Proportion (architecture)

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In architecture , proportion is the relationship between the length, width and height of a building , a facade or a component . Architects from all ages used different systems of proportions. The theoretical examination of proportions in architecture is also known as the theory of proportions .

A theory and practice of proportion theory and research that is sufficient for the possibilities of modern, interdisciplinary and interdisciplinary science will remain a desideratum in the German-speaking area for a long time to come. The traditional architecture built before 1830 in almost all categories was fundamentally characterized by proportionally shaped design qualities ; also the rural architecture of farmhouses and agricultural functional buildings.

In connection with aesthetics , proportion and a number of other design relationships , often related to mathematical algorithms, play an important role insofar as they make it easier for the perception to reduce the amount of information to information order ( information reduction ) and subsequent information enrichment and thus make more or less hidden design qualities easier to grasp. Proportion and other quasi-algorithms mediate the shape between order (unity) and diversity (complexity), and this is an important prerequisite for aesthetics. Order does not degenerate into rigid monotony, diversity does not degenerate into (non-fractal) chaos. For a few decades now, fractal mathematics has opened up many new possibilities for making aesthetic relationships objectively understandable in addition to proportion, symmetry, rhythm and many other gestalt laws .

Numerical ratios

Proportions represent relationships . They can be related to individual parts of a whole or individual parts to one another to form an added whole. To proportion a building using numerical proportions is the simplest and earliest form of setting dimensions. A measure, determined by regional length measures ( foot or cubit ), can be multiplied as desired or furnishings such as the tatami mat serve as a measure of the size of a room. An early building, which is said to have been dimensioned according to numerical proportions, is the Solomonic Temple , its description can be found in the Bible in the first book of kings (chapters 6 and 7).

The Pythagorean discovered using the Monochords that musical harmonies corresponded simple numerical ratios as measured from the length a Tonsaite which is octave at halving (ratio 2: 1) generates a string, the fifth corresponds to the ratio 3: 2 and the fourth 4: 3 The duodecime (3: 1) and the double octave (4: 1) can be read directly on the monochord. These relationships could be transferred directly to geometry and thus to architecture. These relationships can also be found in the Temple of Solomon. Initially, only these proportions were considered consonant, from the Renaissance onwards further intervals were added.

Column orders

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

middle Ages

Sant'Alessandro Maggiore (Lucca) : first construction phase of the facade ad triangulum and today's facade ad quadratum

Contrary to romantic claims, which arose in the early 19th century in the awakening enthusiasm for the Middle Ages, there was no geometric or arithmetic proportioning whatsoever in the Romanesque and Gothic at least until around 1480. The proportions schemes that were subsequently added to the hundreds of medieval buildings lack any basis, as Konrad Hecht has convincingly demonstrated (measure and number in medieval architecture). A simple geometric proportion in buildings of the Romanesque is the quadratic schematic . Geometric design processes such as triangulature and quadrature, as presented in late medieval master craftsmen's books, are controversial in their significance for Gothic building practice.

Renaissance

In the Renaissance , the question of proportion was very important in architecture, and various approaches were followed:

Palladio's Palazzo Antonini in Udine

In his “Four Books on Architecture” Andrea Palladio sets up a hierarchy of spatial proportions that goes back directly to Plato . "There are seven of the most beautiful and best proportioned room types ...":

  • The room is round or square because the edges are the same distance from their center.
  • The square is extended over its diagonal (proportion from the root (2), ratio 1: 1.41 ...).
  • The length is 1 1/3 of its width (ratio: 3: 4 or 1: 1.33; musical: fourth).
  • The length is 1 1/2 of its width (ratio: 2: 3 or 1: 1.5; musical: fifth).
  • The length is 1 2/3 of its width (ratio: 3: 5 or 1: 1.67; musically: major sixth).
  • Let the room be two squares (ratio: 1: 2; musical: octave).

In his four books there are a number of villa and palace designs, the Antonini Palace he shows as the first example, whose rooms are proportioned according to these categories. The height of the rooms corresponds to their width, the height of the mezzanine floor should be one sixth lower than that of the main floor below.

