Music and Math

[bwv 1080]

Try to restart, reframe and remove the discussion that started in the Mahler thread. 
ISTM that there are two unsupportable positions on the topic:

A) the Quantophiliac, who looks for deterministic mathematical relationships to aesthetics, forgetting that music is art and therefore cannot be fully defined by the sum of any set of empirical observations.

B) the Quantophobe, for whom mystical inspiration is all and ignores the fact that math is often a useful tool in achieving and describing aesthetic objectives.

Certainly composers have taken direct inspriation from mathematics.  Bartok w/ golden mean proportions, Ligeti with strange attractors and other fractal phenomena etc.  Music is not math any more than architecture is math, but as Monk sez, all musicians are subconsiously mathematicians. 

[Cato]

In which case one needs to find the "Golden Mean" between the two positions!   

Which, oddly, will not be an even path!   

I have also wondered if there is not a musical connection to playing chess via a (subconscious ?) mathematical ability: e.g. Prokofiev apparently was a very good player.

And mathematicians have remarked upon proofs, etc, with the words "elegant" and "beautiful," with some openly suspicious of any series of equations that shows too much sweat and not enough grace as being on the wrong path.

I have, however, been bored to tears by articles in scholarly musical journals going through "permutations of sets" blah blah blah!  For an elite who might claim they can actually hear such things in a work and follow them, fine!  If that floats your boat to the Isle of Musical Bliss, fine!

But I'm jumping off that boat: throw me a life preserver!  Cherry preferably!

[karlhenning]

Interesting thread!  And I entirely agree that neither A. nor B. is tenable.

Certainly composers have taken direct inspriation from mathematics.  Bartok w/ golden mean proportions, Ligeti with strange attractors and other fractal phenomena etc.  Music is not math any more than architecture is math, but as Monk sez, all musicians are subconsiously mathematicians. 

To this I partly assent.  Artists get inspiration from a wide range of Stuff Out There;  there's certainly no reason why some mathematical something cannot be part of the stuff of inspiration.

I don't really think, though, that all musicians are subconsciously mathematicians, beyond the relatively trivial matter that (for instance) the complex of events in an orchestral score are plotted on a kind of graph, and that individual players count in order to keep their place.  A lot of what goes on in the music, in the sound, can be measured with and expressed in numbers, sure.  But I do not think this makes musicians as a class "subconscious mathematicians" any more than fifty other vocations.

My 2¢

[karlhenning]

I have, however, been bored to tears by articles in scholarly musical journals going through "permutations of sets" blah blah blah!  For an elite who might claim they can actually hear such things in a work and follow them, fine!  If that floats your boat to the Isle of Musical Bliss, fine!

Yes;  whatever tools a composer finds to make the best music he can, he is welcome!  Why not?!

But heaven help Webern if you need to study a set of five graphs in order to "understand" (let alone "enjoy") his music!  (I believe no such thing.)

[sonic1]

Hey. What about the Hamhockophiliacs (of which I am one) who are wholly inspired by ham hocks.

[greg]

what i'm interested in is the relationship between musical mathematics and how they affect one psychologically- it's hard to find any info at all about it, but here's something:

http://pom.sagepub.com/content/vol28/issue1

it has an article titled "Psychological Connotations of Harmonic Musical Intervals", except it looks like you have to subscribe or something  

i might have to begin a study all by myself

[karlhenning]

i might have to begin a study all by myself

Go for it! Don't forget the hamhocks!

[greg]

Go for it! Don't forget the hamhocks!

aye aye cap'n 

[greg]

i just found a good article:

http://mediatheque.ircam.fr/articles/textes/McAdams96a

looks like it might help me with some of my many questions

leave it to IRCAM to deal with interesting stuff! 

[Cato]

Hey. What about the Hamhockophiliacs (of which I am one) who are wholly inspired by ham hocks.

As they say in Guadalajara: El grosso profundo!

Is there music in them thar hamhocks, or any kinda 'rithmetic?   

"Hamlet" is no doubt derived from such appendages through a Boolean subset of Poincare derivatives!
Along with the economic theories of Alexander Hamilton!

And I'm betting David Hockney's photographs can be analyzed the same way!

[71 dB]

Music is organised sounds.

The organisation process is economic. First we define musical scales etc. Then we construct higher level objects, thematic material (themes, melodies, harmonic ideas etc.). Finally we have constructed movements of larger works and complete works.

