Esther M. Zimmer Lederberg
Angela Pintore: Alberti's "Rucellai Sepulchre"1

Few architectural examples remain of Alberti's actual architecture. The "Rucellai Sepulchre"is one that still does exist, and has been studied to determine if the structure actually satisfies harmonic ratios found in music, following the theories of the Pythagorean sect. The Pythagoreans felt that musical harmonies were a divine plan that could be used to study the universe (much as we now believe that the universe can be completely explained as following our mathematical theories).

A close examination of Alberti's architecture yields the following result. Specifically, mathematical terminology is used as follows:
A 2:1 harmonic ratio is called dupla.
A 3:2 harmonic ratio is called sesquialtera.
A 4:3 harmonic ratio is called sesquitertia.
A 9:8 harmonic ratio is called sesquioctavus.

Other terms are used in the first table below. What we find is that Alberti's architecture is in fact composed of harmonic ratios!
  1. Alberti's "Rucellai Sepulchre": front ratios
  2. Alberti's "Rucellai Sepulchre": side ratios
  3. Definitions of terminology used for short and medium lengths
  4. Definitions of terminology used for long lengths
Thus "The very same numbers that cause sounds to have concinnitas, pleasing to the ears, can also fill the eyes and mind with wondrous delight [Alberti 1999, Bk. IV, ch. 5: 305]. With these words Leon Battista Alberti outlines in his De re aedificatoria the correspondence between architectural proportions and harmonic musical ratios that will become the element that characterizes Renaissance architectural theory, inaugurating a tradition that will begin to see a decline only in the eighteenth century." 1

"[T]he ear is struck by sounds in the identical way that the eye is struck by optic impressions,” (Boethius).2

The idea that special numerical or mathematical relationships are pervasive in the universe was not only common in the past (Plato, circle; Euclid, geometry; St. Augustine). Our contemporary views (which are of course undoubtedly correct), including the views of Coppernicus; Issac Newton, and Einstein agree with the Renaissance view of Alberti. Thus finding mathematical relations in music served as a basis of the view that harmony may be found throughout the universe, as well as in architecture.

Ratios of lengths found in Alberti's "Rucellai Sepulchre"
Short Medium Long
Square length: 1 L Doppia/dupla length: 2 L Triple length: 3 L
Sesquialtera length: 3/2 L Sesquialtertia doubled length: 9 L Double+Sesquialtertia length: 8 L
Sesquitertia length: 4/3 L Sesquitertia doubled length: 16 L Quadruple length: 4 L

Summary of Harmonic Ratios
Short Areas Medium Areas Long Areas
1, 3:2, 4:3 harmonic ratios 2:1, 9:4, 16:9 harmonic ratios 3:1, 8:3, 4:1 harmonic ratios

1 "Musical Symbolism in the Works of Leon Battista Alberti from De re aedificatoria to the Rucellai Sepulchre", by Angela Pintore, Nexus Network Journal, Vol. 6, No. 2, 2004, p. 60.

2 Ibid., p. 62.

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