Mathematics and Music

[DavidW]

told once that when mathematicians try produce some music using math, it is usually a very lousy kind of music. Schoenberg is a nice illustration to that opinion. The more composers think mathematically and analyze music, disintegrate it into pieces, the more unnatural it becomes.

Schoenberg didn't use math to write music, and I think you'll find that the consensus has been for quite along time now that he is a first rate artist, one of the greatest composers of the 20th century thank you very much.

[DavidW]

I disagree; maths is not invented, it is discovered. Tied to physics, it tells us about our world.

Platonic view of mathematics, the others posit the view shared by Aristotle.  And I can't believe people still debate this issue to this day!

[knight66]

Yes, now is there any chance of discussing music in relation to maths, or is this now really about the origin of maths?

[DavidW]

Yes, now is there any chance of discussing music in relation to maths, or is this now really about the origin of maths?

If it wasn't clear to you we're talking about the meaning and origins of math because we don't know the answer to your question.

Though I really don't know why prime number beats is not a satisfactory answer.   I don't think it goes deeper than that because the claims of the math in Messiaen are highly inflated because the prof is just trying to do a pr job for his field-- math.  Though my friends say that I'm cynical now.

[knight66]

Well, take it any way you like, I am out of it for a few days.

Mike

[Sarastro]

Platonic view of mathematics

Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. The term Platonism is used because such a view is seen to parallel Plato's belief in a "World of Ideas" (typified by Plato's cave): the everyday world can only imperfectly approximate of an unchanging, ultimate reality. Both Plato's cave and Platonism have meaningful, not just superficial connections, because Plato's ideas were preceded and probably influenced by the hugely popular Pythagoreans of ancient Greece, who believed that the world was, quite literally, generated by numbers.


The major problem of mathematical platonism is this: precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, which is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One answer might be Ultimate ensemble, which is a theory that postulates all structures that exist mathematically also exist physically in their own universe.

I admit that there might be a heavenly realm of mathematics, as well as a realm of music, or Ideas, and great composers and mathematicians just somehow get access to it. But unless the existence of such realms is scientifically proven, I can not believe in it.
Moreover, the Greeks believed in many things we consider nonsense nowadays. They believed in Gods, monsters, half-divine creatures. They believed that Helios rode his sun chariot during the day and at night traveled through the kingdom of shadows - Hades. They thought that an arrow can fly because its biggest in volume part's, feathers', element is air. Correspondingly they thought that a bigger stone falls into earth and makes a deeper print because its natural element is earth, it "wants" to be closer to it. But my major concern is their belief in gods and their kingdoms which could affect also beliefs in mathematics and other worlds.

Schoenberg didn't use math to write music

I know he didn't. It was a metaphor. Speaking about being the greatest, I always remember Malevich's joke - black square, and how people rushed to find the organization of the Universe in there. Like The Emperor's New Clothes tale.

Well, electronic music is very popular now and does touch many people, where have you been?

Electronic music is music that employs electronic musical instruments and electronic music technology in its production. As far as I understand, it means that instead of using traditional instruments, people just use such devices to create patterns and mix them. That is what DJ's do in clubs, if you have been to one. I personally do not like such kind of music, and always resist when friends try to scoop me in such places.

The geometric series showed that infinity isn't a problem for math. Not a number? So what?

I still don't get your point. I was talking about concepts, and all of a sudden you threw a particular problem. And what if the ratio were bigger than one?

Computers should be build to complement human brain rather than replace.

When they start thinking they will absolutely sure start thinking how to replace the humans and be independent.  Heard anything about Isaac Asimov?

I'm not religious at all, but there are things that are better not to be touched. Rutherford, after having discovered the model of the atom and having done some work, later regretted of his discoveries, as he very well understood that we are too small and would never be able to control atoms. Moreover, he knew that the sneaky people would not hesitate to use it as a weapon, and he was bitterly correct, in both cases. We've already experienced atomic bombs (not including experiments with them) and the Chernobyl' explosion. The more we advance in technology, the more retarded we become. Apparently, there will be no life in a while. And computers can not exist separately. Unlike organic life, which continued for millions of years, reproducing itself, sources to build mechanical devices are limited.

"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy." (c) 

[DavidW]

I know he didn't. It was a metaphor.

Um do you know what a metaphor is?  That was not a metaphor.  You were using Schoenberg as an example as your wording clearly indicates.

Speaking about being the greatest, I always remember Malevich's joke - black square, and how people rushed to find the organization of the Universe in there. Like The Emperor's New Clothes tale.

Was that supposed to be a pithy way to mock me for believing that there is some kind of meaning to critical consensus?  Well excuse me for not being a nihilist.

Quotes and allusions to literature that you enjoy might make you sound witty in your mind, but the rest of us grew out of that phase in high school, and frankly it sounds condescending and trite.  Say what you mean, and if it's well argued it will have an impact regardless of the flowery speech you couch it in.

[Sarastro]

My opinion on the subject is stated in my first post here. As for Schoenberg (as well as for Webern and Berg), I find his music highly mathematical, in a sense that it is mechanical - that is for the metaphor. If a mathematician were to compose a piece, something alike would come out. I think I am entitled to my own opinion regardless of what the consensus decides. By the consensus even Britney Spears is one of the greatest singers of our time.

[Florestan]

Computers and robots will be able to do almost anything

Making love is one of the exceptions. 

Soul does not exist.

Proof?

Someday computers will be able to come up with ideas.

Your ideas certainly look like they've been programmed. 

