back to the Crucifixus of a J.K. Kerll mass, and harking forward to the St Matthew and John passions?

Keller himself didn't catch, or at least didn't make any point of, the "fact" that there's an enharmonic B-A-C-H in that same C# minor fugue, 20+ years ahead of Die Kunst.

< The tinyurls don't seem to yield anything. >
They still work for me, today. They go into "Google Print" searches for the book. Or one can go there separately, on the author's name....
> > http://tinyurl.com/8c2c7 (pp138-40) and
> > http://tinyurl.com/8b598 (pp339-40).

< Setting aside gematrian and suchlike debates, how accurate do list members who have read him believe Eidam to be? Does he provide source references? Tomita says not. http://www.music.qub.ac.uk/tomita/bachbib/review/bb-review_Eidam-TLJSB.html
The book's apparent features - claims contradicting most current scholarship, plus lack of verifiable references - are not particularly encouraging. Is he, in fact, a polemicist like Mattheson? (cue gasps of horror...) >
Eidam certainly promotes the triumph of equal temperament (in several places), and his descriptions of unequal options are woefully thin, which was the first thing I checked tosee what the "true life" would yield. And his title about the "true life" of Bach looks rather like an affront against Spitta, Boyd, et al.

See also the reviews at: Amazon.com

< To be sure, the fact that he may have had access to previously-not-considered east German materials makes it conceivable that he could get somewhere. >
Perhaps.

Is This True?

Continue of discussion from: Mass in B minor BWV 232 - General Discussions - Part 13 [Other Vocal Works]

Rick Canyon wrote (July 30, 2006):
I read in Otto Bettmann's book the following:
there are 2345 bars of music in the Mass in b-minor (BWV 232).
2+3+4+5=14
B+A+C+H=14
Are there really 2345 bars?
Bettmann gave 3 different years for Bach's death, as I recall, so I don't know whether to accept the 2345 number.

Ed Myskowski wrote (July 30, 2006):
Canyon Rick wrote:
< Bettmann gave 3 different years for Bach's death, as I recall, so I don't know whether to accept the 2345 number. >
It depends. What are the three years for Bach's death?

Thomas Braatz wrote (July 30, 2006):
Canyon Rick wrote:
>>I read in Otto Bettmann's book the following: there are 2345 bars of music in the Mass in b-minor (BWV 232).
2+3+4+5=14 B+A+C+H=14 Are there really 2345 bars? >
Friedrich Smend, who had done much research into this area of gematria, warns that there are differences in the length of mvts. between the original (Urgestalt) and the final versions (the Symbolum Nicenum, for instance, in its original form did not contain the "Et incarnatus est" and the "Crucifixus was 4 measures/bars shorter than in its present form).

>>Bettmann gave 3 different years for Bach's death, as I recall, so I don't know whether to accept the 2345 number.<<
There was never any doubt historically about the year or date on which Bach died. BTW, what is the name of Bettmann's book, when and where was it published?

If you have any interest in pursuing the topic of gematria further, check out: http://www.bach-cantatas.com/Topics/Numbers.htm
and the sections that follow it.

David Glenn Lebut Jr. wrote (July 30, 2006):
Thomas Braatz wrote:
< Friedrich Smend, who had done much research into this area of gematria, warns that there are differences in the length of mvts. between the original (Urgestalt) and the final versions (the Symbolum Nicenum, for instance, in its original form did not contain the "Et incarnatus est" and the "Crucifixus was 4 measures/bars shorter than in its present form). >
Actually, this is only partly true. The "Crucifixus" was 4 measures shorter in the original form of the Messe h-Moll, but the "Et incarnatus est" was not excluded. Rather it was part of the Duette "Et in unum Dominum", and was (as was the rest of the movement) in G Major. As to the "Crucifixus", if I remember right, it was literally a copying job of Movement 2 from BWV 12 (the Chorus "Weinen, Klagen, Sorgen, Zagen") transposed down a half step from the original Weimar version (in F minor) and 1 and 1/2 steps from the Leipzig version (in G minor). The four introductory measures were added in 1749 when the Messe was compiled in its final form.

