«VISUAL PERCEPTION AS THE BASIS OF THE SYSTEM OF PROPORTION IN THE WORK OF ANDREA PALLADIO»
THE ARTICLE | 1995
ST. PETERSBURG, RUSSIA
«VISUAL PERCEPTION AS THE BASIS OF THE SYSTEM OF PROPORTION IN THE WORK OF ANDREA PALLADIO»
THE ARTICLE | 2024
ST. PETERSBURG, RUSSIA
Author: I.Y. Vitvitsky
Scientific supervisor: O.V. Vasilenko
The work of the great Andrea Palladio (1508-1580) has and continues to have a huge impact on the formation of attitudes towards architecture as an art, based on the principles of harmonious patterns in the organization of space, the creation of volumes, and the nature of design details. This influence can be explained by the fact that Palladio appeals to everyone's sense of beauty, and because he was one of the great architects who could endow his buildings with "divine harmony."
Palladio explains the secret of architectural beauty: "Beauty is a result of beautiful shapes and the correspondence of the whole and parts, parts to each other and the parts with the whole." However, in the simplicity of Palladio's words lies the key to understanding his work.
Beauty is the result of a beautiful form - this is Palladio's first postulate. Palladio considered circles and squares to be beautiful shapes. With the wise instinct of an artist, he understood the aesthetic constancy and symbolic universality of these forms. The concept of beauty dates back to Pythagoras. Circles are symbols of perfect shapes in many cultures. (Taoism asserts that "True nature embodies essential nature and eternal life, and is symbolized by the circle, representing its immaterial substance free from destruction, representing its spiritual body..." We know of Dante's nine circles of hell, we are familiar with Renaissance structures based on interpretations of Pythagorean numbers by Plato and his followers. The cube was considered the most perfect geometric form.
It is interesting to quote Francesco Cattani (1466-1520), a student of the greatest humanist of the XV century, Marcelino Fichino, on this subject. "We also know that a cubic number expresses completeness and perfection, and when a number is raised to the cube, this explains its perfection. We call the number two 'linear' because it resembles a line. If we multiply two by two, we get four, and this number has similarity to space. If we continue to multiply four by itself, we will get eight, which resembles the shape of a body. Multiplication stops at three dimensions: length, width, and height. Therefore, the cube is the final stage of multiplication with a single number, and its final perfection." Cattani then clarifies the Pythagorean postulate as follows: "When the base of the cube is four times the original number, the cube reaches the highest degree of completion and cannot proceed further.. Therefore, in the nature of each cube, the highest perfection is indicated. It is not surprising then if the Pythagoreans swore (as claimed by Theon) that the number four came from a dispassionate nature in our soul. From here come the possibilities for the soul, which gradually moves - it improves. In the subconscious, a cube unfolds into a system of squares as a result of visual differentiation, there are four sides to a square and, in this case, perfection and beauty are integral concepts.
Palladio's second postulate is that beauty, in his understanding, is the result of "the correspondence of the whole to the parts, the parts to each other, and the parts to the whole." To clarify the meaning of what was said, we should turn to Giacomo da Vignola's contemporary Andrea Palladio (1508-1580). The desire to unravel the mysteries of the laws of harmony and create rules for finding beauty was inherent in all great architects of Palladio's era. This was essential, since architecture was based on order systems that had been laid down in ancient times. Vignola wrote, "I have come to conclude that those orders that seem most beautiful and graceful to our eyes have certain definite numerical relations and proportions." Consequently, A. Palladio, speaking about the correspondence of parts, meant proportions. The seriousness of this problem is emphasized by Vignola himself, pointing out that "our every feeling enjoys this proportionality, and how far from it are things that we dislike, which musicians prove beautifully and convincingly."
Now, let's ask ourselves what Vignola meant when he spoke of less complex numerical relationships. And what are these "majority" judgments? Let's try to answer this question. The simplest numerical ratio is 1:1, i.e., ⬜ and ⚪. Most people distinguish between these two shapes from the entire variety of shapes and ratios, subconsciously evaluating the 1: 1 ratio as the simplest one. This can be easily verified by visually evaluating a row of rectangles, where the square is the most recognizable, readable, and guessable shape.
Palladio explains the secret of architectural beauty: "Beauty is a result of beautiful shapes and the correspondence of the whole and parts, parts to each other and the parts with the whole." However, in the simplicity of Palladio's words lies the key to understanding his work.
