[microsound] Subject: Re: Bach and mathematics

Manannan Mac Lir macdara at email.com
Mon Oct 5 12:01:36 EDT 2009


  ----- 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.
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