Architectural Theories of Design

In the architectural example below, the rectangular windows and door contrast with
each other in the matter of size.

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u uJJi ,ul
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rU

r 1 ~ r=1 r==; r= I1
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rectzmglec.:;

4. CONTRAST OF TONE
Tone may be secured by contrast of texture, openings, or planes.

The exterior of the building is given interest on account of the contrast between the
dark roof and the light walls. This feeling is strenghtened by the introduction of the
darks of the openings and by the shadows cast by the projecting wings of the build-
ing. Contrast of tone is secured in the examples below of abstract design, by the use
of black and white, or gray and white, areas.

88

COMBINATIONS ... . .. .

An architectural composition is presented which illustrates in a combined way some of the
various types ot contrast. There is, first of all, contrast of mass - not only with references
to whether it is cylindrical or rectangular , but also with reference to the direc tion of the mass
or volume. The entire composition is decidedly horizontal ; but variety is secured by the ver-
tical direction of the tower, of the end wings, and the chimneys. Contrast of shape is also
present in the rectangular and arched openings of the building, and contrast of ton e is
secured by the darks and lights of the roots, walls, and w indows.

CONTRAST is the opposite of SIMILARITY . If similarity exists to a marked degree, the ef-
fect is monotony . The facade of a building may consist of a simple, unadorned wall pierced
with many uninteresting windows, and the effect may be very monotonous. On the other
hand, it is--possible to go to the other extreme and to have contrast which is too violent. Pi -
laster, belt courses, and decoration may be used too profusely. The resul t will.be a restless
disorganized design which lacks repose . It is thus, necessary that contrast be present in and
just the correct amount: enough to give variety but not an excess; which will cause confu-
sion.

89

CONTRAST IN ARCHITECTURAL SUBJECT:

1. CONTRAST OF MASS

D0tt1it1at1t element

Vertic(~! volu111e
,Tower

This figure show an interesting combination of rectangular masses based upon con-
temporary practice. Here there is contrast of vertical and horizontal volumes giving a
composition in abstract form which becomes capable of housing human interests
through the introduction of windows, doors, and floor levels. A pleasing composi-
tion is secured chiefly by the relationship which exists between the various block-like
units of the buildings and by the disposition of the windows which give interest to
the surfaces of the masses.
In this figure, attention should be called to the manner in which the eye is carried
along to the tower by means of a series of minor vertical units which prepare one for
the climax of the dominant element near the centre. Consideration should also be
given to the horizontal treatment of the windows on the left, which emphasizes the
direction of that portion of the building and opposes the vertical feeling of the forms
near the main entrances.
It is well to remember that contrast is opposition. If verticals did not oppose horizon-
tals, if openings did not differ from wall, and if accents did not successfully compete
for the interest of the observer, contrast would not exist.
There is also here a transition in the relationship between masses . This situation is
shown where the adjacent volumes prepare the observer for the dominant vertical
near the centre of the composition.

2. CONTRAST OF DIRECTION

Here again is an interesting contrast between the horizontal direction of the compo-
sition and the dominant vertical accent of the tower, which is called the major con-
trasting element, while a minor vertical is to be seen at the left. The termination of
the tower gives additional emphasis and contrast to that part of the structure.
There is also present in this connection contrast of tone, which is seen in the deco-
rative treatment of the upper and lower portions of the tower. Interest in other parts
of the facade is secured by the contrast of the windows with the wall surfaces. In the
wing at the right, the upper windows are pointed and are larger than the rectangular
ones below, while at the left the arched openings with balconies are surrounded by
large areas of wall space which again give variety and contrast.

~0

_r,.,.,.-r,-,.~-r of wiHdJW a11d wall -5p~
ofeon+ra~t Tun:;jliiti&ii:il

Minor vertr'cal

It is also necessary that the various units in plan should vary in size and projection in
order that a monotonous exterior effect may be avoided. The different elements
must be wide or narrow. long or short. so that some may be more important than
others . In addition, there should be a variation in the projections of the various parts
of the plan , in order that the proper emphasis may be secured.

3. CONTRAST OF CHARACTER

wmdow;

DOME 7 iiC

~ma liar eKtr.attc.e

The church and the parish house must be similar in general feeling, but the use of the
various architectural details must express the different function of each particular
structure. The church must have ecclesiastical character and the parish house must
harmonize with the former, but not to such an extent that it might be mistaken for a
place of worship. This calls for a subtle balance of contrast and similarity - the con-
trast of character.