[cx]

In mathematics "infinity" is NOT a number and is a mathematical idealization

"Number" is an ambiguous term in mathematics, but it usually refers to an element of the real or natural numbers, for example. Infinity is a "number" in the one-point-compactification of the reals, and defined conveniently in many other situations. Don't know what you mean by "idealization" however


A professor came to my university two weeks ago and gave a talk on mathematics and music. He tries to frame the common rules of tonality (which I think was a controversial point) into the language of geometry via quotient spaces and stuff like that. The beginnings of his talk were quite accessible but (what are supposed to be) his substantial results use rather difficult math. I had mixed feelings about it, but thought it was interesting. The pictures were nice. I'll find his name out when I get a chance. He's currently writing a book to be published as well.

[mikkeljs]

Doesn´t math mean, the well defined language of everything? It´s not the point, that math is still very limited and even full of mistakes, if the idea was to describe the truth, math is telling the truth - even if the truth is only local, I think the local coexists with everything else, like individual minds should all be respected, no matter how f..... up they are, and that our universe coexists with parallel universes (in some sence).
Language will always be primitive, but not necessary the understanding of it. The way we use the language of math is, that we generate it from logic, which is the very light of commonness of an observation. And the way we read it is a reflection into ourselfes, so it is no longer a language but the truth itself. Now the reason, that mistakes still appears, especially in excersises made by students, is that we are too lazy to keep focusing on that light of logic, so that it is not always perfectly executed.

Math is supposed to be dealing with the truth, I think, as far as possible, even in order to describe beauty! 

[71 dB]

I still don't get your point. I was talking about concepts, and all of a sudden you threw a particular problem. And what if the ratio were bigger than one?

The sum becomes infinite. I never got your point, it seems.

When they start thinking they will absolutely sure start thinking how to replace the humans and be independent.  Heard anything about Isaac Asimov?

Why? Perhaps if they were created in evolution. All the emotions must be teached. Why teach machines to hate us? Well, in evil hands of course... 

I'm not religious at all, but there are things that are better not to be touched. Rutherford, after having discovered the model of the atom and having done some work, later regretted of his discoveries, as he very well understood that we are too small and would never be able to control atoms. Moreover, he knew that the sneaky people would not hesitate to use it as a weapon, and he was bitterly correct, in both cases. We've already experienced atomic bombs (not including experiments with them) and the Chernobyl' explosion. The more we advance in technology, the more retarded we become. Apparently, there will be no life in a while. And computers can not exist separately. Unlike organic life, which continued for millions of years, reproducing itself, sources to build mechanical devices are limited.

Ever heard of the benefits of progress? They usually outweight the negative aspects. We can't draw a line when to stop. That's just not possible. It's like trying to "freeze" evolution.

Making love is one of the exceptions. 

You perv... 

Proof?

I don't need to prove that. You have to proof soul exists. If I claim I am 1000 years old you don't need to prove I am not, I must prove I am. That's the way the burden of proof goes. Frankly, I am surprised some people believe in the existence of soul in 21th century.

Your ideas certainly look like they've been programmed. 

What ideas of mine are you preferring to?

[DavidW]

The sum becomes infinite. I never got your point, it seems.

I think he was being inconsistent.  He was trying to argue that mathematics is not tangible or real, but then when you discussed infinity he said that it was not a number, merely an abstraction and so forth... as if real numbers are "real" and not abstractions, which contradicts his thesis.

I agree with you Elgar, infinity is a well defined notion, and has just as much claim to being "real" as real or complex numbers would.

[mahler10th]

Arvo Part - Fratres - wasn't this formed from numbers?

Twelve-tone technique  -  mathematically 'even' music, or at least it's supposed to be.

[Sarastro]

infinity is a well defined notion

Did I say it was not? I was just saying that infinity is not a number in a common sense we put in the word "number." Infinity by the formal definition means charging forever, boundlessness, the unlimited. I tutor calculus and know that many students here have problems with understanding the concept, that is why I mentioned it. And I've never said anything about real numbers. They are just called "real" which does not necessarily mean they are real. Numbers are in your head.

[DavidW]

know that many students here have problems with understanding the concept, that is why I mentioned it.

Suggestion: know your audience.  You were discussing the matter with 71 dB, an experienced engineer, not one of your students.

[Florestan]

Frankly, I am surprised some people believe in the existence of soul in 21th century.

Wonder is the beginning of wisdom...

[orbital]

Numbers are in your head.

that's the way I tend to think as well, but then there is an objective measure that goes by the name of  "less" or "more" which only makes sense in the presence of numbers. And that does exist in nature:
A pack of 40 wolves will most likely defeat an opposing pack of 5. The main, if not the only, reason for the outcome is the number of wolves in each pack. Even if wolves do not know how to count, the numbers will determine the result.

[DavidW]

but then there is an objective measure that goes by the name of  "less" or "more" which only makes sense in the presence of numbers.

Real numbers certainly can be made into an ordered field, and we almost always consider them as such (most of analysis is built on presuming the existence of a least element in subsets of the reals), but I don't there is a unique ordering, I think there are others that also work, perhaps CS can comment.  Complex numbers on the other hand do not form an ordered field.  You can order it, or you can make it a field, but you can't do both.

Anyway I don't think ordering is an absolute, it's merely a restriction that we've applied to our favorite field (albeit a very meaningful restriction).

[Ten thumbs]

Numbers cannot be in your head because it seems that consciousness does not exist. I know this because it is impossible to prove its existence.
On the subject, I'm not sure it was Schoenberg who was criticized for being mathematical. Rather it was Scriabin who was said to be writing paper music that was merely mathematical formulae. I don't think anyone argues that now.
I must say that I am very sceptical of the value of the golden mean in music. It is a valuable spatial tool that should not be applied to temporal duration.