[microsound] Bach and mathematics

Mon Oct 5 07:24:45 EDT 2009

Hi Ismael, I think this is an interesting subject.

Could you please provide the source of the article? There we can see  
how the article approaches the inner workings of Bach's work and maybe  
than can provide a framework for the discussion.

In my opinion, the notion that integrating mathematics into music,  
makes the art form seem more difficult and incomprehensible for others  
is flawed. In this particular case, I think composing baroque music  
already "needs" know-how, and is difficult regardless of the inclusion  
of mathematics into it. It needs previous exposure, ear training,  
analysis, studies, experience, many stuff. One simply isn't born with  
it, and occasional listening just won't cut it for anyone except the  
extremely talented.

And the case is similar with mathematics. Here I must say that some of  
my favorite artists are mathematicians, architects, physicists,  
philosophers etc. (they don't necessarily have to do anything else) so  
I don't discriminate between the sides of an artificially constructed  
border which separates sciences and fine arts. I see nothing wrong  
with pursuing a mathematical integrity in a particular work or between  
a body of works, on various time scales; this is just another approach  
to artistic composition and the approaches are governed by personal  
preferences (i.e. what an individual thinks is worthy of taking  
inspiration from).

Mathematics is accessible to anyone, just like music. Taking  
inspiration from it, and using it as a basis of artistic work does not  
necessarily make things more difficult for anyone. It just might make  
it "look" difficult for those who are not interested enough in  
mathematics to study it in more depth. But the same situation is there  
even if there is no mathematics involved. Composing, (for example)  
baroque music might also look difficult to anyone who is not  
interested enough in studying the stylistic details of the era, this,  
in the same sense make things "look" difficult for others. Art doesn't  
come out of thin air, and everyone has their inspiration sources  
whether they are conscious about it or not. And approaching the  
analysis of ones work from different perspectives (mathematical,  
sociological etc.) would not hurt anyone I guess, I don't see a  
problem with that.

Because of this, judging the quality of artworks by means of the  
difficulty of production doesn't feel right for me, because difficulty  
of something is subjective, depends on the choices (and by effect  
training) of the individual. I see this also makes you feel  
uncomfortable but it seems that this uneasiness is there only for  
mathematics. Because I see that there is a little contradiction in  
what you've just said; you say that you prefer some other artists over  
Escher and some of your reasons for this preference includes "usage of  
color by those people is far more difficult therefore they produce  
real art". This is highly subjective territory. The works of Escher  
has its own difficulties and others have their own. I see no sensible  
way of comparing them objectively, there can only be preferences. And  
I personally feel closer to Escher's works not because I think he  
makes more "difficult and real art", but because the way he approaches  
to material, source, form and other things appeal more to me as an  
individual, I also care about similar stuff. That is my preference as  
an individual, but I can't say that Escher makes "real art" just  
because we care about similar things...

> - Also many people talk about mathematics when they simply see
> repetitive patterns and simetry. For many people "mathematics" is
> simply "arithmetics", and for me mathematics is a far deeper science.
> Why people only talk of mathematics referring to baroc music like
> Bach's and not referring to Liszt Transcendental Studies, which sure
> also contain a lot of mathematics and a lot more sophisticated ones?

