Is Music Maths?

[peter]

This is an expression I've come across recently (and I think in the past) and I believe was even iterated by Pythagoras or somebody else of note in the heyday of Ancient Greek thought - that music and math are one and the same thing.

No doubt this idea was what lay behind the book Godel Escher Bach, but I tried to read it and was lost by the end of page two iirc, so I'll trouble you guys to try to bring it down to a human level for me.

What I'm specifically interested in is the following question. If music is indeed math, this would mean that all of the best classical compositions could be reduced to patterns of numbers, the magic of music, of harmony, tone, rythm etc could be reduced to mathematical movement, to equations and the like. The properties of these manipulations could be studied, analysed and ultimately reproduced by computers to knock out Das Rings der le Nibelungens one after the other. By reducing what constitutes the great art of composition down to a core body of rules (and it would have to be thus reducible wouldn't it), these rules could be followed by computers, given a body of notes to begin with, to produce in seconds the equivalent of what it took Wagner a lifetime to compose?

[samrw3]

I have heard something similar. But what makes music more exhilarating is the passion and emotions that it inspires. Rote computer modeling could possibly create lines of music that touch on emotion. However, how would they do that?

In my way of thinking they could only do it by
1. Pure randomness - enough random sequencing eventually you could create something that stirs emotions
2. Scientific studies - have humans in a room have them answer does this stir your emotions - thus the computer "learns" what musical notes have the best effect on human emotion.

However the advantage human composers have is they already come from a place of emotion and so when they create and play musical compositions other humans can "sense" the emotion the emotion that went behind that musical piece.

Music is more complex then math because you can "embellish" it with speed and dramatic effects - look at how Elton John plays the piano for example - he typically plays it with "flourishes". When we see or hear that the musician is placing emotion behind the performance it builds up increased effect on our emotional connection. I doubt that computer modeling could build that much complexity. Especially considering the breadth of different musical structures across the world. What may be pleasing to human in US may be noise to someone in remote country and vice versa.

[Orlion]

Pythagoras and his followers were those kind of douchebags that really liked something and decided that everything worthy must also be related to and subservient to it.

"Math is the greatest thing ever! Hey, that thing you like? Did you know it's actually Math? Have you heard the good news about Math?"

It's like saying poetry is music or the brain is a computer or a body is a machine. It takes some characteristics of a thing, inflates them and ignores anything else about the object in question.

[wayfriend]

There are components of music that can be expressed numerically.

There are aspects of musical scales that can be expressed as mathematical relationships.

But this doesn't make music "is" math, any more than they make planets and atoms and rockets "is" math.

[Hashi Lebwohl]

Godel Escher Bach

To date, that book still ranks as the most difficult to digest. It should be on everyone's bookshelves and everyone should at least attempt to read it, even if they get lost.

The Pythagoreans were just a group of math nerds who formed a secret society--either you were one of them and you got initiated or you were not. They thought they were hot shit on a stick...but they did not know that the Babylonians had already discovered a rudimentary form of what we know as "the Pythagorean theorem" long before Pythagoras came into existence.

[Zarathustra]

I think people originally linked music and math because they discovered surprising correspondence between things like the length of a string and the notes it would produce. There is a mathematical relationship between notes and waves, but this does not mean that music is math. Some interesting things can be done by mixing time signatures, and there is a little bit of math involved in making them sync up. But rhythm is only one aspect of music. I think that chord progression and note intervals are much more important in defining the mood of a song. And for this all you need is music theory, not math.

[Vraith]

Agree that GEB is a great damn book. BUT it surely goes too far often...lots of things do, though [like the whole "unreasonable effectiveness of math" thing, and "most of western philosophy is footnotes to Plato bullshit.]

On topic: no, music isn't freaking math.
They do seem to share some terrain,,,but I think a lot of that is rooted in how brains work and how physical reality works. It's not just music...why don't people talk about how painting, and architecture/sculpture and linguistic arts [poetry in particular but not even close to uniquely].

But math is in no way the cause, the rule, the structure, the meaning of any of it. Math is just another of the things that shares a relationship---but is not a source/root/cause of---the world.

Math has a great utility because it can be stripped of most context, most meaning, into pure process, definition, and information.

