Number Symbolism

The 'symbolic' number seven / Seven again / Bach's Esoteric Interest in Number Symbolism / Bach and numbers / Bach's Number Symbolism / Bach's Number Symbolism - Hidden or Not? / More numbers / Bach's numbers to the glory of God

Thomas Braatz wrote (March 13, 2001):
Does anyone know why 'Seven' is an important symbolic number for Bach? I'm looking for an answer.

Sybrand Bakker wrote (March 13, 2001):
(To Tomas Braatz) Seven = 3 (the number of heaven) + 4 (the number of earth), the number of days the earth was created in, etc.

Jane Newble wrote (March 13, 2001):
(To Thomas Braatz) I can only guess that it is because in the Bible and Biblical theology the number seven stands for perfection and completeness, and also Jesus Christ. Four stands for Humanity, and three for Divinity, and because Jesus Christ was both man and God, seven symbolizes Christ in his perfection. I have not studied Bach's music enough to know how this relates, but he did study his Bible. I'm sure there are much more erudite people here, who would know the answer.

Thomas Braatz wrote (March 13, 2001):
(To Sybrand Bakker) Thanks for your information: But just where do you see the connection to Bach's music, including the cantatas? I have just read a book, "The Occult Bach," which outlines his very likely use of 'Gematrie' - a numbers system based on the alphabet: A=1, B=2 etc., but nothing I see there uses the number 7 directly so as to tie in with his music. I have a feeling that I should know what it is, but at the moment I am drawing a complete blank.

So, in BWV 97, when Simon Crouch (I believe) indicates that the final chorale has 7 parts instead of the normal four, then Bach is thinking of the creation of the earth? Why? I must be obtuse, since I simply do not see the connection there, as much as I do want to see connections of this sort in Bach's music.

Andrew Oliver wrote (March 13, 2001):
I just wanted to add that, as Jane said, the number 7 stands for perfection and completeness (in Christian theology), and this is doubtless relevant. We know that Bach also made use of this number doubled, 14 being the sum of the letters of his name (B+A+C+H = 2+1+3+8). I wonder if it is also relevant that this cantata was composed in 1734, when Bach reached the age of 49 (7x7)?

Jane Newble wrote (March 14, 2001):
< Andrew Oliver wrote: I just wanted to add that, as Jane said, the number 7 stands for perfection and completeness (in Christian theology), >
Not just in Christian theology either. I am looking at a book I have by a Jewish rabbi, and I'll try to write something about it as soon as I have time, if Thomas is still interested...

Thomas Braatz wrote (March 14, 2001):
(To Jane Newble) Thanks Jane! I am interested. Is it the Kabbalah?

Jane Newble wrote (March 14, 2001):
(To Thomas Braatz, regarding Kabbalah) No, it is not, although some of it touches on the same teachings. I am still working my way through this book, and it is about how the Bible is 'created'. It does use lots of gematria, but it's very complex, so it will take /a while. I have also got another book by a Dutchman, and that has a shorter chapter on each number as used in the Bible, and also a concordance on where they are used. Some of what he writes on 7 follows in digested form:

Seven is a 'rounded' number that does not always denote what happened in reality, but is often also used to give a spiritual significance to an event.

In the Hebrew Bible the Israelites went seven times round Jericho, and Naaman had to immerse himself in the water of the Jordan seven times. Abraham gives seven lambs to Abimelech, and the righteous falls seven times but is raised up again )Proverbs). The Menorah has seven branches. Just a few of the many, many examples. There are more than 200 references to 7 in the Hebrew Bible. The New Testament also has a lot of references, but not nearly as many. The idea is of totality, completeness, perfection. In the Jewish tradition there are also many references to the number seven (including Kabbalah).

Of course, the most important day of the week, the shabbat, is the seventh day. It is the day when the heart takes rest and is reconciled with God, and experiences something of the perfection of God. Seven is a sacred number, and the religious Middle Ages followed in the footsteps of the idea with the 7 meditations, sins, times of prayers, sacraments etc. even turning the five wise and foolish virgins into seven on paintings!

Two times seven makes 14 and is an even stronger expression of a double totality, also used in the Bible, e.g. Jacob served 14 years for Leah and Rachel, the feast of dedication of the temple of Solomon lasted 14 days, and the genealogy of Jesus in Matthew counts three times 14 generations.

Then there are the multiples of seven....

Thomas Braatz wrote (March 15, 2001):
Thanks to all of you, Sybrand Bakker, Andrew Oliver, and Jane Newble, for steering me in the right direction. It all began to make a little more sense. Then I found a reference in my book, "The Occult Bach" that gave me a better perspective. And by coincidence the "Oxford Composer Companion - J.S. Bach (Malcolm Boyd, editor) arrived today. I immediately wanted to prove the value of this book before putting it on the shelf where it might rest for a long time. Surprise! A two-page article on Bach's Number Symbolism. The article is a bit uneven and I would have liked to learn more, but the examples were good and the attempt at classification of the different types of number symbolism very helpful. But for further detail my "Occult Bach" book pointed to the following references: The book is based primarily on the work of Marinus Kasbergen and Kees van Houten's "Bach en het getal" (1985), a book I have tried to order from some German on-line booksellers, but to no avail. Must be a popular book! The other references were to the MGG I, 1028ff and MGG 16, 1971ff (MGG=Die Musik in Geschichte und Gegenwart, the German equivalent to The New Grove Dictionary of Music) Just a few important authors to mention: Arnold Schering, 1940; Martin Jansen, 1937; Friedrich Smend, 1947-8; A. Schmitz, 1950, Walter Blankenburg who wrote one of the articles for the MGG, Henk Dieben (1954-5)"Getallenmystiek bij Bach". This is all very new to me, but very interesting. Please bear with me as I summarize what I found.

Was there a tradition for theological interest in number symbolism in the Lutheran Church in Bach's day? Yes. Examples were given. Look at Jane Newble's message.