Draw the root proportions starting with a square

Daniele Barbaro and Andrea Palladio translate Vitruvius from Latin into Italian and supplement it with mathematical and geometric methods, as well as drawings from geometry and architecture. They also describe the proportions of the root diagonals, which give the architects additional proportions for a harmonious design. Procedure: A square is lengthened on one side by its diagonal, the proportion 1: √2 (1: 1.414 ..) is created. The newly formed rectangle is extended again by its diagonal, the triangulature is created (proportion 1: √3, 1: 1.732 ..). In this way the √4-, the √5-, √n-proportions result one after the other.

Since root proportions usually generate incommensurable numbers, approximations were used in the past that were sufficiently precise for the builders of the time:

  • √2 of 1,414: 1 became 7: 5 or 17:12 or 21:15
  • √3 from 1.732: 1 became 7: 4 or 12: 7
  • √5 from 2.236: 1 became 20: 9
  • √6 from 2,449: 1 became 17: 7 or 22: 9

Root proportions have also become easier to handle through approximations:

  • √3: √2 from 1.723: 1.414 became 26:21
  • √4: √3 from 2,000: 1,723 became 7: 6 or 8: 7 or 15:13
  • √4: √3: √2: √1 became 30: 26: 21: 15

Palladio specified the dimensions of 30: 26: 21: 15 Vicentine feet (approx. 34.7 cm) for his villa design La Rotonda .

In order to harmonize the multitude of different proportions, Alberti and Palladio describe the use of median dimensions . For this purpose, for example, the arithmetic mean (average) of the length and width of a floor plan is determined mathematically or geometrically in order to find the height of the room or the proportion of the subsequent room. The two architects also describe the geometric mean and the harmonic mean to allow for greater variation .

Golden cut

The facade of the Lorsch gate hall has the proportions of the golden section

→ Main article: Golden ratio

Many works of ancient Greece are seen as examples of the use of the golden ratio, such as the front of the 447-432 BC. Parthenon temple built under Pericles on the Acropolis of Athens . Since no plans have survived for these works, it is not known whether these proportions were chosen consciously or intuitively.

There are also numerous examples of golden proportions in later eras, such as the facade of the gate hall in Lorsch (770 AD).

The view that the golden ratio is identical to proportion is wrong from a categorical perspective. At the same time, the golden ratio has a significance for the aesthetic effect ( conciseness of shape ) of objects in architecture, culture, art, nature and all other areas that can hardly be underestimated .

Human proportion

Proportion scheme of the human figure according to Vitruvius - sketch by Leonardo da Vinci , 1485/90, Venice, Galleria dell 'Accademia

Vitruvius , Leonardo da Vinci and Le Corbusier found the basis of their systems of proportions in the human figure. Here all sizes (and partial sizes) were related to each other. From 1940, Le Corbusier developed a uniform system of measurement based on human measurements and the golden ratio. He published it in 1949 in his work The Modulor , which is counted among the most important writings in architectural history and theory .

Compilation of the proportions

The table below shows proportions (selection) arranged from square to double octave. Theoretically there are an infinite number of proportions in this area, but the individual can hardly be distinguished from humans. The background colors assign the proportions to certain systems of proportions.

  • yellow-orange = golden ratio
  • white = musical proportion
  • gray = root proportion
  • lilac = musical and root proportions
designation relationship comment
square 1: 1,000 Musical proportion: Prim
Size second 1: 1.125 Musical proportion 8: 9
Minor third 1: 1,200 Musical proportion 5: 6
Size third 1: 1.250 Musical proportion 4: 5
Fourth 1: 1.333 Musical proportion 3: 4
Root of 2 1: 1.414 Root diagonal from a square
Fifth 1: 1,500 Musical proportion 2: 3
Kl. 6th 1: 1.600 Musical proportion 5: 8
Golden cut 1: 1.618 -
Size Sixth 1: 1.667 Musical proportion 3: 5
Root of 3 1: 1.723 Root diagonal from rectangle from root 2
Minor seventh 1: 1,800 Musical proportion 5: 9
Size Seventh 1: 1.875 Musical proportion 8:15
octave 1: 2,000 Musical proportion 1: 2, root of 4
Small None 1: 2.133 Musical proportion 15:32
Size None 1: 2.250 Musical proportion 4: 9
Root of 5 1: 2.236 Root diagonal from double square
Kl. Decime 1: 2.400 Musical proportion 5:12
Root of 6 1: 2.450 -
Decime 1: 2,500 Musical proportion 2: 5
Undezime 1: 2.667 Musical proportion 3: 8
Duodecime 1: 3,000 Musical proportion 1: 3
Double octave 1: 4,000 Musical proportion 1: 4, root proportion from 16

Proportion analysis

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

The architect Rob Krier pointed out this problem; During his studies he made a survey of the cathedral of Auxerre. He was able to find different systems of proportions in distinctive shapes on this building. So he found convincing proportions from the triangulature, the golden section and certain numerical relationships.

