Proportion (architecture)

In architecture, the proportion is the ratio of the length, width and height dimensions of a building, a facade or a component. Architects of all ages took advantage of different proportional systems. The theoretical analysis of proportions in architecture is also called theory of proportion.

One of the possibilities of modern, professional and appropriate cross- sufficient science theory and practice of the theory of proportion and research will remain in the German language for a long time a desideratum. The traditional architecture built before 1830 almost all categories was basically characterized by proportion embossed shape qualities; the rural architecture of farmhouses and agricultural spatial functional buildings.

In connection with the aesthetics of proportion and a number of other, often mathematical algorithms related shape relations play a major role, as they facilitate the perception of a reduction in the abundance of information on information order ( information reduction ) and subsequent information enrichment and thus make more or less hidden form qualities more readily detectable. So give proportion and other quasi algorithms of shape between order (unit) and diversity ( complexity), and this is an important prerequisite for aesthetics. Ok so degeniert not rigid monotony, variety not to ( nichtfraktalem ) chaos. The fractal mathematics opens up many new ways to make aesthetic relations in addition to proportion, symmetry, rhythm, and many other gestalt laws objectively determining the last few decades.

Ratios

Proportions represent relationships; they can be referred by a whole to individual parts or items with each other in an aggregate whole. Proportioning A building on ratios, is the simplest and earliest form of defining the scale. A measure by regional measures of length determined (feet or Elle ), can be arbitrarily multiply or furnishings, such as the tatami mat, serves as a measure of the size of a room. An early building that should have been sized according to numerical proportions, is the temple of Solomon, its description can be found in the Bible in the first book of Kings (chapter 6 and 7).

The Pythagoreans discovered with the help of the monochord that musical harmonies corresponded simple numerical ratios, measured from the length of a Tonsaite the octave is halved (ratio 2: 1) generates a string, the fifth corresponds to the ratio 3: 2 and the fourth 4: 3. on the monochord can still be the twelfth (3: 1) and the double octave (4: 1) read directly. These ratios could be directly on the geometry and thus transferred into the architecture. These ratios are also found in Solomon's Temple. Initially, only those proportions were considered consonant, from the Renaissance came not add more intervals.

Orders of

Fundamental to the theory of proportion are the classical orders of columns. Depending on whether it is the Doric, Ionic or Corinthian order, a certain ratio of height to width of the column is required and a corresponding form of base, capital and entablature. Architectural treatises such as the seven books of Sebastiano Serlio spread the teachings of the order of columns in the Renaissance. The buildings of Andrea Palladio are characterized by fixed proportions of the rooms from (width to length) and facades.

Middle Ages

Contrary romantic allegations which arose in the Middle Ages awakening enthusiasm in the early 19th century, there were in the Romanesque and Gothic periods, at least until about 1480 no geometric or arithmetic proportions. The hundreds later medieval buildings shaded proportion schemes are baseless, as Konrad Hecht has been convincingly demonstrated ( measure and number in the medieval architecture ). A simple geometric proportion in Romanesque buildings is the square schematism. Geometric design techniques such as quadrature Triangulatur and how they will be presented in late medieval craftsman books are controversial in their significance for the Gothic building practice.

Renaissance

During the Renaissance, the question of proportion in architecture was very significant, as well different approaches were followed:

Andrea Palladio is in his " Four Books of Architecture " a hierarchy of spatial proportions, which goes directly back to Plato. " There are seven of the most beautiful and well -proportioned room types ...":

• The room was round or square, because the edges are far here right from its center.
• The square is extended beyond its diagonal ( proportion of root ( 2), a ratio of 1: 1.41 ... ).
• The length is 1 1/ 3 of its width (ratio: 3:4 or 1:1,33; musically: fourth).
• The length is 1 1/ 2 of its width (ratio: 2:3 or 1:1.5; musically: fifth).
• The length is 1 2/3 of its width (ratio: 3:5 or 1:1,67; musical: Big sixth ).
• The room had two large squares (ratio: 1:2; musically: octave).

In his four books, there are a number of villas and palace designs, the palace Antonini he shows the first example, whose rooms are proportioned according to these categories. The height of the space corresponding to the width, the height of the mezzanine floor to be lower than one sixth of the main floor below.

