The Link Between Music And Mathematics...

GnazzJazz wrote:

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, then where such pleasure, or even displeasure, resides.

This is a common problem EVEN in modern musicology. To think that a technical procedure must massively influence the reception or perception of a composition is, often, false. It is an error of perspective; one thinks that the "formula" of a piece is equal to its realization. Therefore, if a mathematical procedure is found in a compositional technique, then the resulting composition will also be somehow "mathematical" in its sonic result. But it is almost never so! As we said before, mathematics is a means, the sonic effect is the composition. The same means can create very different compositions; Xenakis is different from generative music. It would be dishonest to evaluate such different compositions, such different poetics, by claiming the existence of a mathematical "poetic" principle. There are various poetic principles and aesthetic ideals, and some of them are linked to more or less mathematical procedures.

Mathematics in compositions can be applied at various levels (as already stated); there are pseudo-mathematical compositions that want to result in being somewhat ordered, copying regular distribution models, creating new spatio-temporal relationships similar to logical-mathematical or physical ones. But there are compositions that do not copy mathematics but use it as a compositional technique. And here, only analysis reveals the existence of patterns. Like the famous golden ratio, which seems to be a constant in many artistic works, or contrapuntal numerologies. In the perception of these compositions, mathematics should have no specific role, any more than in the perception of other compositions, in short. That is, you listen to Ockeghem in the same way you listen to Donizetti, despite Ockeghem following mathematical (occult) models.

In essence, one needs to understand where the mathematical means is essential and functional to the compositional result and where it is not.

what do you mean by functional? I suspect this statement hides a judgment of the type "beautiful" or "ugly"...

Actually, I have the impression that you and TheSimon are almost trying to "refute" a thesis. Although I don't understand which thesis 🙂 the most wicked thought with the most wicked word (cit.), on 🙂 what is it that you don't like about modern music?

But no... I don't want to refute anything, also because as I have already said, I am not an expert in modern music; I have listened to some things but I haven't delved into the subject simply because it doesn't interest me. In a word, my argument refers generically to all fields, not just the musical one... I am only asserting that before mathematics, in my opinion, there must be intuition and that mathematics is: a means to explain things or a means to create things once it has been intuited that we can use it. And it's from the first post I sent that I have been trying to say this conviction of mine is an end in itself.

what do you dislike about modern music?

You know, I believe that each of us has our own personality, including musical personality I mean, in which we best locate ourselves and see our reflection. Personally, moving into pop music, to give an example accessible to everyone, I love Lara Fabian very much, while I completely avoid Marilyn Manson. And yet perhaps the latter has more fans than Fabian. Here we are not discussing which of the two is better, but rather the type of emotions that their interpretations convey on a subjective level from person to person. Personally, Fabian gives me emotions that gratify me, relax me, and give me well-being; I cannot say the same for Marilyn Manson who, on the contrary, disturbs and irritates me. I don't want to go into philosophy, but since life is one, at least in the things we can choose to do, I believe it is better to orient ourselves toward the things that do us good rather than toward those that do us harm... In the context of our discussion, I orient myself toward classical period music for this reason. It transmits emotions to me that give me well-being. The microtonality-based prelude gave me a feeling of malaise, I also wrote it in the post (tuning forum -> tuning and microtonality); there will be people who instead will enjoy it... Therefore, I judge nothing and no one, I don't want to refute any thesis, who am I to be able to do so? However, I would appreciate it if my opinion were respected just as I respect yours, without useless polemical phrases aimed at reminding me of the topic subject... (I wrote reading and netiquette myself... 😆 )

thallo wrote:

what do you mean by functional? I suspect this statement hides a judgment of the type "beautiful" or "ugly"...

In reality, I have the impression that you and TheSimon are almost trying to "refute" a thesis. Although I don't understand which thesis 🙂 the least bad thought with the worst word (cit.), on 🙂 what is it that you don't like about modern music?

No, no, I mean: how much the composer is aware of and master of the medium they use, to the extent of having a precise and also verifiable idea of the result they will obtain, and to the extent of being able to say that the end essentially justifies the means, even if not uniquely, at least with a certain significance?

Perhaps I am saying something trivial for a composer and therefore also a bit offensive, but it is always right and useful to investigate, with the aim of understanding and certainly not of destroying.

