by John Krakenberger ©

There is a lot of literature where we can find references to Bach's fascination with numbers, and what is called "gematria" which is simply a method by which letters or notes are expressed in numbers, such as A=1, B=2, C=3, etc, or, in the German music notation, C = 3, C# = CIS = 3+9+18=30, or A = 1 and A-flat = AS = 1+18=19.

The city of Köthen, or more precisely, its Historical Museum, published in 1994 a series of studies on Bach, on the occasion of the 300th birthday of Prince Leopold von Anhalt-Köthen, Bach's patron from 1717 to 1723, when he got the job of "Kantor" at St.Thomas in Leipzig. In one of these monographies, the musicologist Helga Thoene makes an ample study of the 3 Sonatas and 3 Partitas for violin solo, and I propose to mention only a few of the simplest examples of how numbers acquire a somewhat ominous presence in these compositions.

Let us start with a small and simple example: The sequence of tonalities of the 6 Sonatas and Partitas is as follows: G-minor, b-minor, a-minor, d-minor, c-mayor and e-mayor. If we look at the intervals between G, B, A, D, C & E we arrive at the following figures: 3, 2, 4, 2, & 3 (a third, a second, a fourth, etc). Well then, the sum of these figures is 14, and if we multiply all of them we get a total of 144. Applying "gematria" at Bach's name, we get that Johann Sebastian totals 144, and Bach totals 14. Is this a coincidence?

The next example is a little bit more complex. Let us take the last bar of the First Fugue (in G-minor) and assign numbers in accordance with the german notation (there is the arpeggio d-a-g (4+1+7) and so on to the final cord) and we get a total of 158, which is the sum of 14+144, i.e. the full signature of the composer, as if he had wished to underline that he was indeed the creator of this extraordinary feat: A three voice fugue for violin solo.

These are pretty simple calculations: You can check them easily. But there is much more, very time consuming, and I shall simply point out in what they consist. The gematric values of the first complete bars, up-beats included, of the 6 Sonatas and Partitas add, respectively: G-minor 172, B-minor 350, A-minor 112, D-minor 85, C-mayor 22 and E-minor 220, totalling 961.

Another way of assigning values to the notes is assigning a whole note 1, a half note 2, a quarter note 4, an eighth note 8, and so on. The dots will be neglected, therefore an eighth note with a dot continues being 8. If we apply this method again to the first bars of the six compositions under analysis, we arrive at the following figures, respectively: 744, 336, 488, 200, 72 and 160, adding up to 2000.

And now we arrive at the incredible yet incontrovertible result: If we apply "gematria" to the Credo of the latin mass (From Credo in unum to et invisibilium) we get 961 and similarly, the total of the Kyrie & Gloria (from Kyrie eleison to Gloria tuum) we get 2000. Another coincidence?

These are just a few examples taken from the above mentioned monography. For those who want to delve deeper into this, I cite the international publication-code under which this work can be found. It is ISBN 3-928703-55-2, editor being the museum mentioned at the beginning of this article.

There are further surprising revelations in relation with the Chaconne, the creation of which coincided with the death of Bach's first wife, Maria Barbara, and where the words "In Christo Morimur", gematric value 211, acquire a very special significance.
This is but a short introduction to this fascinating aspect of Bach's work. Many musicians have asked, in the past, and to this day, and surely also in the future, what is so special with Bach's music: When we study his works, and delve deeper, our surprise and admiration grows as if we were facing something miraculous. Adding this new dimension, an almost cabalistic ritual of numbers, we cannot but become convinced once more that Bach was one of the pillars of western culture, precisely because his music gets nearer - more than any other - to the very nature of things and their laws, of which we all form part and in which we recognise ourselves.