Here the spire of the church which we associate with ecclesiastical buildings gives a
suggestion of function, and the import ant entrance indicates the public character of
the structure. The house has smaller w indows than the church, their size being regu-
lated by the interior which they are to light. Tt,e shutters and chimneys impart a
touch of domesticity and intimacy which would not be desirable in the church and
which is lacking therein . Contrast of direction is also present . The church is vertical,
whereas the parish house is horizontal. Contrast of size is evident - the large church
over the smaller dwelling.

91

4. CONTRAST OF TREATMENT
a. same material used in different treatment

- t,it Qth--1--.-._.l In this drawing, there is found contrast based, not
1-Cr- on direction or mass, but upon the handling of the
8E eth::l::r ~ R[:::5= various surface. Interest is secured by changing the
fr-1--r- character of the treatment of the upper and lower
L~ nlr--:-rr:::r:=r portion of the facade. The rustication of the lower
fl oor is heavy in character and horizontal in direc-
1:2--r: tion_ The treatment of the upper floors is more re-
l:r:-5= fined in its use of detail, and a vertical feeling is se-
cured by the use of columns and pilasters. The arch
"' entrance also offers the quality of variety when
used with the rectangular door and windows, while
~ I. _,_ _I_ t-r contrast or opposition is secured by the upward
thrust of the columns against the inert weight of
~ ~ .t~yiJ-4<u :I the entablature.

0 1Y1'1Q~.l~ ..1 I b. contrast of pattern different materials
1
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lg~ 1 RI i _l
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g9 II
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This face is based upon old Persian brickwork rs
and shows contrast of tone secured by the al-
ternating pattems of brick and stone. Ac-
cents are also obta ined by the change in di-
rection of the voussoirs of the lower arches.

92

c. contrast of area

The general direction of the building is horizontal, but the treatment of the exterior is given
variety by the introduction of vertical piers. In the roof, the lines of the tile oppose the horizon-
tal direction of the roof itself. A satisfactory contrasting relation exists between the width of
the windows and that of the piers. The piers are wider than the windows and provide for dissi-
milarity of surface, or an interesting proportion of parts.
It is evident that contrast result from dissimilarity, or the association of unlike masses, areas
or tones. Contrast is also opposition -opposition by which one element w ages a successful
battle against competing elements. One shape or color clearly dominates the others. This con-
dition may also be called emphasis , but this emphasis must be present in just the proper
amount. If a doorway, a window, or a panel seems to detach itself from the wall or appears
to be unrelated to the rest of the composition, it may be too emphatic in its appeal. The ele-
ment of contrast is too strong.
There is not a satisfactory transition between the surrounding wall surface and the dominant
architectural motif. Therefore, although contrast is essential to a unified composition, transi-
tion should always tend to alleviate the burden imposed by excessive and sudden changes in
treatment. M ouldings and decorative details should have structural or circulatory elements,
and belt courses, cornices, and quoins should help one surface to member gracefully wit h
the next ·and assist in tying t he entire arrangement together in a pleasing and interesting
manner.

93

PROPORTION . .. • • • relationships

PROPORTION

Proportion is largely a matter of relationships. It is evident by a comparison which the eye
makes between the size, shape, and tone of various objects or parts of a composition. These
are certain geometrical forms which have very definite proportions. These are the:

circle, Triangle and the square

The eye judge them quickly and classifies them with no difficultly.

Just as a circle is more evident and less intriguing than a freehand curve , so is a square less
interesting t han a rectangle. However a rectangle should very definitely take on the propor-
tions of that particular shape. It should not approach a square in its dimensions, because a
state of doubt will exist in the mind of the observer as to its classification.

l too long

DRECTANGLE

too short

The eye will be unable to decide whether it is a square or a rectangle. On the other hand of
the roctangle becomes too long, it approaches the area of two squares, and there is an un-
conscious tendency for the eye to divide it into two equal space. Thus there is competition
b~tween the two parts. To get the most pleasing rectangular porportion. The golden section
or (Goden mean} was introduced.

