arch 6390: t a of proportion - denver, colorado study ancient and modern as well as eastern and...

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ARCH 6390: THE ART OF PROPORTION

Semester: Spring 2011Type: SeminarCredits: 3Schedule: to be determinedLocation: to be determined

Instructor: Cameron P Kruger AIAPhone: 720-937-3127E-mail: [email protected] hours: by appointment

Proportion is "the key to the whole complex affair of architecture" and the "fuel which drives the whole machinery of beauty."–Sir Edwin Lutyens

INTRODUCTION

This seminar will focus on the use of proportional systems in the design of buildings. We will look at systems used in Classical architecture as well as Modern. The primary goal of this seminar is to provide students with usable techniques for developing sound, economical, and beautiful building. I will base grades on a series of graphic assignments; there will be no exams. Students will work individually.

TEACHING PHILOSOPHY

I believe that the only way to understand building fully is through drawing. I will place considerable emphasis on graphic analysis and generation in both traditional and digital forms of drawing.

CONTENT

This seminar will survey the wide variety of proportional approaches to architecture. We will study ancient and modern as well as Eastern and Western systems of proportion.

You will gain an understanding of these proportional systems by completing a series of graphic exercises designed to cover the essential aspects of each system studied.

The primary assignment will be the construction of a classical column drawing in the style of the École des Beaux-Arts.

mailto:[email protected]

ARCH 6390: THE ART OF PROPORTION of 16

LEARNING OUTCOMES

1. Become familiar with the basic proportional strategies of Classical architecture, including the Golden Section rectangle, the root rectangles, the column module, and geometric ratios

2. Become familiar with the basic proportional strategies of Modern architecture, including Le Corbusier’s Modulor, Frank Lloyd Wright’s tartan grid, and other grid-based systems

3. Understand the similarities and differences between Classical and Modern approaches to proportion

4. Study how to rationally compose buildings and building components according to proportional systems

5. Learn how to construct and ink-wash a Classical column

ASSESSMENT (EVALUATION AND GRADES)Your final grade for the term will be a weighted average of the grades you receive on each assignment completed during the semester. See the semester schedule for grading weight by assignment.

I will base your grade on a comparison with the work of other students in the course; with the work of students who have previously taken the course; with my expectations relative to the course objectives described herein; and on the clarity, craft, and completeness of the work. I will not consider individual progress.

I will post grades on CU’s Blackboard website sometime between the assignment due date and the next class meeting. To calculate weighted averages, I translate letter grades to numerical values and back to letter grades following the default Blackboard protocol. If you wish to know more about this procedure, refer to Blackboard or ask me.

REQUIREMENTS

See the “Texts and Readings” section below for required texts. See the individual assignment descriptions for specific material requirements.

In addition to any specific format requirements, you must submit all assignments in digital form. See the Portfolio Requirements section at the end of this syllabus for more detail.

You must have new work to present at each class meeting. I will consider failure to present new work an absence from class. Plot all digital work on paper for class critique.

You are required to provide your own drawing and model making materials.

In general, I prefer concise presentations. Bear this in mind when preparing your presentations. To quote Cicero: "If I had had more time I would have written less.”


I reserve the right to make changes to schedule dates and assignment specifics identified in this syllabus as the term progresses.


ASSIGNMENT 1: SACRED RECTANGLES

"Let this be plain to all: design, or as it is called by another name, drawing, constitutes the fountain-head and substance of painting and sculpture and architecture and every other kind of painting, and is the root of all sciences. Let him who has attained the possession of this be assured that he possesses a great treasure…”

–Michelangelo

Prepare a presentation-quality design study based on a sacred rectangle.

The sacred rectangles include the Golden Section rectangle, the root-two, root-three, root-four, and root-five rectangles. We will discuss this geometry in class. Kimberly Elam also explains these geometries in some detail in her book.

You may use media of your choice, but you must be able to display your work on the wall. Your study should be suitable for display in an art gallery.

You will find a number of examples posted on Blackboard by students who previously took this class.


ASSIGNMENT 2: THE CLASSICAL COLUMN DRAWING

"I do not know what meaning classical studies could have for our time if they were not untimely – that is to say, acting counter to our time and thereby acting on our time and, let us hope, for the benefit of a time to come."

–Friedrich Wilhelm Nietzsche, "On the uses and disadvantages of history for life," 1874.

Contemporary architectural design is essentially meaningless without an appreciation of the mythical backdrop of the Classical Orders. Even today, many architects argue that to do architecture is to do Classical Architecture.