William Rowland (Ludwig) wrote (July 30, 2006):
[To David Glenn Lebut Jr.] What are you trying to say about the numerology? It is not a Fabronaci number if that is what you are trying to get across because Fabronaci numbers are obtained by multiplication =1x2x3x4x5 et al=120 of which could be hypothesized the attribution that 120 represents the Trinity since 1+2+0=3. Fabronaci numbers seem to have a direct correlation with the way nature creates things. Count the petals of a flower and usually it will be some Fabronaci number and the same with many other things. No one has explained if this is a mere coincidence, or there is a correlation, or that this is a clever fallacy.

David Glenn Lebut Jr. wrote (July 31, 2006):
[To Ludwig] That was not my argument. My argument was opposed to this statement:

"Friedrich Smend, who had done much research into this area of gematria, warns that there are differences in the length of mvts. between the original (Urgestalt) and the final versions (the Symbolum Nicenum, for instance, in its original form did not contain the "Et incarnatus est" and the "Crucifixus was 4 measures/bars shorter than in its present form)".

The statement that the "Et incarnatus est" movement was not included in the original form of the Credo is an absolute fallacy. The recent publication of the Neue Bach-Ausgabe of the original forms of the movements in the Messe h-Moll bears this out that the "Et incarnatus est" movement was included in the Duette "Et in unum Dominum", whilst the original form of the "Crucifixus" replecated exactly the 2nd movement of BWV 12, only in E Minor instead of G Minor (Leipzig version) or F Minor (Weimar version).

Rick Canyon wrote (July 31, 2006):
Thomas Braatz wrote:
< There was never any doubt historically about the year or date on which Bach died. BTW, what is the name of Bettmann's book, when and where was it published? >
The book is called "Johann Sebastian Bach As His World knew Him" (Carol Publishing). Bettmann was apparently a member of the Thomanerchor in the early part of the 20^th century, then fled the Nazis. Growing up, I had heard of the Bettmann archive while knowing little of the man, himself.

His book is written in an interesting manner in that it is formatted somewhat like an encyclopedia. The chapters, A-Z, are topics--upon which there is a brief, usually 1-2 page discussion of some aspect of Bach's life. A very easy and enjoyable read. But, as I mentioned I found 3 different dates for Bach's death including the correct one. One of the incorrect dates was certainly in the wrong year, if not both.

Here is a website on Fibonacci numbers: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

Ed Myskowski wrote (July 31, 2006):
Ludwig wrote:
<< What are you trying to say about the numerology? It is not a Fabronaci number >>
David Glenn Lebut Jr. wrote:
< That was not my argument. >
If you will forgive me interrupting, could I attempt to to condense, with minimal attempt at wit?

Numerology is additive, so that 2345 adds to 14. The numerologica equivalents to <bach> (BACH?), 2138, also add to 14.

In order for this to be significant, Bach would have needed to contro the number of measures at 2345, in all permutations of the SMP (BWV 244). I do not want to say this is absurd, because that word has proven (correctly) to be incendiary. It is much more in my daily vocabulary to say, highly unlikely. But in order to make the point, you would need to demonstrate that
(1) in at least one permutation of SMP (BWV 244), this was intentional.
(2) all other permutations also add, are related in some way, or the original (or subsequent) intent was abandoned.

Numerology and Fibonaccci sequences are kissing cousins, at best. Better understood as unrelated. Numerology is additive of numbers of any derivation, Fibonacci is additive of a special sequence. Which creates a spiral. Actually a larips, spelled backwards. Pardon the exception, that is an attempt at wit.

On a more positive, organic, note: thanks to Ludwig (is Bill preferred?) for the summary of organ technology, very informative (carefully concise, noted and appreciated) for the non-specialist. Organism, not organist.

Ed Myskowski wrote (July 31, 2006):
Thomas Braatz wrote:
<< There was never any doubt historically about the year or date on which Bach died. >>
Canyon Rick wrote:
< One of the incorrect datwas certainly in the wrong year, if not both. >
There is a fundamental rule in technical and financial writing. Don't make errors in arithmetic, numbers, or accepted data. One mistake of this nature will discredit your entire argument. Proofreading and data checking, ad nauseum, is the order of the day.

I have never been a musicologist, but I suspect this principle applies. In truth, I don't suspect. I can tell you that it does.

The guy who screwed up the date is the guy with the numerological (2345 = 14) SMP (BWV 244) theory? Well, everyone makes mistakes. But why is it that the people with weird ideas seem to make more of them?

