What makes things aesthetically pleasing

What are some arguments in favor of the golden ratio that makes things more aesthetic?

Most often, artists do not give any arguments in favor of using the golden ratio, they are sufficiently motivated by the long tradition of highlighting it as "golden" that has accumulated since the Pythagoreans and the ancient Greek sculptor / architect Phidias. The perceived presence of golden sections in his Parthenon now seems to be wrong, but the letter φ, which is often used to denote him, comes from the first letter of his name. Plato also "helped" by promoting the dodecahedron to whom the god has embroidered the constellations on the whole sky "and that is full of golden cuts just like the Pythagorean pentagram. Both Pythagoreanism and Platonism flourished during the Renaissance when much of our modern artistic tradition was forged and even Copernicus and Kepler were self-appointed Pythagoreans. The extent of the use of the ratio in art today, however, is grossly exaggerated. Here is Falbo:

" It is noteworthy that prior to Fischler's and Markowsky's work, there appeared to be no set standards for obtaining measurements from works of art. Often times, a proponent of the golden ratio chooses to design part of a work of art in an arbitrary way.Markowsky shows an example in which Bergamini arbitrarily circumscribes a golden rectangle around the figure of Saint Jerome in a painting by Leonardo Da Vinci and the poor guy's name Arm clipping to do this make the picture fit. "

Livio in The Golden Ratio and Aesthetics is similarly skeptical:

Many books claim that if you draw a rectangle around the face of Leonardo da Vinci's Mona Lisa, the ratio of height to width of that rectangle is equal to the golden ratio.There is no documentation to suggest that Leonardo deliberately used the golden ratio in the composition of Mona Lisa and where exactly the rectangle should be drawn.Still, one must acknowledge the fact that Leonardo was a close personal friend of Luca Pacioli, who in 1509 published a three-volume treatise on the golden ratio (called Divina Proportione).

The occurrence of the relationship in nature is also exaggerated, as Falbo points out: " We note that spirals in seashells generally do not have the shape of the golden Cut fit. This is true despite the numerous articles on the Internet and elsewhere in which images appear to have been stretched to fit It is also strange that the relationship was not extracted "from nature" before Pythagoreans, whose interest in it was evidently aroused not by nature but by the "mystical perfection" of the pentagram.

This does not mean that the relationship does not actually exist in nature (along with many others) or that some artists have not used it consciously, e.g. B. Dali in the sacrament of the Last Supper. Le Corbusier, the architect, developed a whole system of proportions called Modulor, which " should provide a standardized system that automatically gives everything harmonious proportions, from door handles to high-rise buildings ".

Aside from the semi-invented tradition, Fechner's psychological experiments were given a boost for this use in the 1860s, showing participants ten rectangles, and 76% chose those with aspect ratios of 1.75 as "the most pleasant" 1, 62 and 1.50, where 1.62 is closest to gold. The problem is that later experiments did not reproduce Fechner's results, and Godkewitsch's 1974 meta-study concluded that the preference was an artifact. According to Godkewitsch: " The fundamental question of whether or not there is a reliable, verbally expressed aesthetic preference for a certain ratio between the length and width of rectangular shapes in the Western world can probably be answered in the negative. "Recent experiments regarding the proportions of faces could not confirm the hype of the golden ratio either. As Livio emphasizes:

" Art history, however, has shown that artists who have created works of truly lasting value are precisely those who have deviated from a formal canon of aesthetics. Despite the truly amazing mathematical properties of the golden ratio ... I believe we should abandon its application as some sort of universal standard for "beauty", either in the human face or in art. "

Nick Seewald runs a website on the topic of the golden ratio, which contains a lot of up-to-date information about its real and mythical occurrences.