Beauty is the result of a beautiful form - this is Palladio's first postulate. Palladio considered circles and squares to be beautiful shapes. With the wise instinct of an artist, he understood the aesthetic constancy and symbolic universality of these forms. The concept of beauty dates back to Pythagoras. Circles are symbols of perfect shapes in many cultures. (Taoism asserts that "True nature embodies essential nature and eternal life, and is symbolized by the circle, representing its immaterial substance free from destruction, representing its spiritual body..." We know of Dante's nine circles of hell, we are familiar with Renaissance structures based on interpretations of Pythagorean numbers by Plato and his followers. The cube was considered the most perfect geometric form.
It is interesting to quote Francesco Cattani (1466-1520), a student of the greatest humanist of the XV century, Marcelino Fichino, on this subject. "We also know that a cubic number expresses completeness and perfection, and when a number is raised to the cube, this explains its perfection. We call the number two 'linear' because it resembles a line. If we multiply two by two, we get four, and this number has similarity to space. If we continue to multiply four by itself, we will get eight, which resembles the shape of a body. Multiplication stops at three dimensions: length, width, and height. Therefore, the cube is the final stage of multiplication with a single number, and its final perfection." Cattani then clarifies the Pythagorean postulate as follows: "When the base of the cube is four times the original number, the cube reaches the highest degree of completion and cannot proceed further.. Therefore, in the nature of each cube, the highest perfection is indicated. It is not surprising then if the Pythagoreans swore (as claimed by Theon) that the number four came from a dispassionate nature in our soul. From here come the possibilities for the soul, which gradually moves - it improves. In the subconscious, a cube unfolds into a system of squares as a result of visual differentiation, there are four sides to a square and, in this case, perfection and beauty are integral concepts.
Palladio's second postulate is that beauty, in his understanding, is the result of "the correspondence of the whole to the parts, the parts to each other, and the parts to the whole." To clarify the meaning of what was said, we should turn to Giacomo da Vignola's contemporary Andrea Palladio (1508-1580). The desire to unravel the mysteries of the laws of harmony and create rules for finding beauty was inherent in all great architects of Palladio's era. This was essential, since architecture was based on order systems that had been laid down in ancient times. Vignola wrote, "I have come to conclude that those orders that seem most beautiful and graceful to our eyes have certain definite numerical relations and proportions." Consequently, A. Palladio, speaking about the correspondence of parts, meant proportions. The seriousness of this problem is emphasized by Vignola himself, pointing out that "our every feeling enjoys this proportionality, and how far from it are things that we dislike, which musicians prove beautifully and convincingly."
Now, let's ask ourselves what Vignola meant when he spoke of less complex numerical relationships. And what are these "majority" judgments? Let's try to answer this question. The simplest numerical ratio is 1:1, i.e., ⬜ and ⚪. Most people distinguish between these two shapes from the entire variety of shapes and ratios, subconsciously evaluating the 1: 1 ratio as the simplest one. This can be easily verified by visually evaluating a row of rectangles, where the square is the most recognizable, readable, and guessable shape.
The clarity of the shape of a square (a perfect shape, as mentioned above), or a circle, can be interpreted as a category of beauty, because clarity is inherent in beauty as one of its properties. And "majority" judges by evaluating the most perfect monuments of antiquity, in order to establish patterns of their formation. Vignola says that "from the totality of ancient monuments", without introducing anything of oneself into them except the distribution of proportions based on prime numbers, great architects strove for clarity and simplicity of relationships to achieve harmony in structure. However, unlike "the majority", the architect also follows the path of logical and mathematical search for patterns in order to harmonize in order to ultimately achieve the desired result.. A hundred years before Palladio, one of the titans of the early Renaissance, the scientist, architect and art theorist, Leon Batista Alberti (1404-1472), wrote: "Scientists have three main ways to obtain the average: their goal is, when there are two extreme numbers, to find a third number that corresponds to them in a certain way. That is, if you will, related to each by ties of kinship." His buildings (the Church of Sant'Andrea in Mantua and Santa Maria Novella in Florence) clearly demonstrate the concept of constructing a facade and volume on the basis of a square, a principle that Alberti adopted from Vitruvius.
Visual representation of what has been said can be seen in diagrams of such series of combinations when a part of one plane or space is superimposed onto another and a zone of resonance appears at the point of overlap. This can be seen on...
Visual representation of what has been said can be seen in diagrams of such series of combinations when a part of one plane or space is superimposed onto another and a zone of resonance appears at the point of overlap. This can be seen on...
In a piece of music, "C" is a zone or field connecting fields "A" and "B".
In watercolor painting, the "C" field harmonizes colors "A" and "B" when they are superimposed. In architecture, there is a method of proportioning architectural masses based on superimposing spatial fields. This can be seen in the work of Andrea Palladio.
