[microsound] Subject: Re: Bach and mathematics

Mon Oct 5 12:41:03 EDT 2009

I think really we would have to address the question "What is a  
number?" first. Obviously, Russell and Whiteheads "Principia  
Mathematica" comes to mind here.

On 5 Oct 2009, at 17:01, Manannan Mac Lir wrote:

>
>
> ----- Original Message -----
>
> I think the question of what the quality of a number is is the  
> interesting one. On this topic I am ignorant.
>
>
> From: "hans w. koch"
> To: microsound at microsound.org
> Subject: [microsound] Subject: Re: Bach and mathematics
> Date: Mon, 5 Oct 2009 15:46:36 +0200
>
>
> actually, if one looks close, bach is much more about symbols and
> numbers, than about mathematics.
> he would e.g. put as many notes into a chorale prelude as was the
> sum of his names letters taken as numbers. etc.
> what makes people think of mathematics is the structural clearness
> of his canons and fugues etc.
> but, on the other hand he had quite a reputation in leipzig for
> playing very entertaining coffee house music with some friends.
>
> whereas beethoven, who comes across so emotional, was known to
> carefully calculate his pieces on whatever was at hand, up to the
> point,
> that once he used the window-shutters of his summer vacation
> residency to scribble calculations all over, which the owner of
> that residency sold for a good price
> as a souvenir to some fans.
>
> in renaissance, when they composed the most complicated canons,
> which sound so expressive and lush (e.g."missa prolationum" by
> ockhegem), the prevailing idea was
> to compose for the greater glory of god. so some aspects of the
> composition were supposed to be only intelligble by god, while the
> other aspects remained accessible for human listening as well.
>
> hans
> www.hans-w-koch.net
>
> Message: 6
> Date: Mon, 5 Oct 2009 14:24:45 +0300
> From: Batuhan Bozkurt
> To: microsound at microsound.org
> Subject: Re: [microsound] Bach and mathematics
> Message-ID: <213FEAC1-79D0-4009-BA02-70C6031BA323 at batuhanbozkurt.com>
> Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
>
> 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.
> > http://twitter.com/ivalladt
> >
> > t. 0034912519850 Facebook: http://profile.to/ivalladt
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> >
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