Daniele Barbaro and Andrea Palladio Vitruvius transferred from Latin into Italian, and supplement it by mathematical and geometrical methods, as well as drawings from the geometry and architecture. It introduced the proportioning of the root diagonals that give architects more proportions for a harmonious design at hand. Procedure: A square is extended on one side to its diagonal, the proportion 1: √ 2 ( 1:1,414 ..) arises. The newly formed rectangle is again extended its diagonal, the Triangulatur arises ( proportion 1: √ 3, 1:1,732 ..). That √ 5 - -, √ n- proportions. In this way, one after the √ 4 result

As root proportions usually produce incommensurable numbers, was used in the past with approximations that were sufficiently accurate for the former builder:

• 1 was 7:5 or 17:12 or 21:15: √ 2 from 1.414
• √ 3 from 1.732: 1 was 7:4 or 12:7
• √ 5 from 2,236: 1 was 20:9
• √ 6 from 2,449: 1 was 17:7 or 22:9

Also root proportions were easier to handle by approximations:

• √ 3: √ 2 from 1.723: 1.414 was 26:21
• √ 4: √ 3 of 2.000: 1.723 was 7:6 or 8:7 or 15:13
• √ 4: √ 3: √ 2: √ 1 was to 30:26:21:15

The dimensions 30:26:21:15 Vicenza foot ( 34.7 cm) Palladio has given for its villas design La Rotonda.

In order to harmonize the multitude of different proportions, Alberti and Palladio describe the application of the funds Dimensions. For this purpose, the arithmetic mean, for example, (average) mathematically or geometrically determined from the length and width of a floor plan, so as to find about the amount of space or the proportion of the next room. For greater possibility of variation is described by two architects, the geometric mean and the harmonic mean.

Golden section

→ Main article: Golden Ratio

Many works of Greek antiquity are regarded as examples of the use of the golden ratio, such as the front of the 447-432 BC built under Pericles Parthenon on the Athenian Acropolis. As to these works, no plans have been handed down, it is not known whether these proportions were chosen consciously or intuitively.

Be found also in later periods numerous examples of the golden proportion, such as the facade of the porch of the gate in Lorsch (770 AD).

The view that the golden section proportion was identical with, is wrong for categorical perspective. Nevertheless, the golden ratio has a barely be underestimated importance for the aesthetic effect ( Gestaltprägnanz ) of objects of architecture, culture, art, nature and all other areas.

Human Proportion

Vitruvius, Leonardo da Vinci and Le Corbusier took the foundations of their proportional systems in the human form. Here all variables were ( and portion sizes ) related to each other. Le Corbusier developed in 1940 a uniform system of measurement based on the human dimensions and the golden section. He published it in 1949 in his book The Modulor, which is counted among the most important works of architecture history or theory.

Compilation of proportions

The table below shows proportions (selection) ordered from square to

Quadruple square. The background colors assign the proportions given proportion systems.

• Yellow orange = Golden Ratio
• White = proportion Musical
• Gray = root proportion
• Lilac = Musical - and root proportion

Proportion analyzes

The proportion analysis is a branch of the theory of proportion. In the literature, there are often hasty attributions of certain proportions of a building. This approach has brought the proportion of research into disrepute, as Erwin Panowsky noted.

The architect Rob Krier pointed to this problem; He completed his studies in an oversize of the Cathedral of Auxerre. He could find on this structure different proportional systems of distinctive forms. So he found convincing proportions from the Triangulatur, the golden section and certain ratios again.

When an earthquake in 1981 the Parthenon on the Acropolis inflicted severe damage, ETH Zurich organized a symposium that brought together world experts who had conducted research on the Parthenon. It turned out that there were about 50 different ones, all differed from each other, not even a single Fußmaß could be determined, it ranged from 29.7 cm to 32.8 cm. From the analysis created Erich Berger, the editor of the Reader, a useful list of quality characteristics for proportion analysis:

• An accurate measurements must be created.
• The dimensions determined shall be transferred to the former, historical dimensions.
• The building is to investigate whether it meanwhile major modifications or repairs were, or whether and where the craftsmen of his time working with tolerances.
• It would be helpful written statement of the former builders or planners.