What is the possible symbolic meaning that Bach may have intended with the number 32 in the Aria with diverse variations?
I have read some papers on possible Bach numerological systems and the significance of numbers like 14 but I don’t recall anything about 32.
A lot of Bach numerology is bunk. But 32 seems so strongly emphasized in the piece. Mere structural design pattern, or something deeper for Bach?
32 is the atomic number for Germanium. But on a more serious note of speculation, 32 has long and deep significance in Judaism, and the words for 32 in Hebrew mean ‘heart’, which is pretty interesting. [reference: What’s in a number? 32 | Jewish News]. Was Bach influenced by Judaism in any way?
@TonmeisterAW thanks. I am sure there are dozens of pieces with 32 parts. As I mentioned 32 is a good number as it has lots of divisors. What I am after is to know if there was any religious/mystical significance for this number for Bach.
Hi Andrew! The point is not the number of divisors, but the fact that they are all 2! In spreadsheet notation, 32 = 2^5. It is therefore most natural that binary pieces, if written with nice internal simmetries, have a number of bars that are multiples of 2: 16, 32 or 64, say. There is no intentional numerology or symbolism in this. It happens more frequently in Bach simply because he was a very meticulous composer, so that similar sections had a similar numbers of bars: this inevitably produces multiples of 2. (D. Scarlatti, for example, on purpose sometimes in binary sonatas you find a passage repeated 3 times in the first section, but only 2 times in the second section.)
But Bach being Bach, I can’t help wondering in off moments if he saw something in 32 apart from its arithmetic qualities. OI course we will never know. I am engraving BWV 988 presently so this is very topical for me.
2, 4, 8 bar phrases are natural in music and I think that 32 in S.988 comes from that, and that only. I would personally discount any Jewish connection. (18: Chai, life, is a more commonly found Jewish number.)
It is easy to find (invent) reason for things: for instance, does the grouping of the variations in 3s have something to do with the Trinity? Who knows?
There may have been previous G major chaconnes or arias with 30 or so variations known to Bach - for example Handel’s G major chaconne or Buxtehude’s La Capricciosa (32!). Bach may have wanted to go one better (Aria da capo?).
I think Ruth Tatlow may have also found out that the total number of bars in BWV 988 is 1000 if you count them properly …
What do you mean by ‘properly’? Do you mean correctly, or by using some particular non-obvious method including/excluding some (e.g. there is a pickup bar in Var 30, count or not?). Henle, many publishers, and engraving programs like Dorico will not count that as a bar number.
Do you have a reference for the Tatlow? She writes quite a lot.
Tatlow would be the 2015 book ‘Bach’s numbers’ - I haven’t read the book in detail but have seen a number of synopses/quotes. Round numbers figure largely in it. In terms of how to count bars, there are always a few choices like to count incomplete bars, repeats, first/second time, and for 988 whether to count Aria da capo or not. You certainly get close to 1000, or 2000 with all repeats.
That’s my point - close, but not necessarily exact. Consequently these numbers may have less significance than ascribed.
I think she may be susceptible to the fudging she criticizes others for. So, include da capo aria or not? Makes a big difference. Is there any evidence that 1000 has any significance for Bach? Did he sit down with the primary intention of writing a piece exactly 1000 bars long? Why would that be a primary driver? It’s speculation of the very sort she criticises.
However, she does claim that that violin solo set has 2400 bars, with four of the pieces making 1600, and the others making 800, which is a 1:2 ratio of which Bach was fond. But maybe I should try counting this lot, as well.
Well, if it was exactly 1000 without ambiguity I think that would be enough of a coincidence to be evidence on its own.
However, getting hold of a PDF for the book I have to issue a correction: the main count (including Aria da capo) is 960, which divides into 240 for each of 4 divisions each containing 8 movements. To get this it’s necessary to count the ‘Alla breve’ movement as 16 bars - the argument being that this is the meaning of ‘alla breve’, and other cut-C movements do not have that marking.
(There are other proportional bar counts involving canons and 1-manual / 2-manual variations…)
I’ll buy that (obviously not the number - that’s objective, but the proportion). It’s certain that Bach was motivated by proportionality. But not by deciding on a bar count to fill, like a required word count for a journalist.
[quote=“andro, post:18, topic:1068”]
I’ll buy that (obviously not the number - that’s objective, but the proportion). It’s certain that Bach was motivated by proportionality. But not by deciding on a bar count to fill, like a required word count for a journalist.[/quote]
As tempted as I am to suggest that this has nothing to do with the music, let me just point out that var 16 is the French Ouverture. Thus we can see that JSB is well ahead of the game, having written the first overture in the hostory of music that closes a major section!
But on a more serious note of speculation, 32 has long and deep significance in Judaism, and the words for 32 in Hebrew mean ‘heart’, which is pretty interesting. [reference: What’s in a number? 32 | Jewish News]. Was Bach influenced by Judaism in any way?
