# Music and Mathematics: Science or Pseudoscience?



## aleazk (Sep 30, 2011)

This is the thread for posting all the arguments in favour or against the 'mathematization' of music.


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## Petwhac (Jun 9, 2010)

aleazk said:


> This is the thread for posting all the arguments in favour or against the 'mathematization' of music.


I'm not against 'mathematization' (new word to me) of music or any ....ization of music on a matter of principal. But I think a lot of the creativity and invention in serial music, especially integral serial music, is in the devising of the 'row' 'set' 'matrix' and less in the musical 'working' of the material. 
Would someone care to point out the criteria by which one may judge if a serial composition has been well executed? After all if pitch, duration, register and dynamics are all tied to a pre determined plan, what are the compositional choices that will set apart the novice, charlatan, journeyman or dilettante from the master, genius or the imaginative _musician_?


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## Philip (Mar 22, 2011)

Electronic musician Caribou has a doctorate of philosophy in mathematics, his music sounds like this:

CARIBOU - Odessa





More recent, as Daphni:

Daphni - Ye Ye


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## Ramako (Apr 28, 2012)

Argument against: I don't like it.

Case closed


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## Guest (Aug 6, 2012)

Philip said:


> Electronic musician Caribou has a doctorate of philosophy in mathematics, his music sounds like this:


Mind boggling stuff and not in a nice way, for me a big turn off.


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## Philip (Mar 22, 2011)

Andante said:


> Mind boggling stuff and not in a nice way, for me a big turn off.


Yes brilliant!


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## norman bates (Aug 18, 2010)

I think that music can be analysed in a scientifical way. The point is that the study of music is not only the study of the object but it must be also a study of what we perceive it with the brain (psychoacoustics). I think that a lot of composers (especially the serial composers) have made the big error of not considering the second one. So it's like a chef that cooks like he's simply a chemist.


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## Morgante (Jul 26, 2012)

The Music is not mathematics.


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## HarpsichordConcerto (Jan 1, 2010)

Judging by the bulk crap that Xenakis produces following his "stochastic music" thing, I don't think music is mathematics ...


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## norman bates (Aug 18, 2010)

HarpsichordConcerto said:


> Judging by the bulk crap that Xenakis produces following his "stochastic music" thing, I don't think music is mathematics ...


and judging by the music of Bach?


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## Ramako (Apr 28, 2012)

norman bates said:


> and judging by the music of Bach?


Counterpoint is not an identity with mathematics.


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## norman bates (Aug 18, 2010)

Ramako said:


> Counterpoint is not an identity with mathematics.


and this?
http://en.wikipedia.org/wiki/Harmonic_series_%28music%29


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## Ramako (Apr 28, 2012)

norman bates said:


> and this?
> http://en.wikipedia.org/wiki/Harmonic_series_%28music%29
> 
> View attachment 6757


That is physics. If you can prove that fugue scientifically follows from that, then I shall reassess my position.


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## norman bates (Aug 18, 2010)

Ramako said:


> That is physics. If you can prove that fugue scientifically follows from that, then I shall reassess my position.


why i have to prove that? I am only saying that music can be analysed in a scientific way, as i've said in my first post. I've said Bach but i've could have used Mozart, Beethoven or whoever you want.


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## Petwhac (Jun 9, 2010)

norman bates said:


> why i have to prove that? I am only saying that music can be analysed in a scientific way, as i've said in my first post. I've said Bach but i've could have used Mozart, Beethoven or whoever you want.


You can analyse anything in any way you want. Why certain patterns of sound have certain psychological effects on certain people at certain times in certain cultures is a rather large question. I wouldn't expect a comprehensive answer in the near future. But I suppose there is no harm in looking for answers.
If a composer wants to base a composition on what he/she thinks is some scientific principle, that's their business. Listening to it is my business.


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## Ramako (Apr 28, 2012)

norman bates said:


> why i have to prove that? I am only saying that music can be analysed in a scientific way, as i've said in my first post. I've said Bach but i've could have used Mozart, Beethoven or whoever you want.


I am saying that Bach is not mathematical in the same way as Xenakis etc. Xenakis deliberately used mathematics, Bach used counterpoint. Music has similar properties to mathematics, in using patterns etc. many mathematical people are musical and vice versa (the personality type poll on this forum shows that). However that is because they both derive from the same kind of stuff IMO, it doesn't make music any more mathematical than maths is musical. Frequencies may be the basis of music, but they have relatively little to do with the way it is used, apart from interesting parallels (not 5ths).

