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In this captivating study, an influential scholar-artist offers timeless advice on shape, form, and composition for artists in any medium. Irma Richter illuminates the connections between art and science by surveying works of art from classical antiquity through the Modernist era. Richter shows the conscious and unconscious ways artists animated their works with geometric principles in an attempt to reconcile the realms of form and design.
This book presents a simple method that can be employed for every kind of designa method that underlies some of the greatest paintings of the Renaissance and was used by the architect of the Parthenon and the craftsmen of ancient Egypt. With research that leads to Florence, Chartres, Athens, and up the Nile Valley, the author surveys the geometric scheme behind the works of art of the past. Seventy-two images help illustrate the philosophical and religious significance connected with the artistic proportioning of space.
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Rhythmic Form in Art
By Irma A. Richter
Dover Publications, Inc.Copyright © 2005 Dover Publications, Inc.
All rights reserved.
a. Architecture, Sculpture and Painting.
THE conditions of artistic production in modern times differ from those prevalent in Florence before and during the Renaissance in more than one respect. The modern student who sets out to learn the art of painting is faced from the outset with a bewildering difference of opinion as to what constitutes art. There is no fixed tradition which he must follow, no apprenticeship which he must serve. In the museums he may study the art of all ages and all countries and he is free to take his choice. After having conscientiously followed a course of study in one art school, he may find in moving to another that his training is considered worthless and even destructive of any native talent he may have had. He feels isolated and must grope his way alone.
Moreover, his art enjoys the same freedom and isolation as he himself ; for modern painting, unlike the art of former days, is self-contained and independent of architecture. A painter rarely has an opportunity of decorating a large wall surface, and he therefore need not adapt his compositions to architectural spacing. The size and proportion of his canvas are more often than not a matter of chance, and his artistic considerations do not go beyond the four corners of his frame.
Circumstances were very different in Florence. The Italian student could profit by an organized and collective experience, which had been handed down through generations from master to pupil. Moreover, architects, sculptors and painters worked in close association. Often one artist excelled in more than one art. Thus the painter Giotto also designed the Campanile, and the sculptures which decorate it. The sculptor Michelangelo painted the frescoes in the Sistine Chapel and raised the dome of St. Peter's ; and when Leonardo da Vinci wrote to the Duke of Milan enumerating his qualifications he said : "I can give perfect satisfaction, and am equal to any other in architecture and the composition of buildings public and private.... I can carry out sculpture in marble, bronze or clay, and I can also paint, whatever may be done, as well as any other, be he who he may."
One of Vasari's most attractive stories is that of the friendship between the architect Brunelleschi and the sculptor Donatello. He tells of their journey together to Rome for the purpose of studying ancient monuments. They measured the plans carefully, digging down to the foundations of partly covered ruins, so that interested onlookers thought they were searching for hidden treasure. On their return to Florence they produced some of their finest work together. There could indeed be no fitter decoration for Brunelleschi's architecture than Donatello's reliefs.
The charming Renaissance chapel of San Giacomo in the church of San Miniato near Florence was designed by the sculptor Antonio Rosellino. He fitted the tomb of a Portuguese Cardinal into one of the walls under gracefully draped curtains. The architectural setting of the monument effectively sustains the statuary. The vault of the chapel is decorated with four tondoes in glazed terracotta by Luca della Robbia. The two painters Alessio Baldovinetti and Antonio Pollaiuolo enriched the walls with frescoes. The interior, which four great artists have combined to make beautiful, appears to be moulded by one great master-mind into graceful unity. This chapel is but one example. The churches and palaces of Italy all tell the same tale of close co-operation between the arts.
Sculptors and painters, therefore, were accustomed to conceive their compositions as part of an architectural design. They were often employed to decorate walls and had to adapt their compositions to tectonic spacing, and therefore the same rhythm which determined the work of the architect penetrated also into the work of the painter and sculptor.
Therefore painters liked to enclose their pictures in architectural framework; they painted temples behind their figures and flanked their open squares with palaces and colonnades, they staged their scenes in lofty halls or in front of vaulted niches, and they seated their Virgin on an architectural throne. The frame of an altarpiece often took the shape of a semicircular arch supported on pillars so that the worshipper appeared to be looking through an archway into another part of the same interior where he was kneeling. These settings accentuated the rhythmic arrangement of the composition. Their function can be compared to that of choral songs in ancient Greek drama. By these means the art of painting, not wishing to throw off its dependence on architecture which had sustained it, seemingly kept up its connection also in easel pictures. However, the painting of architectural backgrounds was only a superficial manifestation of the interrelation. The connection between the arts went deeper.
b. Painting and Music.
In looking at a great painting of the Renaissance the eye is satisfied at once by its completeness and by the unity into which all details are coherently moulded. The care and attention of the artist were fixed on the adjustment of the whole. His composition holds together and seems to be pervaded by some mysterious rhythm. The question presents itself : What is this power of comprehending the whole which artists of the past had at their command?