David Glenn Lebut Jr. wrote (July 31, 2006):
[To Ed Myskowski] I wouldn't mind the interruption, if the interruption was to the point, which yours was not. I was not arguing about the numerology at all. In fact, I think such speculation belongs to Judaic theology than to music, and especially Bach's music since it was embued not with Judaic, but with Evangelical theological precepts. The only numberological concepts that could be applied are not as you propose, but rather symbolic, such as the opening and closing (and especially the closing) of the Klavieruebung, dritter Theil. The three flats and tripartite fugue have been argued to have been used by Bach to symbolize the triune God.

The point I was addressing (again I have to reiterate) is that the "Et incarnatus est" movement was not at all discarded in the earlier versions of the Messe h-Moll. It was incorporated into the Duette "Et in unum Dominum", whereas the "Crucifixus" was literally a replication of Movement 2 of BWV 12 transposed to E Minor.

Ed Myskowski wrote (July 31, 2006):
David Glenn Lebut Jr. wrote:
< I wouldn't mind the interruption, if the interruption was to the point, which yours was not. >
Sorry I conflated your posts with the numerology thread (Is This True), where they appeared, and which I was interrupting.

I think my statements were accurate, concise, and very much to the point of the thread: is the total of 2345 measures in SMP (BWV 244) of numerological significance?

I am not ready to adopt the Brad Lehman approach of eliminating names when responding (not just yet, anyway). But I see the value, Brad.

Rick Canyon wrote (July 31, 2006):
< I think my statements were accurate, concise, and very much to the point of the thread: is the total of 2345 measures in SMP (BWV 244) of numerological significance? >
Well, I asked because if it is true, I think it's quite astounding. Clearly I don't think it would be a coincidence.

Somewhere, however, I read that Bach didn't do these number games with his music for any sort of sinister, "DaVinci Code"-type reason. He did it largely because he could do it. Numbers just added an extra dimension, extra challenge to his composing.

David Glenn Lebut Jr. wrote (July 31, 2006):
[To Canyon Rick] Wrong again. He did not do any such thing, except for the reasons I stated. This whole thread is not at all about Bach and all about Judaic speculation. The only "numbers game" Bach employed was symbolic and in the music itself, not combining movements as has been mentioned. Mozart would later follow Bach's lead in his "Die Zauberfloete" with a different angle (Masonic instead of Evangelical/Christian). Case in point: the Praeludium and (especially) Fuge Es-Dur BWV 552. The work (which opens and concludes the Klavieruebung, dritter Theil) is in three flats and the Fugue is tripartite--both of which were intended to symbolically represent the Triune God.

Douglas Cowling wrote (July 31, 2006):
David Glenn Lebut Jr. wrote:
< Case in point: the Praeludium and (especially) Fuge Es-Dur BWV 552. The work (which opens and concludes the Klavieruebung, dritter Theil) is in three flats and the Fugue is tripartite--both of which were intended to symbolically represent the Triune God. >
Numerical symbolism can be found all over Bach's works, e.g. The Sanctus of the B Minor Mass (BWV 232) stresses the Trinitarian symbolism of the triple Sanctus (Tersanctus) in its 3 oboes, 3 trumpets, and 6 voice choir. And all those triplets!

As to mathematical arcana, it's a slippery slope: you can work out formulae to produce just about any result (the "Bible Code" mania of a few years ago shows the impulse is still very much around). Totalling up the Mass in B Minor (BWV 232) to equal Bach's name, however, doesn't recommend itself to me. If it was in the Art of the Fugue or the Musical Offering (BWV 1079), perhaps, but such self-reference seems inappropriate in this instance.

Ed Myskowski wrote (July 31, 2006):
In my previous posts on this thread, I referred to SMP (BWV 244). I see that the original numerological speculation of 2345 = 14 actually referred to BMM (BWV 232). Sorry for this error, it has no effect on the logic of any of my statements, which I stand by.

Bradley Lehman wrote (July 31, 2006):
< As to mathematical arcana, it's a slippery slope: you can work out formulae to produce just about any result (the "Bible Code" mania of a few years ago shows the impulse is still very much around). Totalling up the Mass in B Minor (BWV 232) to equal Bach's name, however, doesn't recommend itself to me. If it was in the Art of the Fugue or the Musical Offering (BWV 1079), perhaps, but such self-reference seems inappropriate in this instance. >
I agree; such mumbo-jumbo as numerology or gematria doesn't affect the way the music sounds in performance, and therefore it's moot. My general principle (personally) is: whatever's not audible isn't the music.

