# Physics of Music



## Ignis Fatuus (Nov 25, 2008)

Hello! I was wondering if anyone could suggest any books about the physics of music. It's a bit difficult to describe more specifically what I'm searching for... I already know quite a bit about sine waves and Fourier Analysis from my maths degree... I'm looking more for how the laws of physics have affected the creation and development of music.

For example, I'm reading "The Language of Music" by Deryck Cooke and he briefly mentions how the ambiguity of the 6th overtone (B or Bb of the fundamental C) is why C major modulates to F major so easily. This is the kind of topic that interests me but have yet to find any books that focus on it.

Thanks for any replies!


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## Herzeleide (Feb 25, 2008)

_The Musician's Guide to Acoustics_ - Campbell and Greated.

Very pellucid and comprehensive.


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## Ignis Fatuus (Nov 25, 2008)

Thanks for the reply. From the reviews on amazon it seems quite good. But, I'm no so interested in acoustics (though it is a very important subject), but rather the physical basis for composition and musical theory (not the physical explanation of performance).

Sorry, it's hard to describe my topic of interest when I know so little about it! I hope I've done an ok job of describe what I'm looking for!


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## BuddhaBandit (Dec 31, 2007)

Check out Measured Tones by Ian Johnston. It's written very well and takes an interesting historical approach to the physics of consonances, scale relationships, harmonics, etc. My only quibble is that it's got very little math in it (I like math-heavy physics books).


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## JoeGreen (Nov 17, 2008)

BuddhaBandit said:


> My only quibble is that it's got very little math in it (I like math-heavy physics books).


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## BuddhaBandit (Dec 31, 2007)

JoeGreen said:


>


And you don't? 

And does anyone know why the word "physics" was bolded every time it appeared in my post?


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## Herzeleide (Feb 25, 2008)

Ignis Fatuus said:


> (though it is a very important subject), but rather the physical basis for composition and musical theory (not the physical explanation of performance).


Performance = how the music is actually produced = the sound the composer wanted the performers to produce = composition.

There's no physical explanation for music theory or composition (so anything you're likely to find will be pseudo-science) though both electroacoustic and spectral composers use an approach which is based upon the very acoustic foundations of sound.


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## Ignis Fatuus (Nov 25, 2008)

Thansk BuddhaBandit I'll take a look at that.



Herzeleide said:


> Performance = how the music is actually produced = the sound the composer wanted the performers to produce = composition.


Again, I apologise for my poor explanation. I mean "the physics of performance" to be a scientific explanation of how an instrument produces sound and how it transfers to the ear. This is not really what interests me (and also I find it adequately covered by many books). I'm more interested in things like what makes a consonance a consonant. I mean plenty of books explain the overtone series and why octaves, perfect fifths and major thirds sound pleasing etc. But I was hoping for a less introductary book that goes further than this.



Herzeleide said:


> There's no physical explanation for music theory or composition (so anything you're likely to find will be pseudo-science) though both electroacoustic and spectral composers use an approach which is based upon the very acoustic foundations of sound.


I beg to differ on this point. I wonder if our entire harmonic would exist at all if it were not for the single physical fact that a plucked string/blown flute creates overtones on top of the fundamental. To hammer the issue home: I would point out that a score is not pleasing (at least not to the musical layperson), while the audible work is.

Everyone (I hope!) knows that the Beatles made great music, in ignorance of the 'rules' of music, relying on their instinct and subtlety of ear. To me, this seems analogous to a classical composer who is in ignorance of the physical 'rules' of music - and as a composer, I don't want to work with my eyes closed any more! I don't expect a science of music that tells me what I should write to have a particular effect on this listener.. but I don't like the feeling of relying soley on my ears when it doesn't have to be that way.

As an simple example, composers learnt early on that a closely packed chord sounds 'muddy' when played low down. This was discovered by trusting the ear... whereas now we know that it is due to the logarithmic manner in which we hear - the ear's ability to differentiate close notes increases as the frequency increases.