Was it an unconscious process ; and did they work thus without rule and measurement? Was their sense of composition so developed that they produced these masterpieces out of hand, driven only by the creative genius within them? The belief is current that the art of painting is the result of inspiration only, and that nothing in the way of law and order consciously applied must trammel the free improvisation of genius. Romantic enthusiasts on the one hand and contemptuous sceptics on the other assign the art of painting to caprice. According to them the painter works without method. He is supposed to follow a blind inner impulse and does not need to pay any regard to any laws.
Yet if this were true, the art of painting would differ from any other art, and would stand distinctively alone. Because, if the same were said of music, for instance, people would take another view. A piece of music was as a matter of course composed on an underlying mathematical division of time. However great the genius of the composer, he must nevertheless conform to the laws of harmony and rhythm. There cannot, therefore, be any objection on artistic grounds to the same principle being applied to painting. There is a close relationship between the two ; Leonardo has called music the sister of painting, and Michelangelo said : "Finally, good painting is a music and a melody, which intellect only can appreciate, and that with difficulty." A comparison between the two arts widens the outlook and reveals more clearly the fundamental ground which all arts have in common, and in trying to establish the principles of painting it is helpful to consider their correspondence with the principles of other arts.
Let us make one more comparison. Take the art which is simplest, poetry. The very existence of poetry depends on measure, be it hexameter or any other metre. The poet measures his words to fit the rhythmic beat of time ; and the artist draws his forms to fit the rhythmic division of space. What metre is to poetry, that proportion is to painting and the plastic arts.
The Neoplatonist Plotinus said : "What is it that impresses you when you look at something, attracts you, captivates you, and fills you with joy? We are all agreed, I may say, that it is the interrelation of parts towards one another and towards the whole, with the added element of beauty in colour, which constitutes beauty as perceived by the eye ; in other words, that beauty in visible things as in everything else consists of symmetry and proportion. In fact, nothing simple and devoid of parts can be beautiful, only a composite."
The Greeks then were extremely sensitive to the beauty of fine proportions, and we may say of them that they had an eye for proportion just as we speak of people having an ear for music. To them artistic pleasure came through the sense of sight, and it seems to have moved them so deeply that it evoked ethical emotions. Our eyes have not had the training which the Greeks enjoyed for many generations, and we have but faint glimmerings where they saw clearly.
But however gifted with innate and instinctive taste they may have been, the supposition that they obtained their wonderful results without a definite method cannot be entertained. The proportions of their temples and monuments cannot be the result of mere instinct. Such a supposition is, moreover, refuted by the titles of numerous books on the theory of proportion written by ancient Greek architects and other artists.
No doubt an art cannot be learned by rules. It is conceivable that, as poets and musicians are born and not made, and as they at first instinctively apply what afterwards is seen to conform to the laws of harmony and rhythm, so artists and craftsmen may tend instinctively to select certain arrangements and proportions which conform to geometric rules; and this instinctive faculty may have been developed by the practice on the part of generations of craftsmen in using the same proportions. But rules thus established by the practice of the great masters through the ages are fetters only to men of no genius ; "like that armour, which upon the strong is an ornament and a defence, upon the weak and misshapen becomes a load and cripples the body which it was made to protect."
Many centuries later Leon Battista Alberti, the great Renaissance architect and humanist, gave a definition of beauty similar to that of Plotinus. He said that all beauty is the result of fine proportions. According to him the parts must be related to the whole so that not the smallest particle can be added or taken away without disfiguring.
Thus the three fine arts which influence us through the eye, namely, architecture, sculpture and painting, have one quality in common on which their beauty depends, and this quality is "proportion." In painting and sculpture the representation of nature introduces a rival interest, which conflicts and sometimes obscures this fundamental quality. But architecture is unhampered by the representational element, and its expression of beauty can be clear and unalloyed. For next to music it is the most abstract of arts and fine architecture has been compared to frozen music.
Heard melodies are sweet, but those unheard
Are sweeter; therefore, ye soft pipes, play on ;
Not to the sensual ear, but, more endear'd,
Pipe to the spirit ditties of no tone.
Keats, Ode on a Grecian Urn, II.
c. Proportion in Space.
Architecture is the science of fine proportions ; while other artists may neglect them, an architect cannot possibly discard them. They are his only vehicle of expression; he has to deal with proportions all the time, from the laying out of his plan to the last detail of decorative moulding. A quotation from Vitruvius, the Roman writer on architecture, is apposite : "The design of a temple depends on symmetry, the principles of which must be carefully observed by the architect. They are due to proportion, in Greek [TEXT NOT REPRODUCIBLE IN ASCII.]. Proportion is a correspondence among the measures of the members of a work, and of the whole to a certain part selected as standard. From this results the principle of symmetry. Without symmetry and proportion there can be no principle in the design of any temple." In temple architecture the column, with its shaft, base, capital and entablature were moulded and related to form one harmoniously proportioned Order. The column thus forming a whole in itself, with parts proportionately related, was in its turn part of a greater whole, and was incorporated in the rhythmic spacing of the temple.