Was there a strong theoretical precedent for connecting numbers with music? Yes. Almost without a doubt, through Bach's cousin and friend, J.G.Walther from whom we have a statement about his acquaintance with the work of Andreas Werckmeister, in particular the book "Musical Paradoxal Discourses" 1707. Werckmeister, like Bach, was an organist who understood all the technical aspects of organ building and what an organ should sound like. This is the same Werckmeister who was responsible for developing the final steps from unequal to equal temperament (The Well-Tempered Clavier) so that one could play a keyboard instrument without encountering 'howling' tones or the 'wolf'-tone as it was called when one tried to play in a remote key such as F sharp or G flat. Werckmeister still favored lowering the thirds so that there is a fuller sound. If you don't know what I am talking about, check your recordings of organs and harpsichords. I have some modern recordings which clearly state 'using the Werckmeister temperament.' Just remember, that this is not entirely Equal Temperament, but almost. With Bach the final shift to the equal temperament we know today was made: "Es muß alles möglich zu machen sein." In his book, Werckmeister delves into the semantics of biblical numbers and the use of these numbers in music. Another book that Bach most likely had read is J. J. Schmidt's "Der biblische Mathematikus" 1736 Bach's 'librettist' Picander had published a book, "Ernst-scherzhafte Gedichte, III) 1732. In this book Picander uses gematria in hispoetry the same way that Bach did in his music.

Now comes the hard part. I will try to reconcile the differences between the MGG and the Oxford Companion (Boyd): There are four distinct categories describing the way Bach uses numbers in his music. They are:

Enumeration: simple counting of notes, measures/bars, fugal entries, the number of parts (as in the chorale for BWV 97), number of movements, number of repetitions of a word, phrase, figure, etc.

Operation: transformation of the number arrived at by Enumeration. This could be any common mathematical procedure - add, subtract, multiply, divide, read as a triangular number (in a sequence like 1,3,6,10,15,21,etc.)square or cube root, putting the number in a magic square with others.

Translation: use of gematria - the usual alphabet is A=1, B=2, C=3, H=8, I/J=9, U/V=20, Z=24. Using Operation (addition) BACH=14 J.S.Bach=41 (these two numbers constitute a 'crab'; this type of reversal or permutation is not only allowed, but encouraged.)

Interpretation: What is the meaning (usually religious) that the composer intended to convey. When the number 3 appears, one might immediately think of the Trinity.

Often the examples involve more than one category, so I will let you figure out which category/ies any given example will fall under.

In the passions 11 disciples appear with 11 separate entries (Bach was not the first to do this. Another German composer in the previous century (1600's) had already used this device. Bach was following a previous example here). To represent the Trinity, three voices/parts are used. The number 7 was used to indicate the Creator and Creation, or the Beginning and End. The number 12 was used for the Church, the disciples, the congregation.

In the Symbolum Nicenum of the B-minor Mass (BWV 232), consider the two movements, "Credo in unum Deum" and "Patrem omnipotentem"
The total number of measures/bars for these two movements: 129
Apply gematria: C(3)+R(7)+E(5)+D(4)+O(14) = 43
The number 129 comes from (43 + 43 + 43) X 3 3 = Triune God
The word 'Credo' is sung 7 X 7 = 49 times
The phrase 'in unum Deum' is sung 7 X 12 = 84 times
At the end of the fugue in "Patrem omnipotentem" Bach inserts in his own hand the total number of measures/bars: 84 = (permutation: C=3 X A=1 X (B=2,H=8) the letters BACH rearranged, but this is permissible, as well as combining the B and H into one number as he did here) 12 X 7 = 84 a combination of time and eternity!

What is the total number of measures/bars in the next two movements, "Et in unum Dominum" and "Et incarnatus est"? You guessed correctly: 129 And there are still another two instances in the mass of total measures having the same result: 129. Is this getting boring?

One last example, before I put you to sleep entirely. Are you still there?

The first prelude and fugue to Book I of the Well-Tempered Clavier:
Remember BACH=14 !!
There are 549 notes in the prelude and 734 in the fugue and the sum of both is 1283. So what? Well, 1=A; 2=B; 8=H; 3=C ; rearrange the letters and what do you get? Yup!
How many notes in the fugal theme: 14 = BACH
How many entries does this theme have: 24 an indication of how many preludes and fugues are to follow in this book of the Well-Tempered Clavier. Clever, isn't this? And this analysis goes on and on.

When Marinus Kasbergen and Kees van Houten traveled about Europe presenting this information, the members of the audience shook their heads in disbelief. I'm beginning to think, we need to look at this more carefully and consider Bach's esoteric interest in applying mathematical principles to his music. Having just heard Beethoven's Große Fuge on the radio yesterday and realizing what a struggle he had with this form of composition, I now think of Bach not only composing, as it seems, his fugues with great ease, but also accepting the additional (for me almost inconceivable) challenge to make it fit into a preconceived mathematical scheme and not tell anyone about the pride he must have felt, when he accomplished his task. It just boggles my mind!

Jane Newble wrote (March 15, 2001):
< Thomas Braatz wrote: And there are still another two instances in the mass of total measures > having the same result: 129. Is this getting boring? One last example, before I put you to sleep entirely. Are you still there? >
This sort of thing wakes me up!!! I really enjoy it. Any time you have any more like this..... It boggles my mind too! I'm beginning to see another reason for his words: "es muß alles möglich zu machen seyn"

Jim Groeneveld wrote (March 15, 2001):
(To Thomas Braatz) Tom (and others),

I don't believe anything concerning the apparent symbolic meaning of numbers found in the Bible and in Bach's work. I don't deny the meaning of certain obvious numbers in the Bible, but that's it. The rest is rubbish at the occult astrology level to me. I'm sorry to say it that way. I've got several strong objecting arguments:

Being a statistician I know that searching indefinitely very likely results in finding seeming relations which might desirably be explained as causal or intentional, but which in fact are no more than coincidental. Much more other findings do not show a relation at all. Searching long enough until one or more desired and interpretable results are found is not scientifically justified. A reliable way to show possible evidence would be to state a hypothesis in which a result is predicted (finding relations) that deviates from coincidence significantly, and test it using an appropriate sample. This method would probably not yield any significant result. Even if repeating this method over and over again it once or more might yield significant results, but as with the "desired" relations, repeating it indefinitely would yield positive results coincidentally too. That is because statistics is only probability (based on coincidence or rather deviations from coincidence), never certainty.

