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<P>I think the question of what the quality of a number is is the interesting one. On this topic I am ignorant.</P>
<P><BR>From: "hans w. koch" <KOCHHW@NETCOLOGNE.DE><BR>To: microsound@microsound.org<BR>Subject: [microsound] Subject: Re: Bach and mathematics<BR>Date: Mon, 5 Oct 2009 15:46:36 +0200<BR><BR><BR>actually, if one looks close, bach is much more about symbols and <BR>numbers, than about mathematics.<BR>he would e.g. put as many notes into a chorale prelude as was the <BR>sum of his names letters taken as numbers. etc.<BR>what makes people think of mathematics is the structural clearness <BR>of his canons and fugues etc.<BR>but, on the other hand he had quite a reputation in leipzig for <BR>playing very entertaining coffee house music with some friends.<BR><BR>whereas beethoven, who comes across so emotional, was known to <BR>carefully calculate his pieces on whatever was at hand, up to the <BR>point,<BR>that once he used the window-shutters of his summer vacation <BR>residency to scribble calculations all over, which the owner of <BR>that residency sold for a good price<BR>as a souvenir to some fans.<BR><BR>in renaissance, when they composed the most complicated canons, <BR>which sound so expressive and lush (e.g."missa prolationum" by <BR>ockhegem), the prevailing idea was<BR>to compose for the greater glory of god. so some aspects of the <BR>composition were supposed to be only intelligble by god, while the <BR>other aspects remained accessible for human listening as well.<BR><BR>hans<BR>www.hans-w-koch.net<BR><BR>Message: 6<BR>Date: Mon, 5 Oct 2009 14:24:45 +0300<BR>From: Batuhan Bozkurt <BATUHAN@BATUHANBOZKURT.COM><BR>To: microsound@microsound.org<BR>Subject: Re: [microsound] Bach and mathematics<BR>Message-ID: <213FEAC1-79D0-4009-BA02-70C6031BA323@batuhanbozkurt.com><BR>Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes<BR><BR>Hi Ismael, I think this is an interesting subject.<BR><BR>Could you please provide the source of the article? There we can see<BR>how the article approaches the inner workings of Bach's work and maybe<BR>than can provide a framework for the discussion.<BR><BR>In my opinion, the notion that integrating mathematics into music,<BR>makes the art form seem more difficult and incomprehensible for others<BR>is flawed. In this particular case, I think composing baroque music<BR>already "needs" know-how, and is difficult regardless of the inclusion<BR>of mathematics into it. It needs previous exposure, ear training,<BR>analysis, studies, experience, many stuff. One simply isn't born with<BR>it, and occasional listening just won't cut it for anyone except the<BR>extremely talented.<BR><BR>And the case is similar with mathematics. Here I must say that some of<BR>my favorite artists are mathematicians, architects, physicists,<BR>philosophers etc. (they don't necessarily have to do anything else) so<BR>I don't discriminate between the sides of an artificially constructed<BR>border which separates sciences and fine arts. I see nothing wrong<BR>with pursuing a mathematical integrity in a particular work or between<BR>a body of works, on various time scales; this is just another approach<BR>to artistic composition and the approaches are governed by personal<BR>preferences (i.e. what an individual thinks is worthy of taking<BR>inspiration from).<BR><BR>Mathematics is accessible to anyone, just like music. Taking<BR>inspiration from it, and using it as a basis of artistic work does not<BR>necessarily make things more difficult for anyone. It just might make<BR>it "look" difficult for those who are not interested enough in<BR>mathematics to study it in more depth. But the same situation is there<BR>even if there is no mathematics involved. Composing, (for example)<BR>baroque music might also look difficult to anyone who is not<BR>interested enough in studying the stylistic details of the era, this,<BR>in the same sense make things "look" difficult for others. Art doesn't<BR>come out of thin air, and everyone has their inspiration sources<BR>whether they are conscious about it or not. And approaching the<BR>analysis of ones work from different perspectives (mathematical,<BR>sociological etc.) would not hurt anyone I guess, I don't see a<BR>problem with that.<BR><BR>Because of this, judging the quality of artworks by means of the<BR>difficulty of production doesn't feel right for me, because difficulty<BR>of something is subjective, depends on the choices (and by effect<BR>training) of the individual. I see this also makes you feel<BR>uncomfortable but it seems that this uneasiness is there only for<BR>mathematics. Because I see that there is a little contradiction in<BR>what you've just said; you say that you prefer some other artists over<BR>Escher and some of your reasons for this preference includes "usage of<BR>color by those people is far more difficult therefore they produce<BR>real art". This is highly subjective territory. The works of Escher<BR>has its own difficulties and others have their own. I see no sensible<BR>way of comparing them objectively, there can only be preferences. And<BR>I personally feel closer to Escher's works not because I think he<BR>makes more "difficult and real art", but because the way he approaches<BR>to material, source, form and other things appeal more to me as an<BR>individual, I also care about similar stuff. That is my preference as<BR>an individual, but I can't say that Escher makes "real art" just<BR>because we care about similar things...<BR><BR>> - Also many people talk about mathematics when they simply see<BR>> repetitive patterns and simetry. For many people "mathematics" is<BR>> simply "arithmetics", and for me mathematics is a far deeper science.<BR>> Why people only talk of mathematics referring to baroc music like<BR>> Bach's and not referring to Liszt Transcendental Studies, which sure<BR>> also contain a lot of mathematics and a lot more sophisticated ones?