<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">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.<div><br></div><div><br><div><div>On 5 Oct 2009, at 17:01, Manannan Mac Lir wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><br><br> <blockquote style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff 2px solid"><p>----- Original Message -----</p><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: <a href="mailto:microsound@microsound.org">microsound@microsound.org</a><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><a href="http://www.hans-w-koch.net">www.hans-w-koch.net</a><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></ivalladt@gmail.com></batuhan@batuhanbozkurt.com></kochhw@netcologne.de></p></blockquote></div><br> -- <div><b>An Excellent Credit Score is 750</b><br> <a href="http://ad.doubleclick.net/clk;216722518;39159097;q?http://www.freecreditreport.com/pm/default.aspx?pagetypeid=homepage62&sc=669615&bcd=FOOTER5 " target="_blank"> <b>See Yours in Just 2 Easy Steps!</b></a></div> _______________________________________________<br>microsound mailing list<br><a href="mailto:microsound@microsound.org">microsound@microsound.org</a><br>http://or8.net/mailman/listinfo/microsound<br></blockquote></div><br></div></body></html>