Involving numbers in relations which very likely can not have been put together in advance deliberately, like J.S. Bach's name (the letters), and juggling with it, like changing digit orders makes no sense as the seemingly relational result is very much dependent from the notation type of numbers. E.g. 1283 (letters ABHC) decimal is 10100000011 binary, 2403 octal, 503 hexadecimal, ZN in 36-digit notation, and so on and MCCLXXXIII in Roman notation. In other arbitrary notations the seeming relation is absent. And in the same way other relations might seem present (which are not present with the decimal system) if using those other notation systems. For example the 36-digit notation system makes use of all ten numeric digits (0..9) and all alphanumeric ones (A..Z). Some readable and interpretable result (in letters) might appear somewhere (go search for one until you find one, you surely will, after 100 years maybe). But even then that result is just dependent on the alphabetic sequence of letters.

Do you logically believe the numbers have their meanings because Bach intentionally put them together that way, or was it predestinated beyond Bach's influence? Both separate possibilities do appear very unlikely to me. If it wasn't Bach himself, then who was it and why and what would the intention have been? And why would it fit into our decimal number system? Was it God, wanting us to dive deeply to find fitting results to be interpreted by our own judgement? Would God have hidden specific important information in numbers? Would God show Himself that way only to people searching for Him that way? Not to me. Then was it Bach himself? Do you really think he put so much effort together to let those complicated relations fit and still yield a very nice piece of music? No, I don't think Bach was a lunatic that way; he had enough else to do.

To summarize, I don't think it is a good idea to continue this subject on a list about Bach, like this one. I remember another (musical) list or newsgroup discussing the subject some time ago, though I don't remember which one. I don't think Bach kept himself busy with such trash (unless maybe some clear directly obvious number) and falsely attributing him such business does notdo good to his person and his music. Let's stick to the man and his music. The are enough other discussion lists or (news)groups on the internet to discuss such occult subjects. And as a convinced Christian I am not interested in them.

Peter Goldstein wrote (March 15, 2001):
Responding to Jim Groeneveld's arguments against the significance of number symbolism in Bach's music:

I am no expert in this matter, but from my readings, there seems little doubt that Bach was interested in number symbolism. Some scholars find such references everywhere, and I confess that many of these interpretations seem a bit of a stretch. Some, however, make perfect sense to me. My response to
< Then was it Bach himself? Do you > really think he put so much effort together to let those complicated relations fit and still yield a very nice piece of music? >
would be "yes," at least in some cases. This is, of course, a matter of opinion--we look at the evidence and draw our own conclusions. I am more troubled by the assumption that some of the speculations here and elsewhere are "rubbish at the occult astrology level," and that we do a disservice to Bach by exploring them. Without in any way wishing to offend anyone: inevitably, one person's Christianity is another person's occult rubbish. This has been true even among Christian sects for 2000 years--else why all the violent schisms, why the persecutions, why the sect-oriented interpretations of the Book of Revelation, why the Reformation itself? Moreover, whatever the official beliefs of a particular church, it is a fact that individuals tend to live their religious lives individually, and to have tendencies or even solid beliefs that unconsciously go beyond official stated principles. Bach presumably had his own predilections, and to my mind it seems worthwhile to explore them, as long as we are reasonable in our arguments and conclusions.

Jane Newble wrote (March 15, 2001):
< Jim Groeneveld wrote: which one. I don't think Bach kept himself busy with such trash (unless > maybe some clear directly obvious number) >
That is why I thought the number seven might well have been used by him, because it is so obviously used in a symbolic way in the Bible. I agree that, looking back, one could find things that were never meant to be there in the first place, and I certainly am not interested in occultism. I can hardly think Bach was either. But it has to be said that he was inventive.

Andrew Oliver wrote (March 15, 2001):
Generally speaking, I agree with Jim's view of this subject, but with one or two reservations. It does seem that Bach occasionally makes use of the number 7 and its multiples, as in the present instance, most probably because that number has long been regarded as denoting perfection or completeness. I think he also makes use of other numbers when they are either expressly mentioned or implied in the text, and he does this not because he has any interest in occultism or magic, but simply as a means of reinforcing what is already being stated in words. One possible example which occurs to me is found in the B minor Mass (Hohe Messe) (BWV 232), at the Sanctus. Whereas in other movements of the work he uses 4 or 5 or 8 voice parts, here he uses 6 - SSAATB. The original 1724 version of the Sanctus used SSSATB. For the Sanctus section, the voices are often arranged in groups of three, though not always the same three. I think he has probably done this deliberately in order to back up the threefold utterance of the word 'Sanctus'. The bass line shows the text most clearly. When we come to the 'Pleni sunt coeli' section, the 6 voices tend to be in groups of 2, sometimes 3. To me, this all points to the Bible passage from which the text derives, Isaiah 6:3, and the previous two verses telling us that each seraph had 6 wings, three pairs of two, 'and one cried unto another and said "Holy, holy, holy (3) is the Lord of hosts: the whole earth is full of His glory" '.

I do agree that it would be easy to read into Bach's music a great deal of number symbolism which is not there; it only exists because the person looking for it is seeing what he/she wants to see. But although I don't think Bach deliberately set out to incorporate anything of that sort, it does seem to me that he has sometimes predetermined the structure of a movement before writing it, like marking out the foundations before building the house.

Johan van Veen wrote (March 15, 2001):
The subject of the use of numbers in Bach's music is discussed regularly among Bach lovers, experts and amateurs alike. There are two extremes: those who believe Bach deliberately used numbers in his music and was influenced by esoterism. Others think it is all rubbish and almost any relationship between numbers and Bach's music is purely conincidental.

I think both sides are wrong.

First of all, using numbers as symbols was common practice in Bach's time. In fact, it has happened from the early centuries AD. As others have already written, the Bible uses some numbers as symbols. Later on this has been extended, in particular in the Jewish Kabbala, which in some ways also influenced Christianity. Secondly, there can be very little doubt that Bach was a great lover of symbolism. In many of his works we can find proof of that. Therefore it can hardly be surprising that Bach was attracted to the use of numbers as symbols.