Lower level objects are easy to define mathematically.

Music scales are based on simple math. Equal temperament is 100% pure simple math based on simple equations like:

Harmony is based on math too. Consonance and dissonance is related to how simple or complex relation there is between the fundamental frequencies of the notes in chords.

High level objects are difficult/nearly impossible to define mathematically.

Clever statistical analyse of "good" melodies perhaps gives interesting results about how melodies follow certain complex rules. Anyway the math starts to be extremely complex. Trying to define complete symphonies with math would be insane. The math needed would be beyond anything mankind can understand I am afraid. However, the smaller blocks in music can be described with at least some kind of statistical logic.

[sonic1]

Hey, where is pink harp? I thought for sure we would get a diatribe from him by now regarding this subject.

[karlhenning]

[snip]

High level objects are difficult/nearly impossible to define mathematically.

Clever statistical analyse of "good" melodies perhaps gives interesting results about how melodies follow certain complex rules. Anyway the math starts to be extremely complex. Trying to define complete symphonies with math would be insane. The math needed would be beyond anything mankind can understand I am afraid. However, the smaller blocks in music can be described with at least some kind of statistical logic.

Thank you for demonstrating the pointlessness of your own post.

[Cato]

Music is organised sounds.

The organisation process is economic. First we define musical scales etc. Then we construct higher level objects, thematic material (themes, melodies, harmonic ideas etc.). Finally we have constructed movements of larger works and complete works.

Lower level objects are easy to define mathematically.

Music scales are based on simple math. Equal temperament is 100% pure simple math based on simple equations like:

Harmony is based on math too. Consonance and dissonance is related to how simple or complex relation there is between the fundamental frequencies of the notes in chords.

High level objects are difficult/nearly impossible to define mathematically.

Clever statistical analyse of "good" melodies perhaps gives interesting results about how melodies follow certain complex rules. Anyway the math starts to be extremely complex. Trying to define complete symphonies with math would be insane. The math needed would be beyond anything mankind can understand I am afraid. However, the smaller blocks in music can be described with at least some kind of statistical logic.

You are acquiring wisdom, grasshopper!  Especially in that last paragraph!

There are complex, near infinite calculations for which one would need a computer with more atoms than the Universe contains: in fact at such a point at least one physicist throws up his hands and names any such computer "God".   QED

[Daidalos]

Thank you for demonstrating the pointlessness of your own post.

Ouch.

[bwv 1080]

As they say in Guadalajara: El grosso profundo!

Is there music in them thar hamhocks, or any kinda 'rithmetic?   

"Hamlet" is no doubt derived from such appendages through a Boolean subset of Poincare derivatives!
Along with the economic theories of Alexander Hamilton!

And I'm betting David Hockney's photographs can be analyzed the same way!

As Schoenberg's rejection of tonality coincided with a rediscovery of his Judiaism, can we say that atonality is a rejection of 400 years of hamhockery in Western music but perhaps a more kosher alternative?

[71 dB]

Thank you for demonstrating the pointlessness of your own post.

You don't understand the point of my posts (lack of scientific insight?) so you think I demonstrate myself wrong. Who would be so stupid?

Math doesn't always mean exact things like 2 + 2 = 4. I may also mean things like:

"When you throw a dice you get number 6 statistically one time out of 6 tries."

"The estimated value for f(7.1) is between 11.2 and 11.7."

[Cato]

As Schoenberg's rejection of tonality coincided with a rediscovery of his Judiaism, can we say that atonality is a rejection of 400 years of hamhockery in Western music but perhaps a more kosher alternative?

Oy!  Your timing is off a wee bit, but who knows?  Schoenberg was something of a farbisener !       

[Steve]

You don't understand the point of my posts (lack of scientific insight?) so you think I demonstrate myself wrong. Who would be so stupid?

Math doesn't always mean exact things like 2 + 2 = 4. I may also mean things like:

"When you throw a dice you get number 6 statistically one time out of 6 tries."

"The estimated value for f(7.1) is between 11.2 and 11.7."

As a Mathematics major here at the University of Chicago, I confess not to be able to follow any of your theories. What are you trying to accomplish exactly? Are you trying to create a mathematical model for ideal musical compositions? If, so, then how are you using statistics? Are you simply studying great works, and modeling their sound with a function? If so, what kind?

[karlhenning]

Gosh, Steve; perhaps I'm not deficient in scientific insight after all!