To avoid any misunderstanding, since I didn't understand the issue regarding the thesis 😳🙂 I will allow myself a personal statement: I have been listening to Berio, Stockhausen, Boulez, Nono etc. since I was 15 years old (this doesn't mean that I have understood them deeply from a technical point of view, which is also true for Beethoven 😃).

GnazzJazz wrote:

I will venture a personal statement: I have been listening to Berio, Stockhausen, Boulez, Nono etc. since I was 15 years old (this does not mean that I have understood them deeply from a technical point of view, which is also true for Beethoven 😃).

I am pointing you to the link to this discussion

http://www.pianoconcerto.it/forum/index.php?/topic/623-karlheinz-stockhausen-kontakte/

TheSimon wrote:

However, I would like my opinion to be respected just as I respect yours, without useless polemical phrases aimed at reminding me of the topic subject... (So reading and netiquette were written by me... 😆 )

As an external reader, I can say that I don't find the invitation to stay within the boundaries of the topic polemical... sometimes there is an unawareness of being OT, I speak for myself, it happens to me sometimes ...

This is my experience.

Lupino wrote:

As an external reader, I can say that I don't find the invitation to stay within the boundaries of the topic controversial... sometimes there is an unawareness of being OT, I speak for myself, it happens to me sometimes ...

This is my experience.

We are getting there now... 😃

Anyway, I hadn't gone off-topic at all, having finalized all my posts regarding the use of mathematics in music... I invite you to reread the conversation.

Lupino wrote:

I am pointing out the link to this discussion

http://www.pianoconc...ausen-kontakte/

Well, I know that analyses and descriptions are not lacking and I haven't just been left "listening" over time; mine is a remark to say that it is not simple to link project and intentions to the result and that, on the other hand, it is not certain that this connection must be transparent to the listener to whom a work is necessarily directed, and indeed it is interesting to understand what the result of the medium used is on the unaware listener.

In short, to interpret the topic, what is the strength of mathematics on the music heard, beyond the composer's purposes, and how much instead are the two things linked and with the awareness of the composer himself?

Well, I note with joy that this discussion has fully ignited! It pleases me to see your participation....

Related to a newspaper article stating: ''The close relationship between music and mathematics has been studied since antiquity: a classic example is given by the Pythagorean School, to which is owed the discovery (the Pythagoreans assigned mystical meanings to it) according to which the different tones of a scale are linked to the ratios between integers: a string halved sounds an octave higher, reduced to its 3/4 a fourth, reduced to its 2/3 a fifth, and so on.'

Much applied mathematics in the musical field actually derives from the study of acoustic physics and the problems related to it. If the same rhythmic division of the musical meter is indicated by a mathematical fraction, today we know that at the base of any noise there is a contribution from countless standing waves, and that any sound can be decomposed into sinusoidal waves through harmonic analysis (mathematically expressed with the Fourier transformalgorithm).

In a more abstract way, music was also related to mathematics in its compositional aspect (which requires distributing sounds among various pitches, at different points in time and between the different voices of the performers). This type of musical analysis has had illustrious proponents throughout the centuries (think of the musical geometries of Bach's canons) and has seen new success even in times close to ours (in the '900 for example, theKranischstein Institute of Rasmstadt, the Electronic Music Studio of the Cologne Radio, the Center for Musical Phonology in Milan and theIRCAM in Parisarose).

Starting from the XVII century many musicians have demonstrated solid mathematical knowledge (for example, Giuseppe Tartini proved it in Treatise on Music according to the True Science of Harmony in 1754 and thus Iannis Xenakis in Formalized Music in 1971; the same Pierre Boulez and Philip Glass are graduates in mathematics and have drawn inspiration from it for their art).''

why instead of raising our voices and playing who is right, don't we collaborate by putting together all our skills to give a complete definition to the subject at hand "music and mathematics"? the more I read, the more I get the impression that we are all saying the same thing..... 😉

suonileganti wrote:

why don't we collaborate by putting all our skills together to give a complete definition to the subject in question "music and mathematics"?

Honestly, this is already the third time I have tried to write a post and halfway through I stop because the subject is too vast, and in my opinion, the complexity and vastness of the topic require a common knowledge base that I think is lacking, which anyway creates difficulty in a broader understanding of a thorny subject.