The use of numbers also fits into Bach's love and talent for musical architecture. Many of his most famous compositions are known for the architectural structure, like the SMP and the B-minor Mass. We may find it difficult to accept that Bach could have composed works with exactly a certain number of notes or bars, just to express some meaning. We tend to think: didn't he have anything better to do than counting the number of notes or bars? But we shouldn't forget that Bach was an exceptionally gifted individual who had a very deep understanding of the most important aspects of baroque composing and music making. He was well known for his deep understanding of rhetorics, although he never went to university to study the subject. It must have been something that came natural to him. Why couldn't that have been the case with the use of numbers as well?

For me there is no doubt that Bach has used numbers as symbols in his music.

Having said that we need to be extremely sceptical as far as the "results of scientific research" are concerned. As Jim Groeneveld rightly pointed out it is easy to make mistakes in the field of statistics. As someone said: there are lies, d*nd lies and statistics.

The book Thomas Braatz was referring to, by the Dutch musicologists Kees van Houten and Marinus Kasbergen, is a very unreliable source. In the press their "research" has been thrashed as unscientific rubbish. Apart from that, the fact that they both are believers in esoterism has made them speculate about Bach's sympathy for it. They even go as far as suggesting that with numbers Bach predicted the date of his own death in one of his works.

But there is no shred of evidence that Bach was interested in or had sympathy for esoterism nor that he had any connection with supporters of it. Esoterism was certainly unacceptable to the Lutheran church at his time, and sympathy towards esoterism couldn't have remained a secret during his whole life. The conclusions in Van Houten & Kasbergen's book are nothing but wishful thinking.

To sum up, for me there is no doubt that Bach used numbers in his music as symbols. It fits into the picture of Bach's composing and musical thinking. Whether Bach did use numbers more frequently and more extensively than other composers of his time is anybody's guess. We will never know until the works of his contemporaries are as thoroughly studied as Bach's works.

But one needs to look at the statements about the use of numbers in Bach's music with caution. Some time ago a Dutch paper published an article on this subject. The author discovered that in Bach's coffee cantata the number 151 is playing an important role. And that is exactly the sum of "Bach" and "Douwe Egberts" (a Dutch coffee brand) in numbers - that can't be a coinciden! :)

Charles Francis wrote (March 15, 2001):
< Johan van Veen wrote: But there is no shred of evidence that Bach was interested in or had sympathy for esoterism nor that he had any connection with supporters of it. Esoterism was certainly unacceptable to the Lutheran church at his time, and sympathy towards esoterism couldn't have remained a secret during his whole life. The conclusions in Van Houten & Kasbergen's book are nothing but wishful thinking. >
Do a web search with www.google.com on "Atheismus devictus" (a book Bach owned) and you'll get exactly three hits:
1) The Bach cantatas list http://www.bach-cantatas.com/Topics/Religion.htm (OK I mentioned this before!)

2) A German article on Lorenz Christoph Mizler http://hometown.aol.com/LFelbick/mizler.html (Some interesting speculation!)

3) The Jacob Boehme Bibliography http://www.augustana.ab.ca/~janzb/boehmebib.htm ("Atheismus devictus" is a non-biographical source for Boehme!)

Do follow the link on the bottom of the page to: http://www.augustana.ab.ca/~janzb/boehmebib.htm

Thomas Braatz wrote (March 16, 2001):
It seems that I detect a mixed message in the responses that you are giving to Bach's use of number symbolism. I would like to state my reactions to all of this as a newcomer to this type of endeavor:

1) only through a variety of voices, more specifically, judgements, criticisms, viewpoints, experiences, opinions, etc. can we truly learn from each other, even if what we hear from others counters our own viewpoint, it still should force us to reexamine once again the ground that we individually stand on. There is certainly an important value in seeing where we diverge as well as converge as we seek to move toward a common goal.

2) because of the 'slippery' nature of words that are used to convey meaning and bring about mutual understanding, there frequently occurs a breakdown in communication. Sometimes the lack of just a few words can literally bring about a war between countries (not just individuals!) as in the Ems Dispatch that Bismarck ever so carefully edited by removing a few words, so as to elicit an emotional response in a people already predisposed to defend themselves vigorously. Similarly, there are certain words, when used in speech and in writing, that immediately cause one's hackles to be raised, as if holding a red cloth in front of a raging bull. Words like 'occult' and 'esoteric' frequently bring about such negative reactions, that it becomes almost impossible to converse intelligently regarding their real content because of the negative emotional associations an individual may have had with them. Let's look at the word 'occult' in the OED (Oxford English Dictionary, 2^nd Edition) to see what we find there: Of the four possible meaning categories, only one refers to what bothers most people who hear or read this word - [involved with magic, alchemy, astrology, theosophy and the like.] All the other three meanings are just as legitimate, but are conveniently overlooked or by association construed as negative: an occult blood in fecal matter test, etc. An astronomer knows of an occultation in which one heavenly body covers another (it becomes occult-not visible to any instrument we can construct, but it is still there!.) The basic meanings of occult are: [1) hidden from sight or view 2) not disclosed or divulged, privy, secret, kept secret, communicated only to the initiated 3) not apprehended by the mind, beyond the range of understanding or of ordinary knowledge recondite, mysterious.]

Regarding the word, 'esoteric,' the OED states: [of philosophical doctrines, treatises, modes of speech, etc.: designed for, or appropriate to, an inner circle of advanced or privileged disciples; communicated to, or intelligible by, the initiated exclusively. Hence of disciples: Belonging to the inner circle, admitted to the esoteric teaching.] Perhaps I should have assumed immediately that some members of the BCML would have difficulties with these words, and that further definitions on my part should have been necessary. So how does this apply to Bach's music? In the latter case with 'esoteric' with the use of some creative imagination (which, in this case, I think is more appropriate than applying statistical probability), I can easily see a parallel drawn between Christ and his disciples when he tried to explain the parables to them, but not to the general public (this is the true meaning of 'esoteric'), and J.S.Bach and some of his closest friends and perhaps best pupils. I can imagine an esoteric musical tradition being passed on orally from one generation to another, of which we know little or nothing today from the physical records we have at our disposal. Remember also that the Christians in the catacombs were truly part of an 'underground' experience that was secretive and hidden from view. We know little about their traditions, just as we know little about any such 'underground' group in Bach's day, because it was dangerous to profess openly any ideas, thoughts, or beliefs that were discussed, let alone commit them to paper. I think there is a connection here to help explain why it is that Bach, in Leipzig, suffered greatly from the mostly unjust treatment he received there. What would cause others, his superiors as well as his subordinates, to dislike him to such a degree that they would intrigue against him? Along with reasons such as envy because he was very talented, or his application of operatic compositional techniques in his sacred cantatas, could there also have been the suspicion or rumor that he sometimes met in a secretive group? This could raise grave concern among the upper heirarchy of church and city government, the church because everything had to fit into the prevailing doctrine, and the city because they were concerned that they might have a renegade on their hands, and such a renegade could besmirch the name of the city. I, personally, can not easily dismiss the possibility of the idea that Bach met with a few like-minded individuals (remember Leipzig had a university) to exchange ideas regarding matters that a select few could entertain in their minds. These individuals recognized the need to be secretive, lest the torment of persecution should become real, as it did in Bach's case.

