[Ryokan]

Doesn't math go 'out of the window' when first generation stars implode/explode and the colossal pressures and heat produce the building blocks for life, or maybe even all this can be reduced to an equation?

 

[gregorio]

It also means they think like mathematicians.

It’s not really math but it is a very mathematical style.

Yes, I know it seems like I’m contradicting myself and am now agreeing with you. I’m not, you’re assertion is still wrong

It’s just my ability to explain it that’s at fault, which is not surprising, it’s very difficult to explain and has been a point of discussion for a century or more.

Thinking like a mathematician implies (to me at least) a purely rational, objective mental discipline that eschews any subjectivity. We have an equation which has one right answer and anything else is wrong, personal preference or opinion doesn’t come into it.

The theory of harmony is a complex system not unlike mathematics in many ways and thinking about it is quite mathematical in style but there’s one fundamental and massive difference: There is no right or wrong, there’s appropriate and inappropriate (and many degrees in between) and what defines appropriate or inappropriate is personal taste/preference and whether it elicits the desired response in those listening to it. In this sense it’s the exact opposite of mathematical thinking, it’s purely subjective.

In math, 1+1=2, it’s always equaled 2, it will always equal 2.
In music harmony 1+1=2 in the baroque period. In the romantic period 1+1 could equal 2 or sometimes 3 or 1. In the impressionist period it could equal 1, 3 or 19, -7 or almost any number. In the C20th: It could equal 0, no number at all, a blue elephant with 7 legs and a beak, or 2, -7 and a blue elephant all at the same time, in fact 1+1 isn’t even necessarily a valid question, let alone there being a right or wrong answer to it!

G

 

[bigshot]

Doesn't math go 'out of the window' when first generation stars implode/explode

I would think just about everything would go out the window if that happens.

In the impressionist era

.#..............#...............#.....#....
.#..............#............#..........#..
.#......+......#......=............#......
.#..............#................#...........
.#..............#............#.....#.....#.

In the romantic era, 1+1=

With 4'33" 1+1=
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[gregorio]

I would think just about everything would go out the window if that happens.

I would think just about everything including the window would vaporise. A possible exception might be; an audiophile would carry on sitting in their chair, basking in the dynamic range!

G

 

[Ryokan]

In math, 1+1=2, it’s always equaled 2, it will always equal 2.
In music harmony 1+1=2 in the baroque period. In the romantic period 1+1 could equal 2 or sometimes 3 or 1. In the impressionist period it could equal 1, 3 or 19, -7 or almost any number. In the C20th: It could equal 0, no number at all, a blue elephant with 7 legs and a beak, or 2, -7 and a blue elephant all at the same time, in fact 1+1 isn’t even necessarily a valid question, let alone there being a right or wrong answer to it!

Doesn't that just show the values aren't traditional ones but there is still a mathematical structure/formula.

 

[Ryokan]

I would think just about everything would go out the window if that happens.

In the impressionist era

.#..............#...............#.....#....
.#..............#............#..........#..
.#......+......#......=............#......
.#..............#................#...........
.#..............#............#.....#.....#.

In the romantic era, 1+1=


With 4'33" 1+1=
.
.
.
.
.
.
.
.

'Recent advancements in mathematical modeling, numerical methods, and supercomputing allow us to gain new insight on complex phenomena such as Type Ia supernovae'.

https://cs.lbl.gov/assets/CSSSP-Slides/20160623-Nonaka.pdf

 

[gregorio]

Doesn't that just show the values aren't traditional ones but there is still a mathematical structure/formula.

If 1+1 can equal anything at all, including nothing and anything that isn’t a number, and if we don’t accept that 1+1 is even a valid question to start with, what “mathematical structure/formula” do you think we have left?

G

 

[Ryokan]

If 1+1 can equal anything at all, including nothing and anything that isn’t a number, and if we don’t accept that 1+1 is even a valid question to start with, what “mathematical structure/formula” do you think we have left?

G

If there's no structure how can someone create music in baroque period or romantic period style?

 

[bigshot]

The fundamentals are the fundamentals, regardless of style. The difference between styles is in how the fundamental rules are applied. The value of art is in how creative and expressive the differences are. That's true of all art forms.

 

[gregorio]

If there's no structure how can someone create music in baroque period or romantic period style?

And to turn that around; if there is a fixed structure/formula, how can someone create music in a free-form style?

Fundamentally, mathematics doesn’t really change, it certainly expands and we might find new ways of doing/calculating things but all the old proven mathematics doesn’t suddenly become wrong/invalid. Regardless of the huge mathematical advances of the last couple of millennia, 1+1 still always equals 2.

This is not the case with harmony, the rules do change, what was appropriate becomes inappropriate. So, we can go back and apply the rules as they were 300 years ago and write a piece of Baroque style music. We can apply the rules as they were in the 1960’s and write a piece of “free form” or we can choose any combination of rules from any period and combine them.