[Not to say that the stuff exists or doesn't exist in Bach's music; only that it's safely in the who-cares realm that is its own circular reward, and doesn't affect any direct perception of the musical work! It's unscientific/unfalsifiable.]

A few months ago I heard a radio discussion forum including scholar Ruth Tatlow, and she had some remarks about a movement of the B minor mass (BWV 232) that has a bar-count in the margin. She pointed out that the bar-count was written there by a copyist (in this case CPE Bach) not to do anything numerological or mystical, but simply as a checkpoint that the written-out parts for that movement don't have the gross omission or addition of a bar through a copying error.

Santu de Silva wrote (August 1, 2006):
[To Rick Canyon] What were the years? we should add them up ...

David Glenn Lebut Jr. wrote (August 1, 2006):
[To Bradley Lehman] Not to mention that it has no place in it. As I had argued before, numerical symbolism is permissible, but when we go to such extremes as has been talked about, when we start Judaising Bach's music, then we have gone too far.

Ed Myskowski wrote (August 1, 2006):
Santu de Silva wrote:
< What were the years? we should add them up ... >
We never did get an answer to that question. But there was an implication that one of the wrong dates was in the correct year, and one of the wrong dates even got the year wrong.

If the wrong year was 1751 = 14? Or maybe 1750 = 13 was correct, and Bach was actually Bagg? Or Aach!

Tom Hens wrote (August 1, 2006):
Ed Myskowski wrote:
< Numerology is additive, so that 2345 adds to 14. The numerological equivalents to <bach> (BACH?), 2138, also add to 14. >
Of course, so do AAAAAAAAAAAAAA. And BBBBBBB. And AM, MA, BL, LB, CK, KC, DJ, JD, etc... And LAA. And DDF. And DDDA. And AAAAACCC. And on and on and on. As the numbers grow larger, the numbers of letter sequences they can be claimed to stand for grows to near infinity. Huge numbers of such sequences will also be real words or names in some language or other. This is why numerology is such nonsense. CK, hmmm... maybe everytime Bach used the number 14, he was actually prophesying the long-awaited coming of Calvin Klein?

(Note: for simplicity, I've used A=1 to Z=26. Depending on how you deal with the letters J and W, not to mention German umlauts, your prophesies may differ.)

Raymond Joly wrote (August 1, 2006):
Numbers and Judaism [was: Is This True?]

David Glenn Lebut Jr. wrote:
"As I had argued before, numerical symbolism is permissible, but when we go to such extremes as has been talked about, when we start Judaising Bach's music, then we have gone too far".
I think the writer is using the term "Judaising" for the third time, and I would like to know why he is so intent on it.

The conception according to which music is nothing but an acoustic manifestation of the order of the world, which again is just a matter of quantities and proportions, adequately described by mathematics only (as exemplified in the music of the spheres, the music of the nine angelic choirs, not to mention the numerus aureus, etc.): that mathematical conception of music is common Greek, Latin and Christian heritage. Pythagoras, Boethius and Plato were not Jewish kabbalists.

I will not state whether I am Jewish or not and will not declare how I understand the present situation in the Middle East, because that would be completely irrelevant. I am sure it will be in Mr. Lebut's answer too, if he is so kind as to write one. But it is precisely because those things are irrelevant that choosing one's words is important.

Douglas Cowling wrote (August 1, 2006):
David Glenn Lebut Jr. wrote:
< Not to mention that it has no place in it. As I had argued before, numerical symbolism is permissible, but when we go to such extremes as has been talked about, when we start Judaising Bach's music, then we have gone too far. >
Would you please explain what this statement means?

Ed Myskowski wrote (August 1, 2006):
Ed Myskowski wrote:
>< Numerology is additive, so that 2345 adds to 14. The numerological equivalents to <bach> (BACH?), 2138, also add to 14. >>
Tom Hens wrote:
< Of course, so do AAAAAAAAAAAAAA. And BBBBBBB >
I was not defending numerology, indeed, more the opposite. Just explaining how it differs from a Fibonacci sequence. If you check your post, you will notice that the A's only add to 13. Another point I tried to make, probably not very successfully.