I, for one, would like to see whether evidence of such 'higher' (others may consider this 'lower' or 'underground') thinking can be found hidden away in his compositions. I find this to be a legitimate enterprise, not to be taken lightly. I also do not overestimate its value. While it may enhance my respect for this composer as I begin to see connections that I had not even imagined could be possible, I also understand that others do not need this information for their enjoyment or pleasure. Once again, regarding the word, 'esoteric' and thinking of Christ and his disciples as he related the parables: Think of the parables as Bach's cantatas that the masses can listen to as they take away from the story or music some personal meaning or enjoyment, but for those in the inner circle (as the disciples, or the few to whom Bach may have been speaking in his special musical language) the 'truer', deeper meaning is also revealed. These levels are not mutually exclusive!!!

3) it is one thing to enter the fray with criticism, correction or a contrary viewpoint, but it is yet another, on a higher level, to short-circuit a potential discussion and to fault an entire investigative method as useless, senseless and then to call for an end to the discussion because it does not fit into one's doctrinal beliefs or scientific practices. If it were not for the fact that a number of renowned Bach scholars have begun to research this area diligently, I would not be inclined to continue pursuing this particular direction of musical interpretation.

When faced with a growing array of numbers, the thought of probability statistics dicross my mind, but also the use and misuse of these techniques. In this case I have to rely on 'gut instinct', common sense and an inner logic that is also governed by the human heart (Einfühlungsvermögen = the ability to empathize) as I endeavor to uncover, for myself, the truth about this matter. What we need to try to consider in our imagination, knowing all that we know about Bach, is whether, within reason, this type of thinking was possible with Bach and how it applies to his music, as it seems to have played a role in BWV 97. I still have an open mind on the subject and I hope that open minds, with a rainbow of opinions expressed by BCML members, will continue to prevail on this site.

See below how Bach personally felt about his life in Leipzig, after having completed his major cantata cycles.

"...da [ich] nun finde, daß [ich] mithin fast in stetem Verdruß, Neid und Verfolgung leben muß...." Leipzig 28.10.1730

"...so muß [ich] mein Creütz in Gedult tragen..." Leipzig 24.5.1738 JSB

{that I find that I am forced to live in a continual state of annoyance and to suffer envy and persecution constantly}

{so I must bear my cross patiently}

Jane Newble wrote (March 16, 2001):
< Johan van Veen wrote: article on this subject. The author discovered that in Bach's coffee cantata (BWV 211) the number 151 is playing an important role. And that is exactly the sum of "Bach" and "Douwe Egberts" (a Dutch coffee brand) in numbers - that can't be a coincidence! :) >
Hahaha - I love it. That means I can cherish my Douwe Egberts coffee tins as well as my Bach CDs. Thank you for your well thought out e-mail, too.

Jim Groeneveld wrote (March 16, 2001):
Thank you for your various reactions to my contribution on the meaning of numbers in Bach's work. I've read them with great interest and like you I am in for an open discussion. I would not want to impose limitations to anyone. However I think I've got to clarify myself some more. Let me try to express myself very carefully in order to be understood as intented. In the first place I clearly accept the obvious use of numbers and their related meanings in the Bible and Bach's music. I'm getting along quite some way with assigning meaning to some not directly evident numbers. But there is a point where I think any interpretation can not be justified sufficiently anymore.

The reason for my initial rather one-sided reaction was that I thought to observe a sudden emerging and over-admiring interest and enthousiasm for hidden secret numbers in Bach's music; and I just wanted to make it clear that many of those assumptions are very disputable and not at all scientifically shown. My approach to and my opinion about a subject like this is rationally and scientifically oriented. And in order to explain myself I can not refrain from using and describing some statistical terms and methods. I am always very sceptical and reserved towards unfounded allegations; I always ask myself the critical question: where do those statements come from, how have they been investigated and deduced?

Is there any reason to assume Bach may have hidden information in his music in the form of numbers, directly or in complicated combinations? It is commonly known that he actually adapted numbers (and their meanings) into his music in an obvious way. But did he intentionally make puzzles, as complicated as the proposed examples do suggest? Whatever genius he was, I have my objections. Is there any manuscript by Bach or from that time describing one or more concrete cases of the intended meaning of deliberately hidden numbers in Bach's music? Because only if there is one we may have a basis for hypotheses testing; if there isn't one then any interpretation by us is nothing more than an arbitrary guess. We can find anything we want to find if we search long enough. But we will find much more things we don't want long before that; do we throw that away deliberately? Isn't that manipulation of data?

My main objection concerned the searching for numbers, which in a certain combination seemingly showed some interpretable relation, until found. My goal was to explain that the presence of those numbers (and their combinations) is not significant, but coincidental only. By coincidence any number may occur equally often as long as there is no other reason to expect the distribution of numbers otherwise. So every number (or subjectively choosen combinations of them), including those that might look interpretable, can be found, just like other ones; they are only random events. For example, any musical piece must have some number of bars, whether it is 128, 129 or 130, independent of whether one or more of those numbers might be conceptually interesting.