Feel free to digress from the initial topic and discuss this further


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## Herzeleide (Feb 25, 2008)

Ignis Fatuus said:


> To hammer the issue home: I would point out that a score is not pleasing (at least not to the musical layperson), while the audible work is.


That hammers nothing home.

There are no 'rules' of music, no acoustic rules of composition. Acoustics merely explains sound itself, which of course is inseparable from sound produced by instruments.

If you type in 'The Musician's Guide to Acoustics' to Google, one of the results should be a page where you can browse through the book. It appears to contain everything you'd need.


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## PostMinimalist (May 14, 2008)

It seems that you are looking for a mathematical system of logic which would explain why certain conventions in music like cadences, dissonance, resolution, rhythm and modulation etc. are interpreted by the human ear in the way they are. You could start by following through with Cooke's explanation of why dominant-tonic relationships seem to be based on the proximity of upper harmonics of fundamentals a fourth or fifth apart. I'm sorry I cant help you with books but If you apply a more mathematical approach to your google search you'll find something soon!
FC


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## Ignis Fatuus (Nov 25, 2008)

Herzeleide said:


> There are no 'rules' of music, no acoustic rules of composition. Acoustics merely explains sound itself, which of course is inseparable from sound produced by instruments.


I'm tempted not to persue this further as you seem to have made up your mind not to agree in anyway. So you would say that the non-linear nature of our interpretation of frequency combined with the linear design of the ear's frequency detection system has absolutely no bearing on composition?



post-minimalist said:


> It seems that you are looking for a mathematical system of logic which would explain why certain conventions in music like cadences, dissonance, resolution, rhythm and modulation etc. are interpreted by the human ear in the way they are. You could start by following through with Cooke's explanation of why dominant-tonic relationships seem to be based on the proximity of upper harmonics of fundamentals a fourth or fifth apart. I'm sorry I cant help you with books but If you apply a more mathematical approach to your google search you'll find something soon!
> FC


Yes! This is pretty much what I've been attempted/failing to say! Although it might be going too far to call it a 'system' of logic, I think it'could be very useful stuff to know.


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## Herzeleide (Feb 25, 2008)

Ignis Fatuus said:


> I'm tempted not to persue this further as you seem to have made up your mind not to agree in anyway. So you would say that the non-linear nature of our interpretation of frequency combined with the linear design of the ear's frequency detection system has absolutely no bearing on composition?


They have bearing on sound. But this is by no means a _basis_ of composition or theory (with the exceptions that I've already pointed out).


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## Ignis Fatuus (Nov 25, 2008)

The common compositional technique of only using widely spaced chords in the lower register is directly based on the physics of the ear (or these days, perhaps on tradition).

A closed bass chord does not just sound "bad" because that is the way of things - there is a reason (and this reason is not psuedo-scientific - in the lower register, two sine tones a major third apart are dected by the SAME hair cell, whereas at high frequencies, they are dected by different hair cells).

It's perfectly acceptable to compose trusting your ear alone (or rather, trusting the ear of your teacher who tells you not to use closed bass chords!) but it cannot hurt to understand WHY it has its unique character.

I really didn't except such a reaction to this kind of thinking.


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## Herzeleide (Feb 25, 2008)

Ignis Fatuus said:


> The common compositional technique of only using widely spaced chords in the lower register is directly based on the physics of the ear (or these days, perhaps on tradition).
> 
> A closed bass chord does not just sound "bad" because that is the way of things - there is a reason (and this reason is not psuedo-scientific - in the lower register, two sine tones a major third apart are dected by the SAME hair cell, whereas at high frequencies, they are dected by different hair cells).
> 
> ...


You're confusing describing a physical phenomenon with applying aesthetic quality/value-judgement to it.

A closed bass chord only sounds 'bad' because we apply our judgement to it. _Judgement_ being the crucial word here. This is a matter of aesthetics and judgement, _not_ physical, acoustical phenomenon. Science does not/should not trespass on art.