94

THE GOLDEN SECTION

Defined geometrically as a line that is divided such that the lesser portion is to the greater as
the greater is to be the whole.

a square ~/ 1"'-- then take the diapna!
of the half square .
/ I "-.

".

first t ake t l1e center

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' ....., 1 I
\\ i
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11ext trat1sfer the diagonal I

to the 11orizontal or construct A al B a -c

811 arc. draw a vertical line , tl1is is

to check: 11ow The Golden Mean Recfcmgle

<f. ,1 / ;;.quare
.' 'v'

.v square the overall diagonal i9 90° irJ the
Ylew diagonal. This IS called
\
INCL U S I V E .

this 15 Exclusive

95

SOME PRINCIPLES OF PROPORTION USED
IN CLASSICAL ARCHITECTURE

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Tl1e Equilateral T~iangle llli IM one line

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The equilateral triangle, or one with eq ual sides and angles, has long been accepted as a
form with good proportions. It is static and stable. It's centre of gravity is low, and it tapers
in a regular manner from the base of the composition. a triangular arrangement in a painting,
in a sculptural group, or in an architectural massing offers a satisfactory disposition of parts.
It goes so far in insuring good results that the privelege of using it has been abused, and it is
regarded as the easiest way out of a difficult situation.

96

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Gotf1ic wi11dOW using Equilateral Triangle

If the facade of a buidling is developed in such a manner that areas of similar shaped are
repeated through the composition it may lead to a unity of treatment. A sense of harmony
will be the results of use is made of a rythmic repetition of motifs which have a common geo ·
met ric shape as a base .

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classical zmd re11aissa11ce buildit1gs snow
that a;cl1ed at1d rectat1gular openit1gs arB

iwo diameters l1ig~.

97

Classical and renaissance buildings show that arched and rectangular opening are two dia-
meters high .

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The Circle Circie and Sguare

The circle and square have been found to possess certain properties which recommend
them as a base upon which to begin a design . See figure above. It will be noticed that the
diagonals pass through important parts in the composition.

RELATIONS:

One of the most important phases of proportion and one which should be considered in the
development of a facade is the relation of the solids to the voids, of the wall surfaces to the
openings. It is necessary that one clearly dominate the other that the element of a contrast
will be present. If there is a similarity between the width of the windc;,ws and the spaces bet-
ween , indecision or competition will exist.

98

In classical , Romanesque, and Renaissance buildings, where heavy stone construction pre-
dominates. The windows and doors usua lly occupy a minor portion of the facade and the
w all surfaces are quite dominant.

When the Gothic builders learned the art and science of transmitting t he thrust or weight of
the vaults to isolated buttresses. the w alls of the cathedrais became unimportant. Large areas
of stained glass took the place of these walls, and regularly spaced piers carried the load of
the roof and vaults.

In contemporary architecture, the cantilever of concrete and steel f rees the designer from
many restrictions of masonry and construction and there is a tendency to use openings free-
ly.

This 15 a T.h ts IS a more.
lnTe_r"e~T~~
c..ommon ~~n 99

Des1~n

Example of Lack of correct proportiol1

too high

same dista11ce c

more it1teresti11g relatiot1 t?etweett ?olid~ artd void~

a' bigger

lower

==;=. Grnaller

100

Proportions May be Based on the Following Factors:

1. Natural Material Proportions
All building materials in architecture have distinct properties of stiffness, hardness
and durability. And they all have an ultimate strength beyond which they cannot ex-
tend themselves without fracturing, breaking or collapsing .

---_....

when oig artd lot1g iltis stone

will colla~ ul1der- it9 owt1

weight.

stone used aG a ftx* bridge

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.,. .....,. ~- -~ ~
,...,-

wad plank

when lortg will Saj

All materials have rational proportions
that are dictated by their inherent
strengths and weakness. Masonry
units like brick, are strong m compres-
sion and depend on their mass for
strength, and are volumetric in form
logs are also volumetric in element and
is used in log cabin construction.
Wood is flexible and is used as beams
and posts steel are strong both in com·
pression and tension.

~--+)( t
)
c

101

/ 2. Manufactured Porportions

/"-- - Many architectural elements are sized
and proportioned not only according
.~........ -,~/ to their structural properties and func-
tion, but also by the process through
Hollow blocks IS statt:iard i11 which they are manufactured. Be-
cause these elements are mass-
.size;; of .10 x. zo x-40 (4''xe'')( 1a,") - produced in factories, they have
standard sizes and proportions im-
at1d . 15 X.zo X.40 ( t/' X 8" X~") posed on them by the individual manu-
factures.