Do you attribute significance to a solar eclipse, where the sun, moon and earth are in one line? No, of course not, such a relation is part of the coincidental relations between the three. Would you give meaning to the outcome of some sufficient number of throws with a die, in 1/6 of all cases resulting in a number corresponding to the number of fingers on your right hand? Or would you assign such meaning only if the '5' would occur far more often than the other outcomes? Or would you only adopt such a meaning if there was any other independent indication that this specific die was produced to deliberately show precedence for the average number of fingers on a hand? I would do so in the last instance only. You may find these examples too simplistic, but they match the current case of apparently attributed significance to number symbolism quite well.

It would be striking if exactly those interesting numbers would appear to be absent at all, that certainly would indicate something. And only if those numbers would occur significantly more often than would be expected on the basis of coincidence (and I doubt they would), there might be some specific event going on, but only if additionally such an event has been hypothesized in advance, independent of the numbers, e.g. deduced from some theory (or possibly other numbers). In all other cases some effect is nothing more than wishful thinking. For example, any suspected meaning of the number 1283 (and its digits) once found, should statistically be tested by showing significantly more of those occasions in other instances. That is, those occasions should occur clearly more often than other coincidental ones.

Looking at your garden and seeing your grass is green does not yet mean all grass to be green. You would only just have a hypotheses to test against, say ten other grass fields. If the majority of those have green grass, then you may conclude that grass generally is green. But you might also find some dry grass to be brown-yellow. This is an obvious and very simplistic example, but it shows the reasoning that should also be taken in the case of hidden numbers.

I could explain much more, give more examples or a college in statistics, but I think I made my point clear enough. So, I do not support the idea of Bach having incorporated mathematical puzzles in his compositions, because both concrete literature of himself on the subject and a firm scientific proof is lacking. Specifically juggling with digits and (complicated) mathematical operations do not appeal to me. Even if Bach would actually have put in some hidden meaningful numbers into his music, it may be difficult if not impossible to demonstrate that in a justified way. As long as the numeric relations with symbols can not scientifically be "proven" sufficiently or made acceptable conceptually, to me they are not true. The more far-fetched the numbers and their alleged relations with symbols, the more I will judge those stories as ridiculous hoaxes.

Summarizing, I think we don't do good to the image of Bach we have, and we IMHO would fool ourselves if we ascribe him characteristics that we can't prove. Not so much the possible occult character of the numbers, but clearly the known and demonstrable facts give me an argument to plead for a clear, as uncoloured as possible, picture of Bach.

Thomas Braatz wrote (March 16, 200):
(To Jim Groeneveld and all others) Thanks Jim! I understand now even better where you are coming from. I respect and admire your expertise and have taken it into account as I consider all these matters.

Your suggested web-site is very valuable and, most importantly, up-to-date in matters of Bach scholarship. I found much there to reiterate the views you have propounded, but also other things that support my investigation:

A quote from Yo Tomita:(on the Goldberg Variations)
"Such thoroughness of Bach's technical display in the canonic writing can hardly be appreciable in the musical sense but only in the theoretical sense. It is normally believed that this number "fourteen" is intended by Bach to be his numerical signature (BACH = 2 + 1 + 3 + 8 = 14). In June 1747 he became the fourteenth member of the Society of the Musical Science organised by Lorenz Christoph Mizler (1711~78). To join the membership, Bach submitted the thirteenth canon found in the appendix of the "Goldberg" (albeit a slightly revised version, BWV 1076). This is the canon which appears in the famous portrait painted by Elias Gottlieb Haussmann in 1748. As it happened, Bach concluded the "Goldberg" Variations with his musical signature."

Now let me direct you to a web-site that you may already know about: http://jan.ucc.nau.edu/~tas3/crownofthorns.html
Go to the bottom of the long page to find Bach's Seal or Monogram.

A short quote from that source:
"Bach's personal seal--used as early as 1722--includes a crown above the intertwined initials. This crown enables us to see the monogram, like canon, as adumbrating the epigram..."Christ will crown those who carry His cross."

But, unlike its counterpart, the monogram's initials go so far as to identify the crossbearer (Crucigeros). When mirrored, JSB appears to bear the (Greek 'chi') (Christus) as if corporeally. Finally, both JSB and (Greek 'chi') wear the crown (Coronabit). This crown, we cannot help but notice, is studded not with thorns, but with twelve precious stones. These twelve are grouped as seven (the number of completion) imbedded in a crest of five (the number of Christ's passion." and to complete the circle, we are back to the chorale of BWV 97!!

Let me add this from another source: Count the number of tic marks on the periphery of the seal (not the two spikes that the crown sits on). Just another coincidence?

Thanks for your help!

Marie Jensen wrote (March 17, 2001):
Bach died the 28^th of July 1750
28 times 7 is 14 times 14 (his number).
Es muss alles moeglich zu machen seyn, or chance. Hope the last

Thomas Braatz wrote (March 17, 2001):
< Marie Jensen wrote: Bach died the 28^th of July 1750 28 times 7 is 14 times 14 (his number). >
< Andrew Oliver wrote: I wonder if it is also relevant that this cantata was composed in 1734, when Bach reached the age of 49 (7x7)? >
I can understand, how Bach might consciously have thought about what Andrew Oliver suggested, particularly if this was the only cantata that he composed that year. I will need to check that out. But it is really rather weird to consider Marie Jensen's contribution. Is this supposed to be a case of mind over matter? Did Bach actually, with a strong application of will, cause his own death, because he knew how significant the number was? Or did this happen unconsciously on his part? Or was it simply a case of sloppy post-operative care following his eye operation? I don't know!

Pablo Fagoaga wrote (March 17, 2001):
(To Thomas Braatz) I think that the interpretation of Marie's contribution regarding Bach's death is not that it was an act of Bach, but an evidence (if you are willing to believe all the "numbers" stuff and connect it to God) of an act of God, or some kind of mystical "natural order".

Remember that if God really exists, the Bible was dictated by him, which pretty much makes God the guy who actually was goofing around with numbers. Did anyone see the movie "Phy"?? (It is about some jewish guys going after a divine pattern in mathematics. Weird but interesting.)

Harry J. Steinman wrote (March 17, 2001):
(To Jim Groeneveld) My point of view on all this is simple: Random numbers are too important to leave to chance!

I'm not sure what JSB was thinking although I do know that numerology was held in higher esteem by a more superstitious populace than it is by today's superstitious populace.

