The Link Between Music And Mathematics...

suonileganti wrote:

it is obvious that music and mathematics are related if we consider that the former lives in time and space, all forms of art "use" mathematics (painting, sculpture, architecture etc ....) but there is something else in music that does not belong to the world of mathematics, namely being art, a form of human expression in the context of its era; music follows instinct, emotions, fashion, social contrasts, man's needs in repeating it infinitely as if it were the first time, it influences mood and thought (it is skillfully used, for example, in commercials to persuade people to buy)

Oooooo Well said...

I know it's hard to accept, but to produce Xenakis' piece, Metastasis ("sonic magma"), in the technical language called "continuo" (...there are some by Maderna, etc. ... I think I even heard one by Frank 😉) ... there are crude mathematical formulas, exactly those studied by TheSimon in his 4 exams and applied pedantically to make music.

I don't know what to say, I'm not the one saying it, just read the tons of books, some written by Xenakis himself and already suggested at the top of the topic, I don't remember by whom 😉

But excuse me, if music is made with mathematics (and by made I mean composed using mathematical formulas), sculptures are made of mathematics, frescoes are made of mathematics... What becomes of that thing called art??

Perhaps some information is missing, namely what structuralism is 😉 ... but not only that.

At a certain point, in the second post-war period, dynamics entered that were very different from those to which some are appealing. Art is at the service of aesthetics, and there is an aesthetics where not speaking a language that led to extermination camps holds true; for example, a pre-verbal language holds true, see the unconscious one of the infant or aphasia.

You are really missing a large chunk of repertoire, eh! and therefore of aesthetics, which is why certain reasoning seems distant to you.

This does not mean that we must necessarily like it, but the topic title states clearly... there is an aesthetics where the link between music and mathematics is one and the same. In fact, I would venture to say that only mathematics holds true.

Is there something in art that does not go hand in hand with aesthetics?

And then it is not certain that you won't like it; I have read enthusiastic comments on Xenakis' music, made at unexpected times 😉

TheSimon wrote:

But excuse me, if music is made with mathematics (and by 'made' I mean composed using mathematical formulas), sculptures are made of mathematics, frescoes are made of mathematics... What becomes of that thing called art??

Which music?

I mean, what about algorithmic composition and fractals? And I assure you it is evocative and contemporary music... if we want to pretend that half a century hasn't passed, okay... but it's still just pretending. Time passes, needs change, aesthetics change... and those who study composition in higher education pass through, by necessity and by luck, even this music.

It weighs heavily; all of this led, for example, Stockhausen to write the Klavierstücke, does anyone know them, guys? What music, what way of treating the instrument... let's try to update ourselves a bit, eh!

But that is taste... I much more appreciate compositions from the classical period. It's not about staying up to date; I stay up to date if something stimulates my interest, if I'm not interested in something at all, I can listen to it for knowledge, but not cultivate it. It seems clear to me, no? Then we could also think about pulling data and making stochastic music, which is a beautiful mathematical concept, but personally, I don't like it. We could think about using existing algorithms or being inspired by the laws of nature. Personally, I don't like this type of music schematized by mathematical processes and I prefer the classical one. I will miss a large slice of the repertoire, as you say, but perhaps it is I who want to miss this repertoire. After all, one must live with the spirit of exploiting what makes them feel good. I listened to the preludes posted in another forum about microtonality. They are interesting to listen to, but I believe I will never listen to them again because they don't give me a sense of well-being (and perhaps they were written with this purpose). So what do we do? Do we have to endure everything and deepen everything just to say loudly: "I KNOW THE REPERTOIRE!". And what have we solved? I also listen to other things, but fortunately, I have the freedom to choose which path to follow. Whether it's right or wrong. I have listened to Stockhausen several times. If one evening I had to choose between going to a concert where Beethoven pieces are played or another concert where Stockhausen pieces are played, I wouldn't hesitate for a second to choose Beethoven. It is just a matter of personal taste. Nothing to say to those who would have chosen Stockhausen; everyone does what they want.

