In my opinion, if beauty can be measured, it is no longer beauty. Beauty is, above all, a mystery that has no answer. Once they asked the famous Russian bard Vladimir Vysotsky "For what qualities do you love your friend Valery Zolotukhin ?". Vysotsky replied: "If to know about what qualities exactly, then this is no longer love, it is just a good relationship". Why does Beethoven's moonlight sonata make such a strong impression? Because it is an ingenious harmony for a simple melody in the spirit of a funeral march. However, this beauty cannot be explained, much less measured. A masterpiece has the property be priceless.

Quite true. There is a danger that rationalization of beauty can lead to its destruction. Explaining a joke just makes it not funny. However, curiosity, desire for knowledge, seems to be stronger.

Regardless if it is possible to quantify something, what comes out will be non-universal; we cannot even ascertain that the same melody will be graded the same the next time we hear it, or sing/play it ourselves. There is no theory to be found here.

If the amount of beauty is proportional to the quantity and variety of identity relations, then the smallest quantity of beauty would be one identity relation.

Beauty arises at the moment when our reason will recognize an identity relation. Sometimes, when hearing a certain melody, reason can recognize more relations and sometimes less from purely subjective factors (attention for example). On the other hand, the "potential for delivering identity relation" certain melody has is constant. That is universal. That's what we are after.

Yes beauty is measured all the time.

I disagree (pleasantly) with Michael Patriksson ours and every society that has ever existed has come up with standards for judging art and music and poetry as better than or worse than... that there is no precise mathematical formulation possible does not mean that there is measure at all.

The real philosophical question is how is it then possible to measure, if there are no agreed upon OBJECTIVE standards?

There have been beauty contests since time immemorial, look at the beauty contest between Aphrodite, Hera, and Athena (Judgement of Paris).

But what is being measured is not an OBJECTIVE standard identical to everyone like meters and kilos, but SUBJECTIVE relationships between the observer and the observed.

So, though we are all genetically similar, and it is likely that sweet foods hold a greater appeal to most than sour foods ... some still prefer the sour.

There is something we share in our psyche that guarantees most will prefer to decorate their tables with roses rather than radishes, but a few, here and there, may choose the radish.

Innumerable studies have shown that pretty people are waited on sooner and more often in restaurants ... almost every female will tell you that brains are more important than looks ... but she'll spend more time in front of the mirror than at the library.

So beauty cannot be precisely measured as a scientific standard, but we all know a pretty face when we see one.

And when we see one, our world seems to be a little brighter.

Well, just because some do, it doesn't turn into a universal rule, and the "almost every female will tell you that brains are more important than looks ... but she'll spend more time in front of the mirror than at the library" is plain awful male chauvinism. Stop it. This thread I will not return to.

Dear Stephen Martin Fritz,

tell me, when you read a famous novel, and then watch a film based on this novel, you always agree with the image of your hero of the novel in your brain before watching the film and then after watching this film. The image of the hero in your brain before viewing is beauty as the “content”, and the image of the hero from the film is the embodiment of beauty in the form of a specific form. And not always your "content" coincides with the specific "form" from the film. Most likely, on the contrary, you feel discomfort from the complete discrepancy between your representation and the one that you saw from the screen. As for beauty in music, painting, architecture and other creative activities, everything here depends on your education and upbringing. Such a funny case is known when in Moscow there was an exhibition of the famous painting by Leonardo da Vinci “Mona Lisa”. One general from the visitors of this exhibition expressed his opinion "This picture did not make any impression on him." The famous comedian Faina Ranevskaya responded to this statement like this: "This lady has impressed so many people for several centuries that now she herself has the right to choose who to impress and who not to".

Dear all, dear mathematicians, besides the philosophical I would like to provoke another direction of the discussion. For that matter, I am reformulating the question in purely mathematical form:

How can we determine the quantity and variety of identity relations in a given melody-like structure?

Dear Nikola Stojkoski ,

Relations, ratios, geometry, and mathematics play an essential role in showing beauty.

Competitions are dominant to show the best designs for machines:

(buildings, cars, clothes, etc.)

One can observe how the GOLDEN RATIO appears in nature, the human body, music, almost everywhere to grant beauty all around.

See

https://www.goldennumber.net › golden-ratio-design-beauty-face-evidence

The Math Behind the Beauty - Interactive Mathematics

https://www.intmath.com › numbers › math-of-beauty

The Golden Ratio in Nature | HowStuffWorks

https://science.howstuffworks.com › ... › Physical Science › Math Concepts

Why Does The Golden Ratio Seem To Be Everywhere In ...

https://www.iflscience.com › plants-and-animals › why-is-the-golden-ratio-

Hundreds of articles are available in this concern.

Best regards

Your question appears to be about aesthetics, i.e. reception. I suggest you reframe it as one about poetics, i.e. making. My suggestion is underpinned by the following sort of reasoning.

I open myself to the sound and sight of a group of free-improvising musicians. I find one session beautiful, another irritating, and another tedious—same people, same evening, same instruments, same ‘chemistry.’ The question is not whether one can find the beauty, the irritant, and the tedium in the music itself. Sure, one can transcribe the music to make the relations between its ‘rational’ components amenable to quantitative analysis. But the codified object of such an analysis is not the realized experience of the music. The beauty, the irritation, the tedium resides in the latter not the former. One will not ‘see’ the forest by looking at trees. Stravinsky’s music for Sacre Printemps has not significantly changed since its premier on 29 May 1913, which resulted in a riot. Today a theatre full of people is more likely to be enraptured than enraged by its performance; personally, I find it largely tedious.

Now ... how can I learn from Sacre Printemps and write something in a similar vein, but hopefully better? That's a different question.

A milli Helen is the amount of beauty needed to launch one ship.

W. J. Whiten haha

Issam Kaddoura GOLDEN RATIO is a relation of identity between the ratio of the whole to the larger part and the ratio of the larger part to the smaller. Its just one type of identity among the many: rhyme is an identity relation between the final sounds of words; rhythm is an identity relation between time intervals; symmetry is an identity relation between two halves; anaphora is an identity relation between the initial words; meter (in literature) is (1) relation of identity between feet according to their structure; and (2) relation of identity between verses according to the number of feet (and syllables at the same time) they have... etc (see footnote 1).

I want to go deeper and determine every identity that a beautiful structure contains. Music, i.e. melody is the best starting point since it is the most abstract of arts – pure form and its elements have just two modes of comparison.

1) What can you say about the secrets of the vibrations 432 and 528 Hz music?

2) It is exciting to study their companion fractals.

3) The golden ratio includes many more applications than you think.

4) One can see the strong relation between music, Fibonacci numbers and Golden ratio. See

(i)Five Classical Pieces with the Golden Ratio - CMUSE

https://www.cmuse.org › CLASSICAL

(ii) https://www.classicfm.com › discover-music › fibonacci-sequence-in-music

(iii) ww.nntdm.net › papers › nntdm-20 › NNTDM-20-1-72-77