The composition of a picture was based on the same principle. Here the human figure takes the place of the column in architecture. Renaissance artists used a canon of proportion for the human figure which was based on Vitruvius, and elaborated by Leonardo da Vinci and others. This canon is well known and has come down to us in writing. Its proportions are comparatively easy to realize, as they are based on simple numerical relations. Within the composition of a picture each individual figure constituted a whole with parts harmoniously related. But these figures were in their turn part of a greater whole. They were coherently moulded into large compositions and adjusted into the space of walls and frames. Could we but find the principle on which this wonderful unity in the spacing of the greater whole was attained it might help us to a more intelligent appreciation of the art of the past.
Architecture, sculpture and painting not only have one quality in common which contributes to their beauty, namely, proportion, they also have one common sphere of action, namely space. The space of a work of art of the past was divided into harmonious proportions just as the various figures which it contained were built according to a canon of proportion. Space in these arts takes the place of time in music. As a melody is woven through the rhythmic beat of time a composition is traced into proportioned space.
In architecture the space thus proportioned into one harmonious scheme is circumscribed by the total length, width and height of the building ; whereas in a picture the space is represented by the surface of the painting. Artistic Space should be conceived as containing a work of art just as a block of marble potentially contains a piece of sculpture, for it pervades the empty spaces as well as the plastic figures and shares with ether the quality of invisibility, intangibility and pervasion. It constitutes the unifying element in a work of art, for in it all things find their relative shapes and places. The method by which space in the works of art of the past was harmoniously proportioned will form the subject of this inquiry.
Several artists of the Renaissance have written on the subject of proportion from an artistic point of view. Lorenzo Ghiberti, Leon Battista Alberti, Vincenzo Foppa, and Leonardo da Vinci devoted much time to this study. But such of their writings as have survived deal with the proportion of the human figures and not of space. The case is different when we come to the mathematical treatises of Piero della Francesca and of Fra Luca Pacioli. Piero's Libellus de quinque corporibus regularibus dealt with geometric solids. The same subject forms an important part of the book by Fra Luca Pacioli, which was the most celebrated treatise on proportion of the time. Its author was an acknowledged authority on mathematics ; and although not an artist himself he was in close communication with many distinguished artists. He studied under Piero della Francesca, whose ideas he was perhaps unjustly accused by Vasari of having published under his own name. Leonardo was his friend and designed the geometrical figures which illustrated his work. The treatise took the form of a lecture delivered to Ludovico Sforza, Duke of Milan, in 1498. It was published in Venice in 1509 under the title De divina proportione. The subject is better known by the name of "the golden section." This law, as usually stated, relates to the proportion of three magnitudes : "The first part is to the second part as the second is to the whole or sum of the two parts." This seemed to him so wonderful a proportion that he attached mystic significance to it and compared the three interrelated terms to the Divine Trinity. We open the book with great expectations; but we find nothing that was not known to the Greeks two thousand years before. Fra Luca's treatise is based on the Thirteenth Book of Euclid's Elements. We are referred back to the creative genius of the Greeks. In turning to them we are but following the footsteps of Italian Humanists. The science of geometry had not advanced since the fateful days when Rome had placed its conquering and crushing foot on the Hellenic world. Fra Luca knew this himself and paid tribute to the source of his knowledge when he let his portrait be painted with his hand resting on the Thirteenth Book of Euclid. (Plate I.)CHAPTER 2
THE divine proportion was known to the Greeks long before the time of Euclid, who lived in Alexandria about 300 B.C. For Euclid but handed down to posterity the knowledge of his predecessors in a connected and logical series of propositions, and contributed little of his own that was original.
Greek geometry is as old as Greek philosophy; it begins with Thales, who lived about 585 B.C. and was one of the seven wise men. His native town Miletos became the home of those early Greek philosophers who inquired into the ultimate nature of matter.
Miletos lies on the mainland of Asia Minor nearly opposite the island of Samos, which was the home of Pythagoras (sixth century B.C.). Both Thales and Pythagoras are said to have studied geometry in Egypt, where they with great difficulty succeeded in securing access to the carefully guarded secrets of the Egyptian priesthood, which had been preserved and handed down from generation to generation during the course of thousands of years.
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Table of ContentsI. Introduction
a. Architecture, Sculpture and Painting
b. Painting and Music
c. Proportion in Space
III. Greek Art and Mathematics
IV. Mathematical Definitions
a. Geometric Proportion
b. Divine Proportion
c. Geometric Progression
d. Table of Arithmetic Values
e. Pentagon and Decagon
V. Rhythmic Division of Space in Art
a. Creation by Geometry
b. The Timæus in Christian Cosmology
c. Plato and the Renaissance
a. Tombstone of an Egyptian King
b. Pectoral of Senusert II
VIII. The Greek Vase
a. Vase Forms
b. Vase Painting
IX. A Greek Relief
X. The Parthenon
a. The Euthynteria
b. The Stylobate
c. The Doric Order
d. The Peristyle
e. The Capital
f. The Façade
g. The Metope
h. The Cella
i. The Naos
XI. The Middle Ages
b. Aureoles and Nimbi
c. Dante's Zones of Heaven
XII. Italian Painting
a. The Origin
b. The Quattrocento
c. The Cinquecento
XIII. Some Masterpieces of other Schools
Dürer, El Greco, Poussin, Fragonard, Hogarth, Cézanne
XIV. A Retrospect