..pity that the subject is not what we like, but the link between music and mathematics 😉

That's all.

Dino wrote:

..too bad the subject isn't what we like, but the link between music and mathematics 😉

That's all.

No comment... I give up! You're right, so far I've been talking about butterflies...

I know it's hard to accept but in producing Xenakis' piece, Metastasis ("sonic magma"), in technical language called "continuo" (...there are some by Maderna, etc. ... imagine I've even heard one by Frank 😉) ... there are raw mathematical formulas, exactly those studied by TheSimon in his 4 exams and applied pedantically to make music.

@Xenakis

Could you illustrate which formulas are used, and in what context in music? Out of curiosity...

I believe that simply setting fascinating mathematical patterns or processes to music is not enough to make good and modern music. Behind the compositional process, there must be something robust; in short, the end goal or at least the project must justify the means. Experimentation and listening are all well and good, but that is not what we are talking about here. I had the pleasure of collaborating with a composer to create non-linear controls on electronic materials, i.e., products made with mathematical algorithms. Well, there were strong ideas behind it and there was also an intense experimental phase. But it is all this that brings us back to artistic expression. Years of experience with electronic music allow the composer-musician to master the electronic-mathematical medium, which thus rises from a mere toy to a powerful instrument that could not exist before.

But even here, mathematics, while certainly essential, is hidden from the listener, who can enjoy and judge the music without thinking about it. On the other hand, when listening to a Beethoven symphony, one does not need to understand its structure to remain fascinated by it...

Hi

From Wiki regarding Xenakis:

Stochastic music [edit]

In 1956, Xenakis published a theory of stochastic music, which relies, among other things, on John von Neumann's Game Theory. In this context, chance becomes much more than mere "randomness"; contrary to what happens with Boulez (Third Sonata for Piano, or in other contemporary "open" works), or with John Cage and his "renunciations," for Xenakis probability is entirely calculated, and the rules are made explicit (see Achorripsis or ST/10-1 in 1961). The global process is entirely predictable, even if the events that compose it are aleatory. With this compositional philosophy, Xenakis seeks to approach biological phenomena and the natural events of the living world.

His first electronic pieces based on stochastic structures appeared in 1957 with the composition Diamorphoses. For the first time, his theories benefited from technological support thanks to an IBM computer. It was also his first piece written by Xenakis at the G.R.M. (Groupe de recherches musicales), a research and production center for electroacoustic music founded in Paris by Pierre Schaeffer.

I like heated discussions because you learn a lot of things; I wanted to better understand the discussion about extermination camps.

Allow me to provide a summary: mathematics is an indispensable element of music, both because its laws govern organology and compositional languages, and because a mathematical principle can be taken as a starting point for making a composition (e.g., a slice of the repertoire is built this way... structuralism).

If we are here talking about it, history has probably already decided that sometimes mathematics can be enough to satisfy a certain aesthetic need.

TheSimon wrote:

No comment... I give up! You're right, so far I've been talking about butterflies...

But The Simon, this is what you wrote a moment before Dino told you "the subject is not what we like, but the link between music and mathematics"

TheSimon wrote:

Personally, I do not like this type of music schematized by mathematical processes and I prefer classical.

No one is forbidding you from preferring classical, but this music exists... it is a fact.

TheSimon wrote:

@Xenakis

Could you illustrate to me which formulas are used, and in what context in music? Out of curiosity...

Look, there are a lot of large volumes on the subject that I wouldn't want to trivialize with my useless synthesis. I can tell you that writing a functioning continuo assumes that you heavily use mathematical formulas. Everyone has their own, and in fact Ligeti is recognizable from Xenakis..., when I say heavily I mean that in some cases the code is law; in others, see Berio, the artist reserves the right to make choices anyway, but at the base of the compositional procedure there is mathematical reasoning, number grids, etc.

I would only like to add that reality is not always and only beautiful; music must describe everything... then we may or may not like it. With this I close, since everyone sticks to their own idea... even if objectively this music and these procedures exist and all you have to do is a crude little search via any search engine.

