Harmony As a Principle of Composition
The notion of harmony is seen as a fundamental principle of composition in history of architecture. Composition is based on harmony and order as aesthetic categories. The understanding of harmony is based on the mythological person “Harmonia”, the goddess of harmony, who was seen as the daughter of Ares, the god of war, and Aphrodite, the goddess of love and beauty. Harmonia is the symbol of the union of antagonisms. Harmony means the connection of different or opposed things to an arranged whole. The antiquity science itself is conducted by principles of harmony and order.
Pythagoras
In the Pythagorean approach all occurrences are seen under a general principle. This principle wants to be a principle of composition by understanding all processes in mathematical orders. Arithmetic, geometry, astronomy and music, the sciences of Quadrivium are all based on this general principle. Pythagoras was convinced that harmony, all things and principles of being can be grasped by integers and mathematical regularities. He discovered that the music intervals form simple relations according the division of the string and the number of oscillations. The Tetraktys: numbers 1 to 4 (4 elements, 4 cardinal points) form the foundation according Pythagoras. The idea of harmonic proportions is a general principle for all sciences and applications.
Alberti
In reference to this antique understanding of harmony as the union of antagonisms Leon Battista Alberti (1404-1472) developed his principles of architecture. “De Re Aedificatoria” is subdivided into ten books and describes how to achieve harmony in architecture. Beauty was for Alberti "the harmony of all parts in relation to one another," and subsequently based on the Pythagorean ideas "this concord is realized in a particular number, proportion, and arrangement demanded by harmony". Alberti’s ideas remained the classic treatise on architecture from the sixteenth until the eighteenth century and even longer.
Kepler
Harmony as a concept for all sciences and the whole world is also expressed in Johannes Kepler's “Harmonices mundi”. Johannes Kepler (1571-1630) well known as scientist, astronomer and mathematician based his harmony concept on geometry, especially the Platonic Solids. He was a Pythagorean mystic and considered mathematical relationships to be the fundament of all nature and creations. Geometrical concepts are in his theory the fundament of nature and science as well as art and music.
Therefore also creation and design is based on the geometric world concept.
Golden Section
Such a fundamental principle of harmony derived from nature, applied in art, architecture and music can be seen in the golden section. The idea of the golden section shows the coherence of composition and geometry. This idea steps longtime through history of architecture. Hippasos of Metapont (450 B.C.) found it in his research about the pentagon and the relation of its edge length and the diagonal. Euclid (325-270 B.C.) was the first who described the golden section precisely also as a continuous division. In the following time golden section was seen as the ideal proportion and the epitome of esthetics and harmony. Especially in the renaissance, harmonic proportions were based on the geometric relations according the golden section in art, architecture as well as in music. Filippo Brunelleschi built Santa Maria del Fiore in Florence 1296 based on the golden section and the Fibonacci numbers.
The “Modulor” of Le Corbusier is an example of an architectonic concept of designing and creating according geometric rules in modern architecture, but it remains bound to the classical conception of harmony.
The structuring of the windows in Unité d’Habitation, Marseille, 1947 shows various kinds of formations by maintaining the same structure principle subdividing accordingthe golden section. A structural equivalence between music and architecture is obvious in “Ondulatoires” in the music composition “Metastasis” by Xenakis and the façade of “La Tourette” by Le Corbusier/Xenakis 1952. In his book “Architektur und Harmonie” Paul V. Naredi-Rainer characterizes the relation between architecture and geometry: geometry has an important role for architecture in the process of form finding and form development without determining architecture exclusively.
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