Esther M. Zimmer Lederberg
The Views of Rudolf Wittkower1

Click image or caption to return

XXX
Palladio's Palazzo Chiericati
Return

Andrea Palladio's Palazzo Chiericati

Rudolf Wittkower's "Architectureal Principles in the Age of Humanism" analyzes architecture from the viewpoint of musical harmony. Given the vibrations of a string, the lengths found are in the ratios 1:2:3:4. 1:2:4 are octaves, 1:2:3 produce perfect fifths. From these ratios, we find:

2n: 1, 2, 4, 8, 16,... (designated as "female")
3n: 1, 3, 9, 27,... (designated as "male")

Similar "female" and "male" sequences arise in the problem of "mensuration" and "misura" in music (dance). Examine the section dealing with dance, choreography and music for further details, and the relation to "corporeal rhetoric".

See Francesco Giorgi's Harmonic Ratios

These sequences are found in Plato's "Timaeus", interpreted as evidence that the entire universe of god has its origin (male and female souls) in mathematical sequences. Relationships between these sequences were central to the philosophy of the Pythagoreans, as well. Thus the view entertained by Renaissance architects and artists Ficino, Georgi, Alberti, Palladio, Barbaro, and Serli 1 that musical harmony of the universe, as well as the "perfect" proportions of god's greatest creation, man, have a basis in mathematics. Thus harmony and the proportions of man, must be used in art and architecture, all interrelated and bound together using linear perspective and rhetoric tacens.

See the "Vitruvian man"

We focus on musical harmony. Given a triple of numbers found in a ratio: <a:b:c> where the ratio at interest is a:c, then "b" is the mean. Three different means may be found:

arithmetic mean: b-a = c-b
geometric mean: a:b = b:c
harmonic mean: (b-a)/a = (c-b)/c

Thus
<2:3:4> has an arithmetic mean, as 3-2 = 4-3 = 1.
<4:6:9> has a geometric mean, as 4:6 = 6:9 (both are 2:3)
<6:8:12> has a harmonic mean, as (8-6)/6 = (12-8)/12 = ⅓

Ficino, a neo-Platonist (Plotinus) mystic, held the Christian view that man was the image of god embodied in the harmonies of the universe, and was also influenced by Vitruvius' idea of a figure inscribed in a square, the square inscribed in a circle, symbolizing the mathematical relationship of a microcosm within a macrocosm. Thus the harmonies and proportions of man were thought to apply to the entire universe.2

Using these ideas, Palladio and Alberti, as well as others reformulated architecture. Palladio recommends seven rooms that would have musical harmony (in this, he departs from the views of Alberti, as Alberti didn't discuss circular rooms):
  1. Circular 3
  2. Square = <x, x>
  3. Rectangular = <x√2, x>
  4. Rectangular = <3x, 4x> (harmonic ratio = 4:3)
  5. Rectangular = <2x, 3x> (harmonic ratio = 3:2)
  6. Rectangular = <3x, 5x> (harmonic ratio = 5:3)
  7. Rectangular = <1x, 2x> (harmonic ratio = 2:1)
The height of a room could be one of the three means: arithmetic, geometric or harmonic. 4 Thus <6,9,12> has room height of 9 (arithmetic mean), as <6,12> has room dimensions of <3x, 4x>, but could also have a room height of 8 as <6,12> = <1:2>.

An example of a room with 3:2 harmonic ratio may be seen at the Villa Godi (Palladio)

An example of a room which is circular may be seen at St. Nicola da Tolentino (Palladio)

An example by the architect Alberti that uses harmonic ratios is the "Rucellai Sepulchre"


Thus "...the numbers by which the agreement of sounds affects our ears with delight, are the very same which please our eyes and our minds,...". 5

"We shall therefore borrow all our rules for harmonic relations from musicians to whom this kind of numbers is extremely well known, and from those particular things wherein Nature shows herself most excellent and complete."5

"For Alberti, harmonic ratios inherent in nature are revealed in music. The architect who relies on those harmonies is not translating those musical ratios into architecture, but is making use of a universal harmony apparent in music..." 5

"...when Palladio wants churches to be built in such a manner and with such proportions that all the parts together may convey a sweet harmony to the eyes of the beholders'..." and "The proportions of the voices are harmonies for the ears; those of the measurements are harmonies for the eyes."6

"...for both, music and painting, convey harmonies; music does it by chords and paintings by its proportions. Musical intervals and linear perspective are subject to the same numerical ratios, for objects of equal size placed so as to recede at regular intervals diminish in 'harmonic' progression." Quote from Leonardo da Vinci.7

1 "Architectural Principles in the Age of Humanism", by Rudolf Wittkower, W. W. Norton, New York, 1971, p. 104
2 Ibid., p. 16
3 It is not clear that non-circular rooms (square or rectangular) exhausted all possibilities. Thus a room that is a regular hexagon with one length "x" might be included, as well as other regular shapes such as pentagons, etc.
4 "Architectureal Principles in the Age of Humanism", by Rudolf Wittkower, W. W. Norton, New York, 1971, p. 108, 109
5 Ibid., p. 110
6 Ibid., p. 113
7 Ibid., p. 118

Back

© Copyright 2006 - 2018    The Esther M. Zimmer Lederberg Trust     Website Terms of Use