I'm not a believer in numerology but I do find it _somewhat_ interesting to note others' interest... Further, I can't find any evidence of numerology shaping my enjoyment of Bach's music.

Well, gotta go! I'm on hold for my ISP's customer support. I've been told that the queue is 33 minutes long. Hmmm...

Jane Newble wrote (March 17, 2001):
In a book by Johan Bouman "Musik zur Ehre Gottes" which I bought in Leipzig, I found some very interesting things on numbers. I'll just quote from the forword by KMD Professor Rolf Schweitzer:
"Bachs Zahlensymbolik beruhte auf biblischen und antiken Vorstellungen, deren sich auch Augustinus bediente. Johan Bouman beschreibt dies so: "Gottes Wort gebietet den Zahlen. Er hat die ganze Schöpfung, alles geordnet nach Maß, Zahl und Gewicht (Weisheit 11,21). Folgt ein Menschenwerk diesen Proportionen, gibt es Gott die Ehre..." In diesem Sinne hat Bach einen architektonischen Formbegriff in Analogie zu der auch zahlenmäßig geordneten Schöpfung geschaffen. Folgerichtig können Zahl, musikalisch-rhetorische Figur und Wort eine sinnvolle Einheit bilden.
Endzweck dieser Gesamtarchitektur ist in der Musik Bachs die "Laudatio Dei et recreatio cordis" (das Lob Gottes und die Erquickung des menschlichen Herzens)".

For those not into German here comes a rough translation:
"Bachs symbolism of numbers rested on biblical and ancient ideas, also used by Augustine. Johan Bouman describes it as follows: "God's Word commands numbers. He has ordered all of creation, all things in measure and number and weight. (Wisdom 11,20). If a work by human beings follows these proportions, then God is glorified..." In this sense Bach has created an architectural design analogous with the also numerically ordered creation. Numbers, musical-rhetorical ideas and words can logically create a meaningful unity.

The final purpose of this collective architecture is in Bachs music the "Laudatio Dei et recreatio cordis" (the glory of God and the refreshment of the human heart)".

Just thought some of you might like this...

Sets of six

Mario Zama Escalante wrote (March 9, 2002):
I was thinking, having no proof of it and/or having made no profound research, that Bach wrote "sets of six" works in relation to the six workable days (Mon thru Sat) and since Sunday is a sacred day intended for physical rest and reflection, that is why he wrote non-sacred music for each working day, using different musical settings (concerts, sonatas, partitas, suites, ouvertures? , etc) so he could go anyplace and perform with a small possibility of playing the same work for the same people more than once (for example every Monday he would play concert, partite, sonata, etc. intended for that day and he would change his repertoire for the next day) and for Sunday he had to work in such a way he wasn't attempting against God, so he decided to write for/to God, that is why his sacred music was not produced in sets of six ( I know his cantatas - scheduling of 5 sets for Lutheran ceremonies)

Obviously many works like transcriptions of works by other composers and especial occasion works will not comply with this reasoning, because they fall into another group.

I know many of you will think this is a romantic way of answering many questions about the later, but I would like to sustain by theory until somebody demonstrates I'm taking the wrong road.

Thomas Braatz wrote (March 9, 2002):
[To Mario Zama Escalante] I am having some serious difficulties understanding just what you are getting at. Allow me to restate the points that you are trying to make:

1) You are not sure that the points that you are making are valid because you have no proof.
2) You have observed that Bach wrote �sets of six� and that this might be related to the six days of the week, the seventh being a day of rest, hence sacred.
3) Bach might have designated specific works in the set to be played only on specific week days (this would, in essence, force him to provide a more variety for his listeners.)
4) Since his sacred music was not composed in �sets of six� but rather with only 5 mvts for each cantata, there is reason to believe that Bach chose this number for religious reasons.

My comments on your points:

1) Humility is an admirable quality when approaching the subject of Bach.

2) Examples: BWV 645-50 (Schübler Chorales); BWV 806-11 (English Suites); BWV 812-17 (French Suites); BWV 825-30 (Partitas); BWV 933-8 (Six Little Preludes); BWV 1001-06 (Sonatas & Partitas for Violin); BWV 1007-12 (Suites for Cello); BWV 1014-19 (Sonatas for Violin & Harpsichord); BWV 1046-51 (Brandenburg Concertos).

I can find no evidence of a specific connection of compositions (within one set) with any given day of the week. I have never heard or read about this connection in regard to Bach.

3) Ditto

4) Not true. BWV 248 (Christmas Oratorio) consists of 6 cantatas arranged in sequence and compiled with the idea to unify the work as a whole. Possibly also BWV 232 (B Minor Mass) � this is primarily a �speculative cycle� with numerous possibilities of division, but possibly one sequence would be one of a �set of six�: 1. Missa; 2. Symbolum Niceum; 3. Sanctus; 4. Osanna; 5. Benedictus; and 6. Agnus Dei.

The number of movements within a cantata varies, hence it would be incorrect to state that each cantata had only 5 mvts.

This still does not answer the question why Bach used the number 6 deliberately.

Possibilities:

1. A long standing Baroque tradition for composers to present works for publication in �sets of six� and with opus numbers such as 6 and 12.

2. The number 7 has a symbolic meaning of �completion, perfection.� Perhaps Bach realized that he might be overreaching by implying that he had attained perfection. Is this the reason why I did not published the 7^th Partita that had been planned initially?

Gematria and Bach: an experiment

Jerry Kohl wrote (October 10, 2003):
I've been wondering for a long time about the controversy over Bach's alleged use of numerology or, more specifically, gematria, in his compositions. The recent flap over the "Morimur" recording rekindled my interest, so I decided to do some proper research, to prove once and for all whether there really is a connection between the alleged "Bach numbers" and Bach himself. (For anyone not familiar with this, the idea is that Bach's name, when converted into numerals assigned to the Latin alphabet + K and "reduced", if necessary, by summing the digits of the resulting number, produces the numbers 14 and 41, or their reduction, 5. So: B = 2, A = 1, C = 3, H = 8, 2 + 1 + 3 + 8 = 14; add J and S (9 + 18 = 27) totals 41, and so on.) I went up to the attic and dusted off my trusty old ouija board, and set to work. The results were amazing, and prove beyond a shadow of a doubt that Bach resonates with these numbers, and so they must be at the root of all of his compositions, whether he was conscious of them or not. However, I ran into a peculiar thing. But I get ahead of myself. Let me first explain the nature of the experiment, and the results.