Try with the following search terms: "algorithmic music", "fractal music"...

Marzapane wrote:

I wanted to better understand the discussion about extermination camps.

Get informed on "degree zero"

GnazzJazz wrote:

I believe that simply setting fascinating mathematical patterns or processes to music is not enough to make good and modern music. Behind the compositional process, there must be something robust; in short, the end goal or at least the project must justify the means. Any experimentation and any listening is fine, but that's not what we are talking about. I had the pleasure of collaborating with a composer to create non-linear controls on electronic materials, i.e., products made with mathematical algorithms. Well, there were strong ideas behind it and there was also an intense experimental phase. But it is all this that brings us back to artistic expression. Years of experience with electronic music allow the musician composer to master the electronic-mathematical medium.

Exactly, what was once the harmonic medium, in fact by changing the names:

"Years of experience with CLASSICAL music allow the musician composer to master the HARMONIC medium""

Xenakis wrote:

No one forbids you from preferring the classical one, but this music exists... it is a fact.

But in fact I have never doubted it, also because it is not an area of the repertoire where I am an expert, so I leave the floor to others more experienced than me who have referred to this period. My reasoning so far has referred to music of the classical period, in which I have not denied the link between music and mathematics but I have emphasized that perhaps in that case what prevails is taste with all its mathematical corollaries, but still taste.

Answers like

..too bad the subject is not what we like, but the link between music and mathematics 😉

Try with the following search terms: “algorithmic music”, “fractal music“…

Great, I will take a look...

From Wiki regarding Xenakis:

Stochastic music

Imagine that when I mentioned it, I didn't even know it actually existed !! 😆

See how many things are learned by rolling the dice?

To me, this "war" between art and mathematics seems useless...

And, can I be sincere and biting? In a discussion about butter, it makes no sense to say every two seconds "but olive oil also exists!".

Ok, fine, I think we ALL know that music is art, birds chirping and hearts breaking. But if the discussion is "Music and Mathematics," it seems OBVIOUS to me that we are talking about Music and Mathematics 🙄

And, I repeat, WE are not inventing this topic; it is THE HISTORY OF MUSIC that speaks of these things.

Xenakis wrote:

"Years of experience with CLASSICAL music allow the musician composer to master the HARMONIC medium""

exactly, naturally the parallel was as much implied as it was crucial...

thallo wrote:

But if the discussion is "Music and Mathematics," it seems OBVIOUS to me that we are talking about Music and Mathematics 🙄

And, I repeat, it is not US who are inventing this topic; it is THE HISTORY OF MUSIC that speaks of these things.

Well, then, if we want to debate the subject because it fascinates us and does not seem trivial (despite the evidence of its existence, precisely), each of us should focus on the points that stimulate our own interest.

For me, narrowing the theme to the massive use of mathematics in "modern" compositions, it is interesting to try to understand if and why mathematical algorithms can generate pleasure in the final result, thus where such pleasure, or even displeasure, resides. In essence, one needs to understand where the mathematical medium is essential and functional to the compositional result and where it is not. Keeping in mind, however, that such a medium does not come out of nowhere, but is often borrowed from other fields no less rich in charm than music.

Certainly, rambling aside, one can begin to think that the mathematics we have discovered—if not invented—by investigating and trying to understand nature, to which we belong, is therefore a bit of ourselves; we are entangled in it. But then it is interesting to get into the specifics of the pieces we listen to, which is decidedly less trivial...

Question, how does one measure enjoyment or dislike?

There are people who do not like Chopin, so it is possible that some might not like Nono.

All this to say that perhaps one should focus on the less subjective aspect, whereby the validity of a composition .. a parameter could be coherence, but even here... if a piece is a milestone in music history, it is not decided by me or Tiger; we can only acknowledge that it is music that exists and force ourselves to understand it or understand the motivations behind those specific choices. Someone was talking about aesthetics... I think that fits perfectly.

Xenakis wrote:

Research the "degree zero"

I took a look around the WEB, perhaps a precise explanation is necessary.