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## Lang (Sep 30, 2008)

Herzeleide said:


> You're confusing describing a physical phenomenon with applying aesthetic quality/value-judgement to it.
> 
> A closed bass chord only sounds 'bad' because we apply our judgement to it. _Judgement_ being the crucial word here. This is a matter of aesthetics and judgement, _not_ physical, acoustical phenomenon. Science does not/should not trespass on art.


But Ignis is saying that the 'judgement' arises from the physical phenomenon. That there is a physical reason why some intervals are consonant and some are dissonant; why some chords sound better than others.

I don't think that by describing phenomena science is trespassing on art, or, indeed, doing anything that it is not supposed to be doing.

I once had someone (who had very little judgement when it came to music) saying that by knowing how a symphony was constructed, I was somehow compromising my enjoyment. They failed to understand that a knowledge of musical theory and structure if anything _increased_ the aesthetic experience. By asserting that science has no place in the realm of aesthetics seems to me to be applying a very similar argument. Speaking personally, I want to know everything there is to know about music. Got a little way to go, at the moment.


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## Ignis Fatuus (Nov 25, 2008)

Yes Lang, that's a good analogy.

I'm not saying there is a scientific reason why a closed bass chords sounds bad. I am saying that there is a scientific reason for why it has its specific character (different from a high closed chord, or an open low chord etc.)... and then as a composer you can choose whether that character serves your purpose or not - on the whole, not.

Of course, with this simple example a good ear can guide you... but to rely on your soley on your ear at all times seems an unnecessary burdon.

I have huge respect for Giuseppe Tartini, the violinist who discovered combination tones by noticing the subtlety of the sound... there is no way my 'ear' would have been sensitive enough to notice combination tones without them being pointed out to me.

It would be great to leave the word 'science' out of this topic since it evokes a science vs. art kind of image, which is really not the case.

It's also worth pointing out that the examples in this post are psychoacoustic examples (since that's the area I've managed to find books about!) whereas this thread created to ask about books on plain physics (i.e. before the 'subjectivity' of the human ear gets involved)!


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## Herzeleide (Feb 25, 2008)

Lang said:


> But Ignis is saying that the 'judgement' arises from the physical phenomenon. That there is a physical reason why some intervals are consonant and some are dissonant; why some chords sound better than others.


Utter nonsense. For one thing, some chords considered 'bad' at one point in history go on to be considered good in another.



Lang said:


> I once had someone (who had very little judgement when it came to music) saying that by knowing how a symphony was constructed, I was somehow compromising my enjoyment. They failed to understand that a knowledge of musical theory and structure if anything _increased_ the aesthetic experience. By asserting that science has no place in the realm of aesthetics seems to me to be applying a very similar argument. Speaking personally, I want to know everything there is to know about music. Got a little way to go, at the moment.


Except that music theory is not based on science. You've completely misunderstood me. Scientific descriptions of sound phenomenon explain the physical basis of sound, but not the aesthetic basis.

You can go into a great deal of detail to a (colour) blind person about the properties of the colour red, but this will not help them to _know_ what the colour red is _actually_, empirically, aesthetically, like.


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## Herzeleide (Feb 25, 2008)

Ignis Fatuus said:


> I'm not saying there is a scientific reason why a closed bass chords sounds bad.


That is specifically what you related it to:



> A closed bass chord does not just sound "bad" because that is the way of things - there is a reason (and this reason is not psuedo-scientific - in the lower register, two sine tones a major third apart are dected by the SAME hair cell, whereas at high frequencies, they are dected by different hair cells).


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## Ignis Fatuus (Nov 25, 2008)

Herzeleide said:


> That is specifically what you related it to:


Haha, I thought you would realise I was using "bad" in inverted commas in the same sense as most music textbooks do. Sorry for that confusion, I should have spelled it out to be clearer. However, I did infact remove any ambiguity in the next post, please refer to THAT one rather than picking up on the ambiguity of the previous post.

