[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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