As for the whole psycho-analysis thing about music, it will be interesting to see where it goes. However, in my opinion it will never replace "normal" composition because composers learn more about their reactions to music by deep self-analysis than by some external machine showing colours on a picture of the brain. Perhaps I shall be proved wrong in 5,000 years, or even 50, but I am a bit of a skeptic where these things are concerned.


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## norman bates (Aug 18, 2010)

Ramako said:


> I am saying that Bach is not mathematical in the same way as Xenakis etc. Xenakis deliberately used mathematics, Bach used counterpoint. Music has similar properties to mathematics, in using patterns etc. many mathematical people are musical and vice versa (the personality type poll on this forum shows that). However that is because they both derive from the same kind of stuff IMO, it doesn't make music any more mathematical than maths is musical. *Frequencies may be the basis of music, but they have relatively little to do with the way it is used, apart from interesting parallels (not 5ths).*


well, the concept of consonance and dissonance is based exactly on the frequencies. That is basically the base of the study of harmony of any composer. If i remember well Nadia Boulanger used to say that the history of music is the history of harmonics, or something like that. And when we're talking of harmonics and their proportions we're talking of science.



Ramako said:


> As for the whole psycho-analysis thing about music, it will be interesting to see where it goes. However, in my opinion it will never replace "normal" composition because composers learn more about their reactions to music by deep self-analysis than by some external machine showing colours on a picture of the brain. Perhaps I shall be proved wrong in 5,000 years, or even 50, but I am a bit of a skeptic where these things are concerned.


i've never intended to say that psychoacustics have to replace normal composition (it does not have any sense! It's like to say that the study of harmony could replace composition), it's a way to look at music that could improve the awareness of certain aspects of music.


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## Philip (Mar 22, 2011)

Actually, some of the founders of harmony (eg. Rameau, _Traité de l'harmonie_) were very aware of the mathematical implications of harmony. The basis of the treaty relies on the number ratios attributed to each interval, derived from the vibrating string.


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## Ramako (Apr 28, 2012)

This was started by me rejecting Bach as being as mathematical as Xenakis. I would like to state beforehand (afterwards in writing time) that this is not intended to be hostile, or trying to put you down or anything (not that I could if I wanted to); but I like debating and logic and things and I've written a very long post so I might as well post it. Most of it is not considered opinions, and I am happy to discuss and be corrected .



norman bates said:


> well, the concept of consonance and dissonance is based exactly on the frequencies. That is basically the base of the study of harmony of any composer.


The study of consonance and dissonance is one of the cornerstones of the works/studies of any composer, both in harmony, counterpoint, and to a lesser extent structure and melody etc. they are the building blocks of music in a very fundamental sence. That said, allow me to try and be logical about this.

Assumption/axiom:



norman bates said:


> the concept of consonance and dissonance is based exactly on the frequencies.


*Application*. A composer who knows that one frequency is consonant, and one dissonant, but does not know how to use this consonance or dissonance, may be a good mathematician, but a very poor composer. He can get on without the knowledge of frequencies, (i.e. without the science), but not without the skill in using these phenomena (the musicality). Hence the science is more or less irrelevant to a composer.

But that is only a matter of application. Let us deal with the theory as well. I am going to focus on harmony, since you did. If you have more info I don't know about I would be very interested.

*Harmonic progressions*. In harmony, a composer learns about the strength of harmonic progressions, like V-I. Perhaps progressions follow the same hierarchy as intervals? However, a fifth is more consonant than a third and both more consonant than a second, However both I-V and IV-V are 'stronger' (more powerful/consonant?) than I-III. Therefore the progression of a third is weaker than either a second or a fifth. Therefore the consonance or dissonance of an interval does not tell us about strong or weak progressions. Therefore frequencies do not tell us about strong or weak progressions in harmony. If harmonics do not tell us about progressions in harmony, they don't tell us about harmonic motion. Without motion, harmony is not music (barring Cage etc.). Therefore frequencies don't tell us much about music.

This has nothing to do with your post, but is a general issue as I see it:

*Fundamental problems*. Science can show us that consonance is more simple than dissonance in terms of frequencies. Any perceived parallel between consonance and dissonance and frequencies is based on this concept of the simplicity of the frequencies. Consonance is simple, consonance is 'good', right? Well, so it would be nice to think. Science is based on an aesthetic of simplicity and reduction. This has been the problem of physics since its inception, never more so than now (Higgs Boson and gravity). However, there is a common fallacy in progressing from here in assuming that simplicity is good in music. If that were so, 4:33 or _In C_ would be the greatest pieces of music ever. (of course it isn't the point of the pieces, but harmonically speaking). Most people would not say so.