When an earthquake in 1981 caused severe damage to the Parthenon on the Acropolis, ETH Zurich organized a symposium that brought together experts from around the world who had researched the Parthenon. It turned out that there were over 50 different measurements, all of which differed from each other, not even a uniform foot measurement could be determined, they varied from 29.7 cm to 32.8 cm. From the evaluation, Erich Berger, the editor of the reader, created a useful list of quality features for proportion analyzes:

  • An exact measurement must be made.
  • The dimensions determined are to be transferred to the historical dimensions of the time.
  • The structure must be examined to see whether there have been major modifications or repairs in the meantime , or whether and where the craftsmen worked with tolerances at the time.
  • Written statements from the building owners or planners at the time would be helpful.

literature

  • Andri Gerber, Tibor Joanelly, Oya Atalay Franck: Proportions and perception in architecture and urban planning. Publisher: Reimer, Dietrich Berlin 2017, ISBN 978-3496015819 .
  • Andreas Gormans: Geometria et ars memorativa: Studies on the meaning of circles and squares as components of medieval mnemonics and their history of impact using selected examples. Diss. Phil. Aachen 1999.
  • Paul Frankl, Gothic Architecture. Harmondsworth / Baltimore, 1962
  • Konrad Hecht: Numbers and Measures in Gothic Architecture. Hildesheim 1979.
  • Paul von Naredi-Rainer, Architecture and Harmony. Number, measure and proportion in western architecture . 6th edition. Cologne 1999.
  • Joachim Langhein, Traditional Architecture and Proportion. http://www.intbau.org/archive/essay10.htm , 2005/2009
  • Stefan Gerlach: proportions in the Gothic? To the state of affairs. In: Architectura. 2/2006 (2007), pp. 131-150.
  • Rudolf Wittkower: Basics of Architecture in the Age of Humanism. 2nd Edition. Munich 1990 (first time in English, London 1949).

Individual evidence

  1. ↑ Paul of Naredi Rainer: Architecture and harmony. P. 138 f.
  2. ^ Plato, Timaios c7 to c20
  3. ^ Andrea Palladio: Four books on architecture. Venice 1570. (German Munich / Zurich 1983, ISBN 3-7608-8116-5 )
  4. ↑ Roger Popp: The mediocrity in architecture. Hamburg 2005, ISBN 3-8300-1973-4 .
  5. ↑ Andrea Palladio: The four books on architecture. Zurich / Munich 1983, ISBN 3-7608-8116-5 , p. 133.
  6. ^ Lionel March: Architectonics of Humanism. Chichester (West Sussex) 1998.
  7. ↑ Roger Popp: The mediocrity in architecture - nature, meaning and application from antiquity to the Renaissance. Hamburg 2005, ISBN 3-8300-1973-4 .
  8. ↑ Roger Popp: The mediocrity in architecture. Hamburg 2005, ISBN 3-8300-1973-4 .
  9. ↑ The development of the theory of proportions as a reflection of the development of style. In: Erwin Panofsky: Essays on art history. Berlin 1985: “Studies with questions of proportion are mostly received with skepticism. ... The mistrust is based on the observation that research on proportions is all too often subject to the temptation to read something out of things that it has put into it. "P. 169.
  10. ^ Rob Krier: About Architectural Composition. Stuttgart 1989, ISBN 3-608-76266-3 , pp. 236-254.
  11. ↑ Compare Hansgeorg Bankel in Erich Berger, p. 33.
  12. ↑ Erich Berger (Ed.): Parthenon Congress. Basel 1982. von Zabern, Mainz 1984, ISBN 3-8053-0769-1 .