Again, to clarify my postion: the chord's character is based on physical reality (it has a certain 'roughness' or 'muddiness' which can be explained scientifically - and further, it could sound 'clear' if our ears were designed differently). However, it is our taste which decides if that effect is good or bad, and consequently, whether it should be use or not - through most of musical history, we have prefered clarity over the kind of 'roughness' which arises from a closed bass chord - and so it has been refered to as "bad".

EDIT: Also, thanks for taking the time to debate this issue... if I am indeed wrong, you'll be helping me a lot by putting me right. However, I think the arguement has arisen because you think I am speaking in stronger terms than I actually am - I am not suggesting there is a strict science of aesthetics.


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## Lang (Sep 30, 2008)

Herzeleide said:


> Utter nonsense. For one thing, some chords considered 'bad' at one point in history go on to be considered good in another.


Well, sometimes dissonance is seen as good; other times it is seen as bad. That is a matter of aesthetics. But there is a physical reason why we divide chords into consonant and dissonant. Do you disagree with that?


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## Herzeleide (Feb 25, 2008)

Lang said:


> Well, sometimes dissonance is seen as good; other times it is seen as bad. That is a matter of aesthetics. But there is a physical reason why we divide chords into consonant and dissonant. Do you disagree with that?


If this were true, it would be seen in music from all over the world. As it is, it only applies to western music. Thus, it cannot be considered a universal scientific truth.


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## Herzeleide (Feb 25, 2008)

Ignis Fatuus said:


> Again, to clarify my postion: the chord's character is based on physical reality (it has a certain 'roughness' or 'muddiness' which can be explained scientifically - and further, it could sound 'clear' if our ears were designed differently).


Could sound clear? Well yes, not if our ears were 'designed differently' but if we were brought up on such music and it were normal for us.

So essentially, it has nothing to do with its intrinsic scientific properties, but our _judgement_. That is essentially what you've admitted to, in conceding that it could sound clear.


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## PostMinimalist (May 14, 2008)

But... Essentially our judgement in based on something, and even if that something cannot be described with mathematical accuracy it may described within the bounds of scientific description. This is the area of interest to Ignis Fatuus, is it not?


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## Elgarian (Jul 30, 2008)

Reading through this thread a second time, I'm struck by the impression that each contributor is saying something sensible, but that all contributors are not actually talking about the same thing.

It seems more helpful to talk about scientific 'models' rather than scientific 'explanations'; and those models can be useful sometimes, even when they're not particularly good at predicting outcomes. To put this on a really basic level (in the hope that it may help to clarify the fundamentals of what's being discussed), one can make the _scientific_ statement about two sounds, that sound A has twice the frequency of sound B; or one can make the _musical_ statement that A is an octave higher than B. They're not the same thing - one is based on measurement, and the other on perception, but there's no denying that there is a link between them. To say that scientific reasoning can 'explain' musical aesthetics is incorrect; but it would be equally incorrect to insist that there's no relation at all between them.


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## Herzeleide (Feb 25, 2008)

post-minimalist said:


> But... Essentially our judgement in based on something, and even if that something cannot be described with mathematical accuracy it may described within the bounds of scientific description. This is the area of interest to Ignis Fatuus, is it not?


Read IF's posts: he wants scientific explanations/justifications for why things sound good/bad etc.

Unfortunately it doesn't work like that.


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## Elgarian (Jul 30, 2008)

Herzeleide said:


> Read IF's posts: he wants scientific explanations/justifications for why things sound good/bad etc. Unfortunately it doesn't work like that.


Is that really what he wants? I'm not so sure (and that's why I made my previous post). I'm not sure he wants _explanations_, in fact; rather, he wants to be able to compare aesthetic responses with scientific statements and models, and look for parallels between them. Any match that we find between these will always be imperfect of course - as you point out, what sounds' good' in one cultural context may sound 'bad' in another - but the exercise may nonetheless be illuminating. (There are lots of areas where scientific modelling is imperfectly predictive, but still can be helpful.)