Before starting your drawing, choose a recognized source to base your work on. You can follow Palladio, Chambers, or any other recognized authority that provides complete dimensions. You must also select which order you are going to draw: Tuscan, Doric, Ionic, Corinthian, or Composite.

Next, construct – do not trace – the column in graphite on paper. Note that Palladio gives the dimensions in modules and minutes. A module is the diameter of the column shaft where it meets the base. A minute is one-sixtieth of a module. Make your drawing no larger than 20”x28.” Note also that Palladio makes an exception for the Doric.

Once you have finished constructing the column, construct shadows in accordance with McGoodwin.

The heart and soul of the Beaux-Arts presentation technique was the ink-wash. You will learn this technique through a series of demonstrations in class.

Materials List:1. Ink: permanent India, (1) bottle, with eye-dropper, Windsor & Newton or equal2. Watercolor: Rose Madder, (1) tube, Windsor & Newton or equal3. Brushes: pointed, Richeson polyester or equal, (1) #4 and (1) #12 and (1) #244. Watercolor block: 9” x 12” minimum, cold pressed, 140-pound, 100% rag, Arches or

equal5. Paper: watercolor, approximately 22”x30,” cold pressed, 140-pound, 100% rag,

Strathmore Gemini or Lanaquarrel or Arches or equal6. Glue: Lineco Neutral pH White Adhesive or Sobo glue7. Board: solid core drawing board, 24” x 32” x ¾” minimum solid core board (treat

surface with satin-finish latex sealer)8. Sponge: large and brand-new9. Paper towels10. Containers: (6) small

Practice your ink-wash technique by following the exercises described in the class demonstrations. For the simple wash exercise, study the difference between various


dilutions and multiple washes. Draw 1½-inch squares and try washes with 1, 2, 4, 8, 16, and 32 drops and with 1, 2, 4, 8, and 16 washes.

Once you are comfortable with your ink-wash technique, stretch a piece of paper and once more construct the column and shadows. For your construction lines, use a light line weight that will not take away from the final drawing but that will be visible at all stages of the process.

Please make take note of the following (rules of piquage). All washes should be graded. The edge of the shadow furthest from the casting edge will be darkest because reflected light will fill the shadow area closest to the casting edge. It is easier to run washes from light to dark. Openings should be sharply graded from the top down if the plane they occur in is in full light and from the bottom up if they are in a plane which is in shadow. Shadows on walls fade in intensity as they approach the ground plane, because reflected light is most intense near the reflecting surface. Accent the shadows, i.e., increase the intensity of shadows at their extreme edges on elevation drawings, reversing the operation on plan drawings by starting the shadow in its full intensity and grading it out suddenly to nothing. Render near objects darker in tone than objects farther away. Render steps, in plan, darker as they go down. Render steps, in elevation, darker as they come forward. Vertical shadows such as cast by columns, salient features, castings around door and window openings, etc. should be graded from dark at the top to very light at the bottom. Render grilles covering doors, windows, etc., dark at the top to light at the bottom, and reversing the background or shadow, making it light at the top to dark at the bottom.


ASSIGNMENT 3: BUILDING ANALYSIS

Study one of the following systems of building design. Apply your understanding of the system to construct a detailed proportional analysis of a building. Look carefully at the point of control, e.g: centerline of structure versus face of finish.

The Column ModuleGreek and Roman temples were laid out based on column modules and minutes. Use what you learned in the Classical column exercise as well as what Palladio explains to prepare a proportional analysis of a building from Antiquity.

Sacred RectanglesMany Classical and Renaissance buildings were composed based on the geometry of the Golden Section rectangle or one of the root rectangles. Note that in the Middle Ages, the ratio of 7:5 was typically used to approximate the square root of two in ad quadratum constructions; and the ratio of 7:8 approximated the square root of three over two (the square root of four) in ad triangulum schemes. Prepare an analysis of a building that follows these principles.

Harmonic or Geometric ProportionsMuch has been made of the relation between music and architecture. A closer look reveals that musical harmony does not involve the Golden Section. In fact, the Golden Section is not to be found in Vitruvius, Alberti, Serlio, or Palladio, all of whom show clear preferences for commensurate ratios. Palladio makes great effort in his Four Books to explain his geometric proportioning system. Analyze a Palladian or other building that exhibits such a system.

Equilateral TrianglesInvestigate the role of the equilateral triangle in Italian Gothic and high-Victorian architecture. Alternatively, study Borromini’s Roman Baroque San Carlo alle Quattro Fontane or Sant‘Ivo. Both derive from a combination of circles and equilateral triangles.