I'm pretty sure, mathematical integrity is not considered only for  
Bach's music. In my opinion, any time you analyze a work by using some  
sort of abstract thinking, logical reasoning and try to reduce the  
vast amount of musical information by grouping similarities etc. you  
are essentially doing some sorts of maths on it. I can only speculate  
about your question here, but in the case of Bach's music (and in the  
body of some other baroque music too), the mathematical integrity on  
some of the works tend to stand out more, because the creator of the  
particular work seems to be mainly inspired by abstract thinking.  
Sometimes you can really see that the artist tried to limit him/ 
herself to pursue a mathematical integrity in a particular work. One  
can approach analyzing, say, Escher's repetitive, self-similar tile  
based works by abstract thinking and it immediately becomes obvious  
what he tried to achieve, how he tried to be creative between the  
borders of self imposed limits for creating something. Similarly, one  
can also do the same while trying to analyze how Picasso dissects and  
reduces a form of something to its essentials, and might conclude that  
while there is some deterministic direction in how he tries to achieve  
the final form of something, his intentions are not directly guided by  
mathematical constructs. That would mean that he mainly relies on  
other inspirational sources (and/or self imposed limits for artistic  
expression) which might be obvious for someone who knows what he is  
really concerned about. It might be very easy to see it for someone,  
but really difficult for others who are not familiar with it.  
Essentially the same with how the integration of mathematics in  
analysis makes a work seem like for others.

That said, as a last note, I don't really believe that Bach was a  
hardcore mathematician in any sense, and relied primarily to that  
while creating his pieces. His ability to take really simple,  
seemingly natural mathematical constructs and use them in really  
efficient and striking ways astonishes me, and one can see that in  
some pieces he really tried to achieve a strict mathematical  
integrity. But most of those mathematical constructs are more or less  
common for the baroque era, I personally care about how he used them  
to create such beautiful music.

I haven't seen the paper you've mentioned, so I must say that, while  
looking for hidden patterns, little mathematical wits are fun and  
educating, but searching for very advanced stuff and attributing them  
to Bach's conscious compositional thinking model would be highly  
speculative in my opinion (thought I can't cite anything about this,  
I'm speculating). Those constructs might really be there, but after  
all, there must be a formal way of explaining why one likes a  
particular piece of music anyway (which probably will never be  
expressed with an elegant mathematical formula). As an example, one  
might be able to find "golden ratio" in effect in just about any  
artistic creation; but not all artists know what golden ratio is  
formally, it might be here and there, just because of exposure and  
familiarity. Similarly one might also analyze a Bach piece to death,  
to find advanced mathematical constructs that makes it sound  
beautiful, but finding them doesn't necessarily mean that the artist  
put them into the piece by making rigorous mathematical calculations  
consciously. Nonetheless, I think there is no problem in approaching  
analysis in that way unless the results of findings are attributed to  
the artist in that way.

Best,
Batuhan Bozkurt
/* http://www.earslap.com */

On Oct 5, 2009, at 11:34 AM, Ismael Valladolid Torres wrote:

> Recently we have discussed about an article in a very popular spanish
> blog talking about the relationship between J.S. Bach's music and
> mathematics. It's very common to relation both, but that relationship
> has always made feel uncomfortable, mainly because of two reasons.
>
> - Many people suffer because they feel they don't understand art (as
> if art were understandable at all!) and they often search for ways to
> "measure" art. This makes them feel comfortable, as thus they can call
> "artist" to someone that simply makes use of his know-how to make
> something apparently difficult for the rest. Internet people often
> treat Escher as the best painter ever. Escher's drawings were tricky
> and enjoyable, but i.e. usage of color by people like Picasso, Miro,
> Malevich, Kandinsky, etc. is for me far more difficult and real art.
>
> - Also many people talk about mathematics when they simply see
> repetitive patterns and simetry. For many people "mathematics" is
> simply "arithmetics", and for me mathematics is a far deeper science.
> Why people only talk of mathematics referring to baroc music like
> Bach's and not referring to Liszt Transcendental Studies, which sure
> also contain a lot of mathematics and a lot more sophisticated ones?
>
> Nonetheless I'd like to know the truth about the relationship between
> Bach and mathematics, even if he really worked as a mathematician as
> some say. Also of course I'd like to know your opinion about the
> relationship between Bach's music (and others' music!) and
> mathematics.
>
> Any comments, ideas, welcome, so thanks in advance.
>
> Cordially, Ismael
> -- 
> Ismael Valladolid Torres      Hey there! ivalladt is using Twitter.
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