We have moved from: "mathematics cannot be a construct of a compositional technique, but an element implicitly understood already in all the arts" to "ok, mathematics can be used as a construct ... but to what extent?".

A good step forward, but the 'how' implies that one must work on a certain aesthetic and a certain poetics. The suggestion is to choose an author and a work and try to understand more about it, while premising that from a certain point onwards individualism has prevailed, with its own syntaxes, and it is not at all easy to analyze a masterpiece without indications from the composer.

For example, there is no truly reliable analysis available regarding Berio's sequences, because these were written according to grids that are essentially impossible to find.

Without the code ... only suppositions ... little understanding... but great enjoyment, no one can take that away.

Then in general, one can talk about certain compositional procedures ... but in a broad sense.

I share the idea of playing legato, but as Frank says, the subject is too vast...

Frank wrote:

Honestly, this is already the third time I've tried to write a post and halfway through I stop because the subject is too vast, and in my opinion, the complexity and breadth of the topic require a common base of knowledge that I think is lacking, which anyway creates difficulty in a broader understanding of a thorny theme.

We have moved from: "mathematics cannot be a construct of a compositional technique, but an element implicitly understood already in all arts" to "ok, mathematics can be used as a construct ... but to what extent?".

A good step forward, but the 'how' involves how one is expected to work on a certain aesthetic and a certain poetics. The suggestion is to choose an author and a work and try to understand more about it, while premising that from a certain point onwards individualism has prevailed, with its own syntaxes, and it is not at all easy to analyze a masterpiece without indications from the composer.

For example, there is no truly reliable analysis circulating on Berio's sequences, because these were written according to grids that are essentially impossible to find.

Without the code ... only suppositions ... little understanding... but great enjoyment, no one can take that away.

Then in general, one can talk about certain compositional procedures ... but in a broad sense.

One of my professors used to claim that we will only truly start to know something about Berio after the death of Talia Pecker Berio. According to her, there are many private papers that the widow does not make available to scholars (even though she herself is a musicologist...).

Regarding the discussion, since it was started by Giusantsot for a specific need (a discussion with his mathematics professor, if I remember correctly), it would be interesting to follow his leads. I mean: do you have particular needs? Do you need to do research, prepare for an exam perhaps, or is it just your own curiosity?

... I'll also add one thing ... so far we have focused essentially on:

1) acoustic physics

2) general musical aesthetics

3) a little something about general harmony and counterpoint

4) individual poetics of individual composers...

5) organology

but there are also other fields; the first, which I culpably forgot to mention, is analysis! There are analysis techniques that use mathematical concepts and methods quite heavily. One for all: set theory. But also statistical analyses, which are widely used in ancient music and ethnomusicology.

Who knows if we can find even more fields...

thallo wrote:

set theory

A good foray had been made into this, but it could be discussed again in a more structured way.

thallo wrote:

But also statistical analyses, which are widely used in early music and ethnomusicology.

I don't know the first thing about these, other than having read about a procedure in composition, perhaps analogous, to derive the weighted scale.

I have just proposed this topic

http://www.pianoconcerto.it/forum/index.php?/topic/698-analisi-lied-di-luciano-berio/

I think it could be interesting, anyway I find that document very useful.

thallo wrote:

One of my professors maintained that we will only truly begin to know something about Berio upon the death of Talia Pecker Berio. According to her, there are many private papers that the widow does not make available to scholars (even though she herself is a musicologist...).

Exactly! And being aware ... she could sell them.

Just for ... she thinks that instead, the widow Bettinelli is much more available

Hi guys!! I'm sorry that I'm not participating in the discussion, but I'm a bit busy.

I'm posting something I found a while ago and that I want to read carefully.

See if it piques your curiosity... ciaooo

http://digilander.libero.it/initlabor/musica-simmetria/*index-vitali.html#Anchor-35326

thallo wrote:

I wonder if we can still find other fields...

... videos, images and graphic representations (in motion) for support?

I don't understand what you mean, Ludovica

thallo wrote:

I don't understand what you mean, Ludovica

I meant that often music that is born, in a "pure" way, from mathematical rules or that wants to represent geometries, is accompanied by videos that are somewhat its three-dimensional result... of geometric figures or "senseless" shapes or anyway that have equations or things like that behind them.