The Japanese Tatami MatTraditional Japanese structures are laid out on a modular system derived from the woven straw Tatami mat, which was typically 71 inches by 35.5 inches by 2 inches in size. The consistent use of these mats led to a building proportional system of 2:1. Analyze a traditional Japanese structure based on the Tatami mat.

Wright’s Tartan GridWright is famous for his use of the so-called “Tartan Grid,” which allowed him to organize servant and served spaces into a unified composition.


Giuseppe TerragniTerragni is well known for his carefully proportioned designs. Under Colin Rowe, Peter Eisenman put together a detailed analysis of this great Italian’s work.

Le Corbusier’s Le MODULORCorbusier developed this system as an update to Classical planning proportioning systems. It utilizes a red and blue scale in an attempt to cover the variety of problems an architect typically encounters.

Rudolf Schindler’s Four-Foot GridSchindler, a builder as well as an architect, worked out this system to accommodate standardized modular building components such as plywood and drywall panels. He ordered most of his house designs with a three-dimensional four-foot grid. However, he also worked with two-foot, three-foot, five-foot, and 37-inch grids on specific projects. Working with the four-foot grid, human height is 1-1/2 units or 6'-0," door height is 1-2/3 units or 6'-8," room height is 2 units or 8'-0." Fractional units of 1/2, or 24;" 1/3, or 16;" and 1/4, or 12" make up the rest of his standardized system, requiring limited dimensioning of drawings. Note also that Schindler often composed his building elements according to an interlocking rhythm based on fractions of his four-foot module: for example, 12,” 4,” 8,” 8,” 4,” 12” – or, put another way: 3 + 1 + 2 + 2 + 1 + 3.

Harwell Harris’s Three-Foot GridHarris developed this system as a way of working with one of the most human components of any building: the door.

Mies’s gridsStudy Mies’s Barcelona Pavilion. He supposedly designed it on 110-centimeter-square paving blocks, but they vary in dimension from 81.6 centimeters to 114.5 centimeters.

Spend as much time as necessary to create a museum-quality drawing that clearly explains the proportioning system employed. Note that it often takes more time to abstract a drawing to its essentials than simply including everything one can think of. I must approve your proposal before you begin work. Media choice is yours.


TEXTS AND READINGS

RequiredElam, Kimberly. Geometry of Design. New York: Princeton Architectural Press, 2001.Palladio, Andrea. The Four Books on Architecture. Translated by Robert Tavernor and

Richard Schofield. Cambridge, Massachusetts: The MIT Press, 1997.

Highly RecommendedAd Quadratum generation (1999):

http://www.cooper.edu/engineering/me/sphere/adquad2.html. Clark, Roger H. and Michael Pause. Precedents in Architecture. New York: Van

Nostrand Reinhold, 1985; Second edition, Wiley, 1996.Le Corbusier. Le Modulor and Modulor 2. English edition.The Gabriel Prize: http://www.gabrielprize.org/index.php. Hambidge, Jay. The Elements of Dynamic Symmetry. New York: Brentano’s, 1926.Hersey, George L. Architecture and Geometry in the Age of the Baroque. Chicago: The

University of Chicago, 2000.The Library of Congress, Historic American Building Survey:

http://lcweb2.loc.gov/ammem/collections/habs_haer/.McGoodwin, Henry. Architectural Shades and Shadows. Boston: Bates & Guild Co,

1904; Washington, DC: AIA, 1990.March, Lionel. Architectonics of Humanism: Essays on Number in Architecture.

Chichester: John Wiley & Sons, Academy Editions, 1998.March, Lionel and Judith Sheine, editors. RM Schindler: Composition and Construction.

London: Academy Editions, 1993.Microsoft PowerPoint Viewer 2003 (2005):

http://www.microsoft.com/downloads/Search.aspx?displaylang=en.Padovan, Richard. Proportion. New York: Spon, 1999.Raynolds, Mary and Brian Betsill. Constructing and Shading the Doric Order. 2004.Roma Antiqua: Forum, Colisée, Palatin. Paris: Ecole nationale supérieure des Beaux-

Arts, 1985.

SuggestedAlberti, Leon Battista. On the Art of Building in Ten Books. Translated by Joseph

Rykwert, Neil Leach, and Robert Tavernor. 1755; Cambridge, Massachusetts: MIT, 1988.

Brown, Frank C., Frank A. Bourne, and J.R. Coolidge. Study of the Orders. Revised edition. Chicago: American Technical Society, 1948.

Chambers, William. A Treatise on the Decorative Part of Civil Architecture. 1791; New York: Benjamin Blom, 1968.

