10 of 19 people found the following review helpful:
5.0 out of 5 stars
More than just Architecture!, March 9, 2004
Already recognized since 1949 as "a masterpiece in scholarship" in its field by several eminent architects, the 173 page tome: ARCHITECTURAL PRINCIPLES IN THE AGE OF HUMANISM, 4th ed. (1971) by Rudolf Wittkower; had, incidentally, also provided an in-depth explanation on proportion and ratio as they differed in usage between architectural procedure and Boethian mathematics.
Of special importance is part four 'The Problem of Harmonic Proportion in Architecture' (p. 101) where the author made the salient point that "Although the Pythagoreo-Platonic concept of the numerical ratios of the musical scale never disappeared from mediaeval [sic], theological, philosophical, and aesthetic thought, there was no over-riding need to apply them to art and architecture" (p. 159).
Rudolf Wittkower unknowingly provided in part four the distinction between an elite Quadrivium education containing Boethian "mathematical arts" while "the 'liberal arts' of painting, sculpture, and architecture were regarded as manual occupations" (p. 117). The author explained "That the high Renaissance architects shunned theory" and "that they were practitioners rather than thinkers" (p. 30). And further "Italian architects strove for an easily perceptible ratio between length, height, and depth" (p. 74). So then according to this author, all of the Renaissance architects conception of architecture was based on a "commensurability of ratios" (p. 108).
Rudolf Wittkower indicated "that the [Renaissance] architect is by no means free to apply to a building a system of ratios of his own choosing, that the ratios have to comply with conceptions of a higher order and that a building should mirror the proportions of the human body" (p. 101). In developing the centrally planned church, Renaissance architects faced the dilemma of the pragmatics of church construction combined with the belief in divinity and the acceptance of Roman Catholic dogma.
The Church was to provide the "easily perceptible ratio" with the simple logic that "As man is the image of God and the proportions of his body are produced by divine will, so the proportions in architecture have to embrace and express the cosmic order" (p. 101). That cosmic order and harmony are contained in certain numbers Plato explained in his TIMAEUS.
Assigned to the architects, a Quadrivium trained Roman Catholic friar and musical theorist, Franchino Gaffurio (1451-1522) "in a truly Platonic spirit he regarded this principle of harmony as the basis of macrocosm and microcosm, body and soul, painting, architecture, and medicine" (p. 124). It was under this famous Renaissance musical theorist in 1525 that "the old belief in the mysterious efficacy of certain numbers and ratios was given new impetus" (p. 102). "It was Pythagoras who discovered that tones can be measured in space. What he found was that musical consonances were determined by the ratios of small whole numbers. If two strings are made to vibrate under the same conditions, one being half the length of the other, the pitch of the shorter string will be one octave (diapason) above that of the larger one" (p. 102). "Thus the consonances, on which the Greek musical system was based - octave, fifth, and fourth - can be expressed by the progression 1:2:3:4. One can understand that this staggering discovery made people believe that they had seized upon the mysterious harmony which pervades the universe" (p. 103).
"The musical consonances are determined by the mean proportionals; for that the three means constitute all the intervals of the musical scale had been shown in the TIMAEUS. Classical writers on musical theory discussed this point at great length. An exhaustive exposition is to be found in Boethius' DE MUSICA, first printed in Venice in 1491-92, and of very great importance for the doctrine of numbers throughout the Middle Ages and during the Renaissance" (p. 111).
Yet Boethius's DE MUSICA was de-emphasized by Renaissance architects in recognition that the "harmony of the universe which Plato had described in the TIMAEUS on the basis of Pythagora's discovery of the ratios of musical consonances" prompted the "application of Pythagoreo-Platonic system of harmonic ratios directly to architecture" (p. 125). As it turned out (not surprisingly) "Gafurio [sic] was regarded by his contemporaries as a critic in architectural matters" (p. 125).
The author of ARCHITECTURAL PRINCIPLES IN THE AGE OF HUMANISM provided the evidence that although the Quadrivium of the mathematical arts of music, astronomy, geometry, and Boethian proportion and ratio, was known to the Renaissance high architects, they preferred the 'harmonic proportion'; 'proportion of excess'; and the 'proportio proportionum'; derived directly from Plato's TIMAEUS and Pythagoras's three means (arithmetic, geometric, and the harmonic) over Boethius's DE MUSICA, though it was a substantial part of friar Gaffurio's ecclesiastical education. This resulted in "proportionally integrated 'spatial mathematics', which we have recognized as a distinguishing feature of humanist Renaissance architecture" (p. 26).
In comparison, for the practical application of Boethian proportion and ratios, please read: THE PHILOSOPHER'S GAME (2001) by Dr. Ann E. Moyer, where the rules of Boethian proportion found in rithmomachia, had been clearly defined, though inadvertently, by Rudolf Wittkower.
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1 of 4 people found the following review helpful:
1.0 out of 5 stars
Virtual gibberish, June 6, 2011
This review is from: Architectural Principles in the Age of Humanism (Paperback)
Written with pompous, pretentious and convoluted style, this book is an exercise in tedium. I had to read this book in architecture school, on more than one occasion; I wanted to throw it out the window. Only read this book if you enjoy being condescended to and/or must for school.
I can summarize the book in one sentence: Proportion is important in architecture.
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