Ed Myskowski wrote (August 1, 2006):
Raymond Joly wrote:
< I think the writer is using the term "Judaising" for the third time, and I would like to know why he is so intent on it. >
I noticed this as well, and found it offensive. Enough said?

Tom Hens wrote (August 1, 2006):
Ed Myskowski wrote:
< If the wrong year was 1751 = 14? Or maybe 1750 = 13 was correct, and Bach was actually Bagg? Or Aach! >
My favourite bit of numerological nonsense related to Bach is from the infamous Dutch book "Bach en het Getal", by Kees van Houten and someone called Kasbergen (can't remember his first name right now). In the course of showing with mathematical precision that Bach encoded the exact date of his own death in his music, decades before it happened of course, they come up with the following gem (no, I'm not making this up, and I'm quoting a full paragraph of their book):

175 = 1750

In the face of such arithmetical prowess, who can possibly doubt numerologists? (175, BTW, according to them, and I didn't bother to go check, is the combined numbers of bars of all the variations in the Goldberg Variations that have an additional description beyond "variation no. X" in the printed edition. It all makes such perfect sense when you just think of it, doesn't it?)

Tom Hens wrote (August 1, 2006):
Ed Myskowski wrote:
< I was not defending numerology, indeed, more the opposite. Just explaining how it differs from a Fibonacci sequence. If you check your post, you will notice that the A's only add to 13. >
I checked. I typed 14 A's. I'm so proud I got it right!

< Another point I tried to make, probably not very successfully. >
I was just trying to amplify that point. Because of the recently much-discussed problem of (non-existent) threading on a mailing list, I followed up to your message rather than one of the earlier ones.

William Rowland (Ludwig) wrote (August 1, 2006):
[To Ed Myskowski] I missed this but based on what Ed states I find it offensive also. It is one thing to talk about the factual anti-semitism of Martin Luther' teachings and how they affected Bach et al and quiet another to engage in this horrid practice.

Ed Myskowski wrote (August 1, 2006):
Ed Myskowski wrote:
<< that the A's only add to 13. >>
Tom Hens wrote:
< I checked. I typed 14 A's. I'm so proud I got it right! >
Right you are, my error. I neglected to follow my own advice and double-check. Always the way. I think we agree on:

(1) Numerology is nonsense, in any serious sense. Significance of individual numbers as symbols is a cultural matter (3, 5, 13, etc.)

(2) Bach may have had a fascination with numerology, but it has no effect on the sound of his music (thanks, Brad), and at most a minor effect on the architecture. Or maybe he didn't have a fascination with numerology. Not a problem, I have no opinion one way or the other. No data on which to form an opinion, although I do intend to check the BCW archives..

(3) Herreweghe is at (or near) the top of the list for the cantatas he has recorded.

William Rowland (Ludwig) wrote (August 1, 2006):
[To Ed Myskowski] My opinion is that numerology is a bunch of hogwash.

Tom Hens wrote (August 1, 2006):
Ed Myskowski wrote:
< There is a fundamental rule in technical and financial writing. Don't make errors in arithmetic, numbers, or accepted data. One mistake of this nature will discredit your entire argument. Proofreading and data checking, ad nauseum, is the order of the day. >
It's "ad nauseam". This mistake in Latin grammar means anything else you stated is therefore discredited. (Sorry, I couldn't help myself.)

Alain Bruguieres wrote (August 1, 2006):
[To Ludwig] Never heard about 'Fabronaci'. Google never heard about it either. Where did you find this name???

What you call 'Frabonaci numbers' is what mathematicians call a factorial : n!= 1 x 2 x ... x n.

Number of petals has nothing to do with factorials. Factorials grow horredously fast... only flowers growing in an infinite dimensional space could afford so many petals. The rate of growth is well appoximated by Stirling's asymptotic formula.

Number of petals has something to do with Fibonacci numbers more likely. Fibonacci numbers are defined recursively thus :
F(0)= 0
F(1)=1
....
F(n) = F(n-2)+F(n-1).

Their growth is that of a geometric sequence whose ratio is the 'golden ratio'.

Continue on Part 3

Number Symbolism: Part 1 | Part 2 | Part 3