Drexler, Arthur, editor. The Architecture of the Ecole des Beaux-Arts. New York: The Museum of Modern Art, 1977.

Edwards, Edward B. Pattern and Design with Dynamic Symmetry (Formerly Titled Dynamarhythmic Design). The Century Company, 1932; New York: Dover, 1967.

http://www.microsoft.com/downloads/Search.aspx?displaylang=en

http://lcweb2.loc.gov/ammem/collections/habs_haer/

http://www.gabrielprize.org/index.php

http://www.cooper.edu/engineering/me/sphere/adquad2.html


d’Espouy, Hector. Fragments from Greek and Roman Architecture. New York: W.W. Norton, 1981.

Hersey, George. The Lost Meaning of Classical Architecture: Speculations on Ornament from Vitruvius to Venturi. Cambridge, Massachusetts: MIT, 1988.

Jacques, Annie and Riichi Miyake. Les Dessins d’architecture de l’Ecole des Beaux-Arts. Paris: Arthaud, 1988.

Krier, Rob. Architectural Composition. New York: Rizzoli, 1988.Middleton, Robin, editor. The Beaux-Arts and Nineteenth-Century French Architecture.

Cambridge, Massachusetts: MIT, 1982.Onians, John. Bearers of Meaning: The Classical Orders in Antiquity, the Middle Ages

and the Renaissance. Princeton New Jersey: Princeton University Press, 1988.Paris, Rome, Athens. Paris: Ecole nationale supérieure des Beaux-Arts.Serlio, Sebastiano. The Five Books of Architecture. 1611; New York: Dover, 1982.Summerson, John. The Classical Language of Architecture. Cambridge Massachusetts:

MIT, 1963.Vitruvius, The Ten Books on Architecture. Translated by Morris Hicky Morgan.

Cambridge, Massachusetts: Harvard, 1914; New York: Dover, 1960.Vitruvius, On Architecture. (2006):

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/home.html.Wright, Frank Lloyd. Drawings and Plans of Frank Lloyd Wright: The Early Period

(1893-1909). Berlin: Ernst Wasmuth, 1910; New York: Dover, 1983.

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/home.html


SCHEDULE

Wed Jan 17 IntroductionLecture 1.1: golden section & root rectangles

Wed Jan 24 Pin-up 1: Rectangles (5% of grade)Lecture 2.1: column constructionStudio Session: column construction

Wed Jan 31 Pin-up: constructed columnLecture 3.1: ad quadratum & ad triangulumStudio Session: column construction

Wed Feb 7 Pin-up: building precedentsDemo 2.2: shadow castingStudio Session: shadow casting

Wed Feb 14 Pin-up: draft shadow studyDemo 2.3: stretching paper

Wed Feb 21 Pin-up: final shadows & stretched paperDemo 2.4: simple ink-wash

Wed Feb 28 Pin-up: simple ink-washesDemo 2.5: graded ink-wash

Wed Mar 7 Pin-up: graded ink-washesDemo 3.2: Schindler wall sections

Wed Mar 14 Pin-up: column & shadow constructionDemo 2.6: example books, ruling pen

Wed Mar 21 Spring Break

Wed Mar 28 Pin-up: partially rendered column Demo 3.3: Japanese Tatami mats

Wed Apr 4 Pin-up 2: Classical Column (55% of grade)Demo 3.4: Classical proportions

Wed Apr 11 Pin-up: proportional analysis of buildingDemo 3.5: Modern proportions

Wed Apr 18 Pin-up: layout of proportional analysisDemo 3.6: presenting proportional analyses

Wed Apr 25 Pin-up: sketch of final proportional analysisCritique: small group critiques

Wed May 2 Pin-up: final analysis progressCritique: small group critiques


Wed May 9 Pin-up 3: Building Analysis (40% of grade)

Note: Dates to be revised to match Spring 2011 calendar.


PROFESSIONAL PROGRAM ACCREDITATION CRITERIA

The following are the NAAB Student Performance Criteria identified by the College for this course.