The problem is that science the aesthetic of science is reduction to the simplest possible axioms; the aesthetic of music is life.

Ok. Now, to get back to the point:



norman bates said:


> If i remember well Nadia Boulanger used to say that the history of music is the history of harmonics, or something like that. And when we're talking of harmonics and their proportions we're talking of science.


Following that you get the chain of reasoning.

The history of music=the history of harmonics.
Harmonics is a subset of science.
Therefore the history of music is a subset of the history of science.

There might be many scientific musicians who might support such a claim. Scientists certainly might.

However, I would prefer to point out that harmonics, atoms, light, the sun, dogs, my foot or whatever may be the subject of scientific study, but that doesn't make them "science".

From my previous, I would prefer to go with:

the history of music is a subset of the history of life.



norman bates said:


> i've never intended to say that psychoacustics have to replace normal composition (it does not have any sense! It's like to say that the study of harmony could replace composition)


I agree! I wasn't only aiming my remarks at you, and I'm sorry if it came across that way.



norman bates said:


> it's a way to look at music that could improve the awareness of certain aspects of music.


That's true I suppose. I am inclined to believe, however, that music will probably be generally a step ahead of psyco-analysis, in the same way it has been ahead of the 'rules' of the past.


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## norman bates (Aug 18, 2010)

Ramako said:


> This was started by me rejecting Bach as being as mathematical as Xenakis. I would like to state beforehand (afterwards in writing time) that this is not intended to be hostile, or trying to put you down or anything (not that I could if I wanted to); but I like debating and logic and things and I've written a very long post so I might as well post it. Most of it is not considered opinions, and I am happy to discuss and be corrected .


there's absolutely no problem 



Ramako said:


> The study of consonance and dissonance is one of the cornerstones of the works/studies of any composer, both in harmony, counterpoint, and to a lesser extent structure and melody etc. they are the building blocks of music in a very fundamental sence. That said, allow me to try and be logical about this.
> 
> Assumption/axiom:
> 
> *Application*. A composer who knows that one frequency is consonant, and one dissonant, but does not know how to use this consonance or dissonance, may be a good mathematician, but a very poor composer. He can get on without the knowledge of frequencies, (i.e. without the science), but not without the skill in using these phenomena (the musicality). Hence the science is more or less irrelevant to a composer.


well, the fact that one doesn't know that a note and his fifth are in a relation of 3/2 does not imply that that mathematical relation however doesn't exist.



Ramako said:


> But that is only a matter of application. Let us deal with the theory as well. I am going to focus on harmony, since you did. If you have more info I don't know about I would be very interested.
> 
> *Harmonic progressions*. In harmony, a composer learns about the strength of harmonic progressions, like V-I. Perhaps progressions follow the same hierarchy as intervals? However, a fifth is more consonant than a third and both more consonant than a second, However both I-V and IV-V are 'stronger' (more powerful/consonant?) than I-III. Therefore the progression of a third is weaker than either a second or a fifth. Therefore the consonance or dissonance of an interval does not tell us about strong or weak progressions. Therefore frequencies do not tell us about strong or weak progressions in harmony. If harmonics do not tell us about progressions in harmony, they don't tell us about harmonic motion. Without motion, harmony is not music (barring Cage etc.). Therefore frequencies don't tell us much about music.


i can't say a lot about this argument that is very complex (and we should have to consider also modal harmony, atonality, bitonality, microtonality) but i think that for example behind the concept of the cadence there's some kind of mathematical relationship.



Ramako said:


> This has nothing to do with your post, but is a general issue as I see it:
> 
> *Fundamental problems*. Science can show us that consonance is more simple than dissonance in terms of frequencies. Any perceived parallel between consonance and dissonance and frequencies is based on this concept of the simplicity of the frequencies. Consonance is simple, consonance is 'good', right?


not necessarily. The point is what the consonance means in a certain moment of a certain piece, and it could be good or absolutely uninteresting, boring or even out of place.



Ramako said:


> Well, so it would be nice to think. Science is based on an aesthetic of simplicity and reduction. This has been the problem of physics since its inception, never more so than now (Higgs Boson and gravity). However, there is a common fallacy in progressing from here in assuming that simplicity is good in music. If that were so, 4:33 or _In C_ would be the greatest pieces of music ever. (of course it isn't the point of the pieces, but harmonically speaking). Most people would not say so. The problem is that science the aesthetic of science is reduction to the simplest possible axioms; the aesthetic of music is life.


you are talking with a person that is obsessed with strange harmonies, weird progressions, unique harmonic effects so definitely i don't think that simplicity is good in music. But said that, i have some problem to get your point, because science studies also phenomena that are incredibly complex, and because the fact that in a piece of music there are mathematical/physical relations is just a part of the story, after that there's the brain and how it filters all those relations (for example a lot of serial music is perceived as total chaos, even if it seems a contradiction). So we have two well separate things.