Incidentally (and I say this with misgivings, because I mustn't cause the discussion to veer off topic), I feel very uneasy about bringing in the idea of 'universal scientific truth', as mentioned above (#21). There's no such thing. _All_ the statements of science are provisional; even the strongest scientific theory is only trustworthy up to the last time it was tested. So I don't think the difference between cultural responses is a good reason for calling a halt to IF's project - though of course it makes it more difficult, and perhaps less likely to reach a satisfactory outcome.


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## Ignis Fatuus (Nov 25, 2008)

Herzeleide said:


> Read IF's posts: he wants scientific explanations/justifications for why things sound good/bad etc.


I no longer have the will to make a point-by-point correction of your mistakes - since you are clearly not taking the time to read my posts properly. I have been very patient toward your blunt and forceful attitude so far but when you either do not read my posts, or delibrately misunderstand my position, I consider that insulting.

Of course different cultures have different attitudes, reactions and interpretations. I'm fascinated by psychology, sociology and philosphy (for example it's intriguing how the Ancient Greeks seem not to have associated pitch with altitude) - however this only augments and increases my scientific interest.

Consider a sound at 21000Hz. If I were to call this note 'silent', is that my aesthetic judgement kicking in, or a result of the culture I live in? Or perhaps it is just a fact that the design of my ears cannot detect sounds that high. Please note that many creatures on Earth would be able to hear that sound - so ear design is crucial.

Of course, I use an English word ("silent"), I pronounce it with an East Anglian accent, I choose "silent" instead of the other alternatives (e.g. "inaudible"). These are all results of my culture and my upbringing. The fact that I just cannot hear the bloody sound, is not!  This physical situation has an effect on composition in that we use flutes instead of dog whistles.

[I'm conveniently ignoring the studies that suggest that humans do infact have some way of detecting hypersonic sound!]


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## Herzeleide (Feb 25, 2008)

Ignis Fatuus said:


> This physical situation has an effect on composition in that we use flutes instead of dog whistles.


But:



> I mean "the physics of performance" to be a scientific explanation of how an instrument produces sound and how it transfers to the ear. This is not really what interests me


So you have now changed your mind and are claiming to have meant the sounds of instruments.

Originally you stated you wanted to know the scientific basis of music theory.


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## Ignis Fatuus (Nov 25, 2008)

You made one (2-line) constructive post at the start of this thread and the rest has been useless negativity. Pointing out perceived contradictions (which, even if accurate only shows how my interest topics have changed) is not a worthwhile activity.

If you have no desire to help then why post?

To reiterate my initial point: if anyone has an book suggestions I would be very grateful to hear them.


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## SPR (Nov 12, 2008)

this thread looks like several others I have seen recently. Unfortunately. I think it better to not to fall all over myself in my haste to discredit harmless commentary and requests for assistance. Usually, I would simply look like an a_ss_ - which I can do well enough without trying.

regardless....

unsure if any of this would fit your interests....

http://www.amazon.com/exec/obidos/ASIN/0486217698

http://www.amazon.com/exec/obidos/ASIN/0387941517

http://www.amazon.com/exec/obidos/ASIN/031322644X

http://www.amazon.com/exec/obidos/ASIN/0403016223

http://www.amazon.com/exec/obidos/ASIN/0882756567

http://www.amazon.com/exec/obidos/ASIN/048626484X

http://www.amazon.com/exec/obidos/ASIN/0306704226

http://www.amazon.com/exec/obidos/ASIN/0393090965


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## Ignis Fatuus (Nov 25, 2008)

Thanks for the links! I'll take a look.


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## Herzeleide (Feb 25, 2008)

Ignis Fatuus said:


> which, even if accurate only shows how my interest topics have changed


Glad to hear that.


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