G

 

[Ryokan]

And to turn that around; if there is a fixed structure/formula, how can someone create music in a free-form style?

Rules/formula for Baroque, Romantic and free form style. Each obeys (or incorporates) a different set of parameters.

So, we can go back and apply the rules as they were 300 years ago and write a piece of Baroque style music. We can apply the rules as they were in the 1960’s and write a piece of “free form”

There you go you can apply the formula as it was laid down to create that style.

 

[gregorio]

Rules/formula for Baroque, Romantic and free form style. Each obeys (or incorporates) a different set of parameters.

If the rule is: There are no parameters. Then how can it obey a set of parameters?

There you go you can apply the formula as it was laid down to create that style.

Sure, or of course not apply the formula and create something in a different style. I don’t see how not applying a formula or subjectively choosing and combining different conventions is “mathematical thinking”?

G

 

[bigshot]

All art follows basic fundamental rules of organization. The most basic of these are hard wired into humans as pattern recognition / expectation of how repeating patterns will repeat. Other fundamentals are more complex and are transparent to the lay person, but not to other artists. It's the job of the artist to apply the rules by picking and choosing the ones to focus on, and by bending them to his will to create something unique and expressive. An artist can't bend rules until he can follow them.

No art is completely without structure. Structureless art isn't art... it's noise... audible noise, visual noise, volumetric noise. An artist communicates, and you can't communicate without some sort of language made up of fundamental rules. Mondrian followed rules just as much as Michelangelo did. If you don't see structure in art, either it's crappy art, or you are unable to discern it yourself.

I could talk on this subject for hours. It's one of the things I discuss with students in my educational non-profit.

 

[gregorio]

No art is completely without structure. Structureless art isn't art... it's noise... audible noise, visual noise, volumetric noise.

That again all depends on what you mean by “structure”. If you mean “structures”/structural elements then your assertion could be true or at least I can’t think of any music off the top of my head that doesn’t employ any structural elements at all. If you mean as you actually stated “structure”, IE. The structure of the piece (the “Form”), then your assertion is clearly false.

An artist communicates, and you can't communicate without some sort of language made up of fundamental rules.

That all depends on what the composer wants to communicate and how they want to communicate it. Maybe a composer wants to communicate the concept of a lack of communication, maybe the composer doesn’t want to communicate a specific thing, maybe it’s the act of trying to figure out a meaning the composer is trying to communicate/elicit (and whatever meaning an individual listener comes up with is fine or irrelevant). In these and other similar cases, there doesn’t necessarily have to be “some sort of language made up of fundamental rules” or a least a language with fundamental rules the listener understands.

If you don't see structure in art, either it's crappy art, or you are unable to discern it yourself.

Again, if you mean “If you don’t see any structures” then you might have a point, although you’re eliminating the possibility that a composer might want the listener to be unable to discern any structures (that they’re indiscernible). In which case it’s not a crappy piece, it’s the opposite, it would be a good piece because it has elicited from the listener exactly what the composer was trying to elicit.

If you mean as you stated though; “structure” (Form), that is clearly an incorrect assertion. The idea of not following a strict or fixed Form (and therefore a Form/structure that is not necessarily discernible) dates back 500 years or so and is not uncommon. The idea that fundamentally music should not follow a traditional or fixed Form dates back at least to Debussy, and the concept of “without Form” (free of Form) encompasses various post WWII classical music genres and genres outside classical music, “Free-Form Jazz” for example.

G

 

[Vamp898]

All art follows basic fundamental rules of organization. The most basic of these are hard wired into humans as pattern recognition / expectation of how repeating patterns will repeat. Other fundamentals are more complex and are transparent to the lay person, but not to other artists. It's the job of the artist to apply the rules by picking and choosing the ones to focus on, and by bending them to his will to create something unique and expressive. An artist can't bend rules until he can follow them.

No art is completely without structure. Structureless art isn't art... it's noise... audible noise, visual noise, volumetric noise. An artist communicates, and you can't communicate without some sort of language made up of fundamental rules. Mondrian followed rules just as much as Michelangelo did. If you don't see structure in art, either it's crappy art, or you are unable to discern it yourself.

I could talk on this subject for hours. It's one of the things I discuss with students in my educational non-profit.

You must be from the U.S. I might be wrong but this is the most american way of thinking i ever read on the internet

"In America, its like that, so it must be an universal law"

Every culture has a different definition on what ""Art"" is. In a lot of languages, there doesn't even exist a proper translation of what is called Art in the american/britisch language.

Take german for example. There is the word "Kunst" but the meaning is quite different to "Art". There is no translation for the word "Art" in the german language that carries the same meaning. And the same is true for Japanese, Korean, Chinese and so on.

What Art is and what Art isn't is only true for the culture that uses that word.