I'm sure someone will mention---if no one was starting to think it, they should have been---AI created arts, the growing successes of it, and AI is [currently] all math.
Such people should keep in mind that it takes many people creating many algorithmic approaches and rebuilds---and then the AI's have had millions [at least, more likely many billions] of failures, and never yet equaled what even one person...say Beethoven...did in one work.
I can't emphasize the difference enough. The machine that won at GO required the input of dozens of people, and had to practice the equivalent a human playing the game non-stop for 20 THOUSAND YEARS. Just during the actual games played [not the training part which was even greater] It burned the energy of several thousand human brains all playing at the same time...AND IT STILL COULD ONLY PLAY GO. [the brain of the human opponent was LITERALLY doing hundreds of other tasks...or more...at the same time it was playing.

Z, I'm slightly surprised...I expected you'd be SLIGHTLY more on the math side [though not mostly on that side].
On music theory...that depends on the genre and purpose. And doesn't suffice alone...it might be a little like D's "theory laden" which I also have a quibble about.

Oh, but back directly on topic:
In all the fields...and not entirely excluding math...the REAL genius/art...AND the real aesthetic attraction...is nearly always due to the precise points where a thing BREAKS the frame/rules. The difference/dissonance NOT the similarity/consonance/assonance/form obedience.
Though raw violence/breaking/randomness won't do at all, usually.

[peter]

Interesting answers guys! I'm going a step further than V and saying I'm a little surprised that you aren't *all* a bit more on the side of math - and not displeased thereby!

I suppose when you come to think of it, if it were true, that music and math were one and the same, by now we would have whole university departments of Musical Mathematics and the like - but however, if what I understand of 'deep learning' and the potential developments of AI that we are on the cusp of making, I'm also a bit surprised that none of you seem to place the 'art of music' as being anywhere near being created artificially as yet (by that I mean that nebulous thing that stirs our emotions, that *is* music, at the end of the day, rather than simply a combination of notes).

I read that by monitoring out neurological responses to a limited number of tracks from our playlists, such tech will shortly be able to create specifically tailored songs for each and every one of us that will hit the spot every time a coconut. Surely if tech is already at this point, it isn't far from nailing down in similar fashion the laws that underwrite what we consider as 'great art' (which I imagine differs only in degree from the lesser 'art' of a good popular song that we like?

And what of chess? We now have a situation where deep learning (ie self taught) programs have recently beaten for the first time programs of the 'deep thought' type that beat Kasparov (or whoever) all those years ago. This program taught itself from the basic rules of chess in minutes, what 'deep thought' had had programmed into it in the form of a bank of tens of thousands of previously played games at grand master level to fall back on - and then beat it in straight sets. If there is art in the game of chess - and I think it would be hard to deny it surely- then such programs have mined it. And if it can be done here then surely the same feat will be achieved by music generating algorithms in due course. One of the most insane things about this whole area of deep-learning programming as I understand it, is that it is already at a point where, mirroring the layer upon layer nature of the human brain neurology, the programmers can see that the programs can successfully solve problems, say of a mathematical kind, set for them - but the can't see how they (the programs) have done it!

Spooky or what

[Vraith]

Spooky or what

It is spooky. But the thing is that all the AI is doing a fundamentally different thing than living brains are.
It's not a composer, it's an analyser and simulator.

And way less spooky than robot mates.

The music BUSINESS is both interested in and terrified of AI creation. If they can control it, they can make money off music and never pay another cranky pain in the ass "musician" another dime. If they CAN't own/run it, the entire business dies. Good fucking riddance.
Musicians, OTOH---at least all the interesting, real ones---are interested in AI as a tool to enhance their creations/creativity. [[same for author-AI and painter AI, etc.]]

Which brings back my hobby-horse. We could really fuck this up, and replace humans. Ruin us. And the current structure of power makes this a real risk.
BUT, we could do it right...merge/meld, enhance. Instead of making everyone [or nearly everyone] basically useless or happy little pets sleeping, eating, and fucking in our simu-stimulated false-lives, we COULD wire up, fire up, and make everyone and every thing they do valuable, rising, transcending. Every life could be meaningful...and not in the generic pseudo-spiritual sense of "All lives matter," but in a fully-participatory, actively meaning/value creating way.

What often bugs me is the very large segment of this arena involved in making machines do what humans can do perfectly well, thank you. [[and often more easily]]. Why work so hard to do that???
The smaller segment, but more important, is working on making machines do what we NEED done but CAN't do ourselves.

[Cord Hurn]

Many things use math that are not math. Music is not just math, therefore it is not math.

