Hi there jhnbrbr,
Thanks for this. For almost a century there was a sort of denial going on within Bach studies that such things are really to be found in Bach's music. At least in musicology. It was considered to be too 'messy' and imprecise. Critics said no published works existed at this time which Bach could possibly have been influenced by to use any such system. And even if he had been influenced by them it was said he could not possibly have produced such a vast amount of great music by systematically applying meanings to number sequences etc.
But a lot has changed. Smend's publication of 1947, for example. Then many others. Firstly, we now know several works on theories of numbers already existed in print in Bach's time. Secondly, we have various clues from writers who knew Bach.
Various excellent books on this subject are available online, Ruth Tatlow's 'Bach and the Riddle of Number' is one, though highly critical of work that has been done so far it still acknowledges there are many remarkable things to be found in his works from a mathematical perspective. She acknowledges too that baroque composers were definitely influenced by the study of 'gematria' or the rather obvious association between music and mathematics - an association which was recognised to be obvious even in Bach's time.
Bach may even have been aware of beliefs that biblical verses were themselves mathematically amazing. Work revived on Hebrew and even Greek texts in the late 19th century by Russian mathematicians such as Ivan Panin, for example.
http://books.google.co.uk/books?id=...&hl=en&sa=X&oi=book_result&resnum=3&ct=result
Hope you find that interesting. Any search for 'Bach Gematria' gives lots of interesting information.
There can be little doubt Bach was not so much inventing music but was, in some highly individual sense, deciphering it from texts according to orderly principles. And this within his over-arching idea of a fugal/contrapuntal music of astonishing simplicity and complexity.
The whole subject fascinates me and I want to read more of it. In one sense Bach was perhaps only scratching the surface of what was possible. Even in fugue. At least, I think of it that way since we, today, have opportunities to examine such wonderful things more closely from different perspectives. Certainly, no music known to us is able to be judged according to fair rules as that left by composers of the late baroque, of which Bach's is undoubtedly some of the greatest. In Bach's mind it seems he knew instinctively what the musical potential was for a given theme, almost instantly. And this theme determined to him not only its melodic and rythmic possibilities but also the way it would be treated harmonically. An organic music of the most astonishing simplicity and depth.
J.S. Bach - BWV 1069
Orchestral suite no 4 in D Major
BWV 1069/2
Bourree
Academy of St Martin in the Fields
Sir Neville Marriner
http://www.mediafire.com/?e2jdz1wmmiz
Best wishes
Robert