In his work "Four Books on Architecture", A. Palladio shows an interest in the ratio between the dimensions of the parts of a composition in length and height. He gives recommendations on the relationship between the height of an arch and the thickness of its supporting column, draws attention to the proportion of spaces into which one element of a composition fits, as well as to the sizes of rooms, loggias and courtyards. After careful study of Palladio's statements, it becomes clear that initially, when designing a building, the main role is not played by any specific element (module) but by the overall height and length of the structure. Our analysis of his buildings shows that proportional proportions of architectural volumes are based on square modules determined by the size of the building and combined and superimposed onto each other like spatial fields.
In watercolor painting, the "C" field harmonizes colors "A" and "B" when they are superimposed. In architecture, there is a method of proportioning architectural masses based on superimposing spatial fields. This can be seen in the work of Andrea Palladio.
In his work "Four Books on Architecture", A. Palladio shows an interest in the ratio between the dimensions of the parts of a composition in length and height. He gives recommendations on the relationship between the height of an arch and the thickness of its supporting column, draws attention to the proportion of spaces into which one element of a composition fits, as well as to the sizes of rooms, loggias and courtyards. After careful study of Palladio's statements, it becomes clear that initially, when designing a building, the main role is not played by any specific element (module) but by the overall height and length of the structure. Our analysis of his buildings shows that proportional proportions of architectural volumes are based on square modules determined by the size of the building and combined and superimposed onto each other like spatial fields.
The size of the intermediate proportional divisions of masses (or "fields") is determined by the amount of layering, which is also dictated by scale, on the one hand, and the ability to obtain rows of correlated simple shapes of inscribed squares, on the other. Using the example of a hypothetical reconstruction of the proportional structure of the portal of the Olimpico Theatre, it is possible to trace how, in the process of proportional construction of this structure, successive layering occurs - the alignment of fields of squares.
When studying the master's drawings, one can find and emphasize that the relationships in all structures are taken along the axes of columns and the upper edges of cornices. In our design, the alignment field, "a" value, is determined by the scale of the structure and its proportional composition. But it is precisely in this area that the key compositional elements fall - the arches and openings in the stage. Figure 4 shows a diagram for constructing proportional relations based on overlapping square grids for the Villa Rotunda by A. Palladio. Surprisingly, such a complex spatial composition structure also follows a method that seems to us to underlie the harmonization of Palladian structures.
It should be noted that, in this case, we are dealing with a deep tradition that was not interrupted during the Renaissance, but rather developed and improved, passing from the creative experience of one great master to another. Alberti clearly states the following regarding the choice of proportions: "So, if someone wants to build a wall twice as long as wide, they should use those proportions that make up an octave (2:1), not those that make a duodecimal (3:1)." Hence, according to Alberti's opinion, the connection between a building's facade and its plan follows this rule.
Perhaps, we should consider the extent to which, in many modern architectural buildings, a lack of connection between visual perception of a facade and spatial movement in a plan causes discomfort, or, as Vignola would say, "our every feeling."
There are many more examples that confirm the validity of the conjectures expressed in the article on one of the methods of harmonizing architectural forms used by A. Palladio. In particular, we need to point out the continuity and interrelation of works of Palladio and Daniel Barbaro. When comparing them, it becomes clear that Vitruvius, as interpreted by Barbaro, was the Vitruvian from which Palladio derived.
Above, we have shown the philosophical and symbolic significance of the circular and square shapes. We could have done the same with respect to laws of proportion in terms of the "golden ratio", but there is a lot of literature on this topic, and it was not worth developing this topic further in this article. However, we understand that it should not be overlooked when addressing the issues we raised.
The main result and conclusion of this research is:
Perhaps, we should consider the extent to which, in many modern architectural buildings, a lack of connection between visual perception of a facade and spatial movement in a plan causes discomfort, or, as Vignola would say, "our every feeling."
There are many more examples that confirm the validity of the conjectures expressed in the article on one of the methods of harmonizing architectural forms used by A. Palladio. In particular, we need to point out the continuity and interrelation of works of Palladio and Daniel Barbaro. When comparing them, it becomes clear that Vitruvius, as interpreted by Barbaro, was the Vitruvian from which Palladio derived.
Above, we have shown the philosophical and symbolic significance of the circular and square shapes. We could have done the same with respect to laws of proportion in terms of the "golden ratio", but there is a lot of literature on this topic, and it was not worth developing this topic further in this article. However, we understand that it should not be overlooked when addressing the issues we raised.
The main result and conclusion of this research is:
- An attempt is made to substantiate the version of the method of harmonization of architectural forms apparently used by Palladio.
- Based on the proposed version, we seem to suggest a simple, easily understandable, and hand-drawn method for drawing the proportions of a "beautifully shaped" building.