<BR><BR>I'm pretty sure, mathematical integrity is not considered only for<BR>Bach's music. In my opinion, any time you analyze a work by using some<BR>sort of abstract thinking, logical reasoning and try to reduce the<BR>vast amount of musical information by grouping similarities etc. you<BR>are essentially doing some sorts of maths on it. I can only speculate<BR>about your question here, but in the case of Bach's music (and in the<BR>body of some other baroque music too), the mathematical integrity on<BR>some of the works tend to stand out more, because the creator of the<BR>particular work seems to be mainly inspired by abstract thinking.<BR>Sometimes you can really see that the artist tried to limit him/<BR>herself to pursue a mathematical integrity in a particular work. One<BR>can approach analyzing, say, Escher's repetitive, self-similar tile<BR>based works by abstract thinking and it immediately becomes obvious<BR>what he tried to achieve, how he tried to be creative between the<BR>borders of self imposed limits for creating something. Similarly, one<BR>can also do the same while trying to analyze how Picasso dissects and<BR>reduces a form of something to its essentials, and might conclude that<BR>while there is some deterministic direction in how he tries to achieve<BR>the final form of something, his intentions are not directly guided by<BR>mathematical constructs. That would mean that he mainly relies on<BR>other inspirational sources (and/or self imposed limits for artistic<BR>expression) which might be obvious for someone who knows what he is<BR>really concerned about. It might be very easy to see it for someone,<BR>but really difficult for others who are not familiar with it.<BR>Essentially the same with how the integration of mathematics in<BR>analysis makes a work seem like for others.<BR><BR>That said, as a last note, I don't really believe that Bach was a<BR>hardcore mathematician in any sense, and relied primarily to that<BR>while creating his pieces. His ability to take really simple,<BR>seemingly natural mathematical constructs and use them in really<BR>efficient and striking ways astonishes me, and one can see that in<BR>some pieces he really tried to achieve a strict mathematical<BR>integrity. But most of those mathematical constructs are more or less<BR>common for the baroque era, I personally care about how he used them<BR>to create such beautiful music.<BR><BR>I haven't seen the paper you've mentioned, so I must say that, while<BR>looking for hidden patterns, little mathematical wits are fun and<BR>educating, but searching for very advanced stuff and attributing them<BR>to Bach's conscious compositional thinking model would be highly<BR>speculative in my opinion (thought I can't cite anything about this,<BR>I'm speculating). Those constructs might really be there, but after<BR>all, there must be a formal way of explaining why one likes a<BR>particular piece of music anyway (which probably will never be<BR>expressed with an elegant mathematical formula). As an example, one<BR>might be able to find "golden ratio" in effect in just about any<BR>artistic creation; but not all artists know what golden ratio is<BR>formally, it might be here and there, just because of exposure and<BR>familiarity. Similarly one might also analyze a Bach piece to death,<BR>to find advanced mathematical constructs that makes it sound<BR>beautiful, but finding them doesn't necessarily mean that the artist<BR>put them into the piece by making rigorous mathematical calculations<BR>consciously. Nonetheless, I think there is no problem in approaching<BR>analysis in that way unless the results of findings are attributed to<BR>the artist in that way.<BR><BR>Best,<BR>Batuhan Bozkurt<BR>/* http://www.earslap.com */<BR><BR><BR><BR><BR>On Oct 5, 2009, at 11:34 AM, Ismael Valladolid Torres wrote:<BR><BR>> Recently we have discussed about an article in a very popular spanish<BR>> blog talking about the relationship between J.S. Bach's music and<BR>> mathematics. It's very common to relation both, but that relationship<BR>> has always made feel uncomfortable, mainly because of two reasons.<BR>><BR>> - Many people suffer because they feel they don't understand art (as<BR>> if art were understandable at all!) and they often search for ways to<BR>> "measure" art. This makes them feel comfortable, as thus they can call<BR>> "artist" to someone that simply makes use of his know-how to make<BR>> something apparently difficult for the rest. Internet people often<BR>> treat Escher as the best painter ever. Escher's drawings were tricky<BR>> and enjoyable, but i.e. usage of color by people like Picasso, Miro,<BR>> Malevich, Kandinsky, etc. is for me far more difficult and real art.<BR>><BR>> - Also many people talk about mathematics when they simply see<BR>> repetitive patterns and simetry. For many people "mathematics" is<BR>> simply "arithmetics", and for me mathematics is a far deeper science.<BR>> Why people only talk of mathematics referring to baroc music like<BR>> Bach's and not referring to Liszt Transcendental Studies, which sure<BR>> also contain a lot of mathematics and a lot more sophisticated ones?<BR>><BR>> Nonetheless I'd like to know the truth about the relationship between<BR>> Bach and mathematics, even if he really worked as a mathematician as<BR>> some say. Also of course I'd like to know your opinion about the<BR>> relationship between Bach's music (and others' music!) and<BR>> mathematics.<BR>><BR>> Any comments, ideas, welcome, so thanks in advance.<BR>><BR>> Cordially, Ismael<BR>> -- Ismael Valladolid Torres Hey there! ivalladt is using Twitter.<BR>> <IVALLADT@GMAIL.COM>http://twitter.com/ivalladt<BR>><BR>> t. 0034912519850 Facebook: http://profile.to/ivalladt<BR>> m. 0034609884094 (Yoigo) http://groups.to/lamediahostia<BR>><BR>> Google Talk/Jabber/MSN Messenger: ivalladt@gmail.com<BR>> Jaiku/Twitter/Skype/Yahoo!: ivalladt<BR>> AIM/ICQ: 264472328 GnuPG key: DE721AF4<BR>> _______________________________________________<BR>> microsound mailing list<BR>> microsound@microsound.org<BR>> http://or8.net/mailman/listinfo/microsound<BR><BR><BR><BR><BR>_______________________________________________<BR>microsound mailing list<BR>microsound@microsound.org<BR>http://or8.net/mailman/listinfo/microsound<BR></P></BLOCKQUOTE></DIV><BR>
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