2 Graphic SkillAbility to employ appropriate representational media, including computer technology, to convey essential formal elements at each stage of the programming and design process

4 Critical Thinking SkillsAbility to make a comprehensive analysis and evaluation of a building, building complex, or urban space

9 Use of PrecedentsAbility to provide a coherent rationale for the programmatic and formal precedents employed in the conceptualization and development of architecture and urban design projects

10 Western TraditionsUnderstanding of the Western architectural canons and traditions in architecture, landscape, and urban design, as well as the climatic, technological, socioeconomic, and other cultural factors that have shaped and sustained them

16 Formal Ordering SystemsUnderstanding of the fundamentals of visual perception and the principles and systems of order that inform two- and three-dimensional design, architectural composition, and urban design


POLICIES, RULES, AND REGULATIONS

Students with DisabilitiesStudents with disabilities who want academic accommodations must register with Disability Resources and Services (DRS), 177 Arts Building, 303-556-3450, TTY 303-556-4766, FAX 303-556-2074. DRS requires students to provide current and adequate documentation of their disabilities. Once a student has registered with DRS, DRS will review the documentation and assess the student's request for academic accommodations in light of the documentation. DRS will then provide the student with a letter indicating which academic accommodations have been approved. Once you provide me with a copy of DRS's letter, I will be happy to provide those accommodations DRS has approved.

Absences, Tardiness, Quizzes and Examinations, and HomeworkExcept for documented health or disability reasons, I will not accept excuses for absences, tardiness, missed examinations, or homework not submitted. Documentation of disability or health related issues must be provided to Disability Resources and Services, 177 Arts Building, 303-556-3450, TTY 303-556-4766, FAX 303-556-2074.

Classes begin and end on time. One absence will be allowed before an academic penalty of one-half grade reduction is imposed. If you are late to class and/or leave class early more than one time, an academic penalty of one-half grade reduction will be imposed. Homework, papers, projects, or any other required assignments that are turned in late will receive one grade reduction for every day they are late. Any student who misses quizzes and/or examinations or fails to turn in homework and/or papers will receive an F for the work missed.

Classroom DecorumThe following ground rules apply to all students and are designed to ensure a classroom environment conducive to learning for all students:

1. Pagers, beepers, cellular telephones, and handheld internet devices must be deactivated before class begins and remain deactivated throughout the entire class period.

2. Do not bring children to class.3. Students who engage in disruptive classroom behavior will be reported to the Office

of Student Life for appropriate disciplinary action under the CU-Denver Code of Student Conduct and, when appropriate, to the Auraria Campus Police for investigation of possible criminal action. The Code of Student Conduct can be found on the CU-Denver website, under Office of Student Life and Student Activities. Disruptive behavior includes, but is not limited to, arriving late to class without explanation or apology; leaving class early without explanation or apology; reading a newspaper or magazine; reading a book with no connection to the content of the course; engaging in prolonged private conversations; sleeping in class; eating, drinking, and/or gum chewing; passing notes; being under the influence of drugs or


alcohol; harassment or verbal or physical threats to another student or the instructor; failing to deactivate pagers, beepers, cellular phones, and/or handheld internet devise; bringing children to class.

Special thanks to Taisto H. Mäkelä for his contributions to this course and syllabus.

© Copyright by Cameron P Kruger, AIA, 2005. All rights reserved.

Students are prohibited from selling, or being paid by any person or commercial firm, for taking notes or recording class lectures without the advance express written permission of the faculty member teaching this course. Exceptions are permitted for students with a disability who are approved in advance by Disability Resources and Services for note taking or tape recording as an academic accommodation.


PORTFOLIO REQUIREMENTS

Submit all assignments in digital form according to the following directions. Failure to adhere to these requirements will result in an Incomplete for the assignment.

Email me your digital files by the class meeting following their due date, typically. Email files for the final assignment within two days of the assignment due date. Alternatively, submit files on CD-ROM to me in class or to my mailbox on the third floor.

When emailing to my Gmail account, please be aware that I cannot receive messages larger than 10 megabytes. If you are attaching multiple files, you may need to send multiple emails or compress your files using WinZip.

Submit JPEG files of all work. Do not submit any other file type. To create JPEGs in AutoCAD, type “JPGOUT” on the command line. For models, provide a minimum of three images of each model presented: a bird’s eye view, a street-level view, and a plan view.

When creating JPEG files from scans, use a minimal resolution of 1600 x 1200 pixels at 150 dots per inch. Save each file as JPEG Quality 10 (maximum).

When creating JPEG files from digital camera, use a minimal resolution of 2048 x 1536 pixels (3.3 mexapixels). Save each file as JPEG Quality 10 (maximum).

Your JPEG files should be between one and four megabytes in size. Smaller files will lack necessary detail and resolution unless the drawing itself is small. Larger files take too much memory.

When naming files, begin the file name with your full name, first then last. Follow your name with a one or two word description of your subject. Follow that with numerals for multiple images. For example, if you are submitting three images of a Doric column and you name is Cameron Kruger; you would name your files Cameron Kruger – Doric 1.jpg, Cameron Kruger – Doric 2.jpg, and Cameron Kruger – Doric 3.jpg.

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