I set up the board in the usual way, clearly formulated the question in my mind and, concentrating on the name "Bach", or "J. S. Bach", etc., or humming one of his familiar tunes, let the board freely do its work. Amazingly, each and every time, the board produced either 5, 41, 14, or a number that would reduce to these figures, such as 329 (3 + 2 + 9 = 14), so long as I maintained my concentration on the subject. I tried this with several other composers as well, and the board never once failed to produce the correct numbers. But now comes the inexplicable part.

At one point, I became momentarily distracted (a fleeting insanity, I expect) and involuntarily the name "Tholen" popped into my mind. Now, that ought to have produced 19 + 8 + 14 + 11 + 5 + 13 = 70 or, adding in "David" (4 + 1 + 20 + 9 + 4 = 38), 108. But for some strange reason, the board consistently produced the number 522! Can anyone explain this?

RBP wrote (October 10, 2003):
< Jerry Kohl wrote: [snip] But for some strange reason, the board consistently produced the number 522! Can anyone explain this? >
522 in VERY significant. And now that you've discovered it, they will probably try to kill you, just as they succeeded with Mozart. Add the Masonic number 33, and you get 555 which is the height of the Washington Monument. Washington was a mason and he plotted to overthrow the Monarchy. Now in 522 BC, Darius took over Persia in a coup. This allowed Pythagoras to return to Samos. In that same year, Zoroaster dies under strange circumstances.

Now Darius allowed the Jews to rebuild their temple in Jerusalem, which of course makes Darius the world's first non-Jewish Zionist. Which of course brings up Pat Robertson...

555 BC is also significant. That's when Nabonidus took over Babylon (i.e. Iraq) and force everybody to worship a god called Sin. No kidding.

Just in case you think that this is all ancient history, consider this: This year 2003, is the 555^th aniversary of the Concordat of Vienna. So the Vatican is involved too!

There are 12 semitones in the scale. 12 x 12 = 144. Add 144 to 522, and you get 666- Satan's number. Turn the number upside down and you get 225 which is equal to 15 squared. SQUARED!

Are you following any of this? Do you get it? Have your eyes been open?

Well here is the kicker...522 is most significant in that K. 522 is Mozart's masterpiece. Go look it up!

Charles Francis wrote (October 10, 2003):
[To PBP] Are you a musicology post-doc by any chance?

RBP wrote (October 10, 2003):
[To Charles Francis] Maybe...but you ought to attribute the above rubbish to a savvy Google user.

Jerry Kohl wrote (October 11, 2003):
< PBP wrote: 522 in VERY significant. And now that you've discovered it, they will probably try to kill you, just as they succeeded with Mozart. Add the Masonic number 33, and you get 555 which is the height of the Washington Monument. Washington was a mason and he plotted to overthrow the Monarchy. Now in 522 BC, Darius took over Persia in a coup. This allowed Pythagoras to return to Samos. In that same year, Zoroaster dies under strange circumstances. >
nodnodnod.

< Now Darius allowed the Jews to rebuild their temple in Jerusalem, which of course makes Darius the world's first non-Jewish Zionist. Which of course brings up Pat Robertson... >
nodnodnod.

< 555 BC is also significant. That's when Nabonidus took over Babylon (i.e. Iraq) and force everybody to worship a god called Sin. No kidding. >
nodnodnod.

< Just in case you think that this is all ancient history, consider this: This year 2003, is the 555th aniversary of the Concordat of Vienna. So the Vatican is involved too! >
nodnodnod.

< There are 12 semitones in the scale. 12 x 12 = 144. Add 144 to 522, and you get 666- Satan's number. Turn the number upside down and you get 225 which is equal to 15 squared. SQUARED!
Are you following any of this? Do you get it? Have your eyes been open? >
nodnodnod. nodnodnod! nodnodnod!! Up to this point, I am grateful for your erudite response, and it all sounds perfectly reasonable to me. And I might add that the Greater Tholen Number, or GTM, of 108 reduces to 9 (1 + 0 + 8), just like 522 and the Number of the Beast (6 + 6 + 6 = 18, 1 + 8 =9), and 9 is the Spectre's Mirror, in which no change is created by interaction with other numbers (addition always returns the other number, while multiplication always returns 9). But your last observation:

< Well here is the kicker...522 is most significant in that K. 522 is Mozart's masterpiece. Go look it up! >
This is absolutely ridiculous. How do you ever expect me to swallow such a preposterous story?! I mean, what connection, however tenuous, could Tholen ever have with Mozart, who was a composer of classical music! And as we have all been so thoroughly taught (all together now, boys and girls): "HAS THOLEN GOT TO DO WITH CLASSICAL MUSIC?" ;-)

Marcello Penso wrote (October 11, 2003):
[To Jerry Kohl] Well, for one thing, both have six letter names, share the letters 'o' and 't', and both names have two syllables and the same amount of vowels and consonants. And, when you string their letters together, you get 'aehlmnoorttz'.....

Jerry Kohl wrote (October 11, 2003):
[To Marcello Penso] Nonsense. Classical Music has, separately, both more and fewer than six letters in its name and, perforce, more than six letters when taken together. Furthermore, it has neither an O nor a T, etc.

Prai Jei wrote (October 11, 2003):
< PBP wrote: ... Well here is the kicker...522 is most significant in that K. 522 is Mozart's masterpiece. Go look it up! >
What's so special about 522 in this context? Almost any number from 1 to 626 identifies a Mozart masterpiece.

Dr. Matthew H. Fields wrote (October 11, 2003):
[To Prai Jei] Or a thousand, as we heard for a few months on this newsgroup [re.music.classical] a few years ago...

Peter D. Daniels wrote (October 11, 2003):
[To Prai Jei] You have a loose notion of "masterpiece."

Did you check which work is K.522? This thread began shortly after I posted the information in a different context.

Peter D. Daniels wrote (October 11, 2003):
[To Marcello Penso] I can't believe that this has gone unchallenged all this time. Zoroaster is now believed to have lived something like 1000 years earlier than the 6^th c. BCE.

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