[Avatar]

In before Fist.

The Glass Bead Game



--A

[FindailsCrispyPancakes]

Nature is quantised.

So yes, it's all maths - music included.

[Lazy Luke]

Peter, your question is actually rather [silly]. You only need to produce some music to know the answer. And you wouldn't have to compose a lifetimes work like Wagner, a simple jingle or a momentary strain would do it.
The composer doesn't use maths to make music. Neither does the listener use maths to hear it. Only the mathematician uses maths in order to understand it.
Fortunately for me, I enjoy making music on my computer, which happens to be built by mathmaticians.

[Vraith]

Peter, your question is actually rather dumb.

You only need to produce some music to know the answer.

No, it isn't dumb.
And that following sentence [and most of the rest] is non sequitur, not evidence.
Don't call questions dumb here...unless they're actually dumb like "do co2 emissions cause warming" or "do vaccines cause autism."

Cuz I WILL delete shit.

You can call things silly, though. Like if someone says

Nature is quantised.

So yes, it's all maths - music included.

Even IF nature is quantized...which is on pretty solid ground at least for now...that does not, in any way, necessitate, demonstrate, or even weak things like imply, or hint, or suggest any identity or causality between things and mathematics.
Not even close.
It only shows [if true] that mathematics is a useful [and more or less accurate] descriptive tool for events/relations.

[Skyweir]

Intriguing discussion that raises questions.

There are allegedly no dumb questions .. and as a self proclaimed dummy myself I would think twice about engaging my dumb ass in almost all the forums here if I feared to engage.

Funny thing .. when recruiting intelligence officers we preferenced music degrees. Because they are astute at pattern recognition and identification. In general such skills enabled them to see connections where a humanities grad etc May not.

I always found that a rather intriguing selection factor.

I too am surprised like Pete ... I expected a very different set of responses and input.

Cheers dudelies a very satisfying read

[FindailsCrispyPancakes]

Even IF nature is quantized...which is on pretty solid ground at least for now...that does not, in any way, necessitate, demonstrate, or even weak things like imply, or hint, or suggest any identity or causality between things and mathematics.
Not even close.
It only shows [if true] that mathematics is a useful [and more or less accurate] descriptive tool for events/relations.[/color]

Well, this is pretty a deep subject for my first posts here. Very odd to think it all started as a casual comment on the nature of music. Anyway...

There is no 'IF' about it.

At the most fundamental level nature is quantized into single quanta, hence the statement 'nature is quantized'. Energy itself is quantized and only occurs in integer multiples of Planck's Constant.

There is a direct relationship between integer numbers and the quantization of nature (i.e. all 'things' larger than elementary particles being comprised of multiple quanta).

The uncertainty principle acting as a restriction on the accuracy of measurements does not falsify the statement 'nature is quantized' in any way.

Such a statement does not refer to a hint, indication, suggestion or anything else you would consider 'weak'. It demonstrates a one to one mapping between the countably infinite set of natural numbers and nature itself.

In other words, it demonstrates an existential link between nature and mathematics.

[FindailsCrispyPancakes]

You can call things silly, though. Like if someone says

Nature is quantised.

So yes, it's all maths - music included.

In order to partially falsify the statement 'nature is quantized' you will need to:

A) Develop a quantum theory of gravity that somehow does not invoke quantum mechanics in any way.

This will be your first step towards fully falsifying both the statement and all non-gravitational quantum mechanics by:

B) Proving particles do not exist

or,

C) Providing a description of a system in which energy is not quantized.

This will inevitably involve

D) Inventing a system of mathematics that contains no reference to quantities/values and consists only of operators.


'Silly' anthropic arguments will NOT suffice.

Good luck.

[Skyweir]

Gotta say again Im loving your input Findail .. very interesting indeed.

Again a brilliantly described explanation of your point.

[wayfriend]

The problem with Models is that they are a one way relationship ... the thing being modeled doesn't give a ***k about what the Model is.

You can model music with math, but music is not affected. It has no requirement to be mathematical. It just is.

Saying it another way ... music happens to be mathematical, but if it wasn't ... it would still be music.

Music is mathematical is a contingent truth, not a necessary truth.

[FindailsCrispyPancakes]

This is fantastic. Page 1 of a thread discussing of the mathematical properties of music and we're already delving into objective reality and the nature of truth.

I certainly never expected this when I first read Lord Foul's Bane.

I like this place.