Ramako said:


> Ok. Now, to get back to the point:
> 
> Following that you get the chain of reasoning.
> 
> ...


No, i think that science is deeply involved but not that music is science or a subset of the history of science. Music can be object of scientific studies and you can approach a lot of different musical aspects in a scientifical way.

By the way, that sentence of Nadia Boulanger does not consider for example music that is simply percussive...


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## Ravndal (Jun 8, 2012)

Philip said:


> Electronic musician Caribou has a doctorate of philosophy in mathematics, his music sounds like this:
> 
> CARIBOU - Odessa
> 
> ...


Loving caribou's style. Especially some of the collabs with four tet.


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## elgar's ghost (Aug 8, 2010)

Re: Daphni's Ye Ye - unless it's an unfortunate choice of his work DAF were churning out stuff like this 20 years ago.


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## Ramako (Apr 28, 2012)

norman bates said:


> there's absolutely no problem


Good 



norman bates said:


> well, the fact that one doesn't know that a note and his fifth are in a relation of 3/2 does not imply that that mathematical relation however doesn't exist.


Yes, I agree. However, it does put up a significant amount of distance between 'musicality' and science as we know it.



norman bates said:


> i can't say a lot about this argument that is very complex (and we should have to consider also modal harmony, atonality, bitonality, microtonality) but i think that for example behind the concept of the cadence there's some kind of mathematical relationship.


I sort of agree, but I followed my argument to what I saw was its logical close. I suppose I was only dealing with standard tonal music.

The cadence is an interesting point. It seems to pervade even many non-classical types of music. I don't feel I understand its full significance yet: is it really no more than just a full stop in music?



norman bates said:


> you are talking with a person that is obsessed with strange harmonies, weird progressions, unique harmonic effects so definitely i don't think that simplicity is good in music. But said that, i have some problem to get your point, because science studies also phenomena that are incredibly complex, and because the fact that in a piece of music there are mathematical/physical relations is just a part of the story, after that there's the brain and how it filters all those relations (for example a lot of serial music is perceived as total chaos, even if it seems a contradiction). So we have two well separate things.


About science. It seems to me as someone who lives in a family of physicists, that the scientist's aim is to try and reduce an incredibly complex system (e.g. the universe) to something very simple. So reducing all forces to 4 fundamental ones, trying to unite gravity to the other three, essentially to unite quantum mechanics with Relativity. The emphasis is on unity and simplicity.

The importance of the basic frequencies cannot be denied, but mostly they seem the building blocks of music - the fifth and octave for example, have importance in melody and moving harmonies for sure. I think there are however important points to balance this. The most important of these is stepwise motion. This is a very logical idea (one note to the one next to it) based in common sense (always dangerous) which practically disintegrates when examined in frequencies as far as I can see.

Perhaps music can be examined in a variety of ways roughly parallel to numbers being able to be manipulated by adding, multiplying, powers etc.? Still, until scientists can understand what people 'like' then all of these things will remain curiosity, with about as much cosmic significance as the fibonacci sequence and the golden ratio. :hides into corner at the mention of *the ratio*:


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## Guest (Aug 6, 2012)

Of course Music is Math and nothing else but it is what is done with it that matters !


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## Ramako (Apr 28, 2012)

Andante said:


> Of course Music is Math and nothing else but it is what is done with it that matters !


Lol over-argued true, but I'm not sure where the 'nothing else' fits in. Anyway, the whole frequencies thing is physics not maths. A pedant would argue over it, but moving on...

What is more important to this thread I think is the use of mathematics in music, which isn't what Bach and people did but what Xenakis and people did. For myself, I think the logic of music is different to the logic of mathematics. Possibly this is because music is perceived through time and maths through space.


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## Guest (Aug 7, 2012)

Ramako said:


> Lol over-argued true, but I'm not sure where the 'nothing else' fits in. Anyway, the whole frequencies thing is physics not maths. A pedant would argue over it, but moving on...
> 
> What is more important to this thread I think is the use of mathematics in music, which isn't what Bach and people did but what Xenakis and people did. For myself, I think the logic of music is different to the logic of mathematics. Possibly this is because music is perceived through time and maths through space.


I agree with you I got carried away,


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