While plywood is common in 1.20 .!C
2.40 or 4' x 8' so that the spacing of
wood nailers are fitted into this sizes.

102

1.20 L .eo Doors and window units are sized and
proportioned to fit into modular ma-
sonry openings.

~~.:. .!·§+ 3. Mode of Construction or Structural
tJ ~ Proportions
siael :@
woodet1 P'5t The size and proportions of structural
~.J.pl~ elements such as beams, columns, are
po5t bigger directly related to the structural tasks
Iaiiy column they perform and can be, therefore;
visual indicators of the size and scale
T r------'J ~ ......__---4 of the spaces they help enClose.
r-~
Since beams transmit their loads nori-
zontally across space to their vertical
supports, its depth, therefore is the
critical dimension. and its depth to
span ratio, is a good indicator of its
structural role.

-

0 oo The proportion of a column may de-
pend upon the spacing or its height.
bigger co/umHs .?ma/ler columns
103
OH f1igher keigHt~ OH tower hetg~rt~

w deptk iG
alwayG bigger
COHcrete ~am
them widtk

.()5

woo:ijoist

The proportion of a truss may depend
upon its type.

CHB wall~ are tHicker tha11 reil1forced
concrete wafl.

4. Requirements of the Program, Function or Govern-
ment Ordinances
a. The proportion of the height of a room is controlled by
local building ordinances, logic and artistic sense.

I It Lobby

b. Auditorium proportions are influenced by visual and
acoustical considerations.

~f~t-.••••. · .....-······.,
....-···-·
.-·""' ········
······

104

c. Proportions between heights and areas of rooms are
controlled by the capacity and lighting requirements of
the room .

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I

I .''·.'

I ."

e diameter 5. Traditions and Generally A ccepted Taste

a. At the exterior, the height of an edifice should be in

proportion to the character th;H the edifice demanc1s .

b . Buildings of w orship such as : hurches and temples
usually have traditional proportions.

c. Classical buildings usually have proportions based
upon traditional rules.

l

0

classica l order

hig~er height
of ceili11g

higher heigHt o( door

105

Distinction between 'Relative' and 'Ab-
solute' Proportion.

WHOLE' ii

WliotE PART~

DOOR WINDOW

1. Relative Proportion -deals with the re·
lationship between the parts of an object
and the whole e)(ample ratro between the

diameter of a Classical column and its

height or the relation of the panels of the
door and the whole door.

WHOLE WKOL.E

~PART 2. Absolute - deals with the relationship

106 between the different parts of an object
or the whole to the various parts.
Example-ratio between the sizes of

H WHOLE windows and the blank walls.

Proportion of a cabinet or appliance to
the room.

The ' KEN ' modular grid is a Japanese
w ay of proportioning the size of rooms

where one MAT is 3.1 5 x 6.30 or 1 x 2 ken

in Kyo-man method. The standard Tata -
cni floor mat is 3 x 6 shaku or 1/ 2 x 1 1<en

This uses 6 shaku = 1 ken grid in the

lnaka-Ma Method.

0

PLYWOOD MAT TILE

RJ Proportions of Room Designs by Using
the KEN METHOD (Applicable in Mat,
Tiles or Standard Plywood Sizes).

ITO

3 - Mat Room

4 - Mat Room

4~ 1/2 Mat Room

t---

6 - Mat Room

107

I

l

l 8- Mat Room

1-- r---

10- Mat Room

ANTHROPOMORPHIC PROPORTIONS

These systems are based on the dimensions and proportions of the human body. Anthropo-
morphic proportioning methods seek not abstract or symbolic ratios, but functional ones.
They are predicated on the theory that forms and spaces in archite<:ture are either containers
or extensions of the human body and should, therefore, be determined by its dimensions.

The dimensions and proportions of the human body affect the proportion of things we
handle, the height and distance of things we must reach, the dimensions of the furniture we
use to sitting, working, eating, and sleeping.

In addition to these elements that we used in a building, the dimensions of the human body
also affect the volume of space we require for movement. activity and rest.

108

Le Corbusier.S ' MODULOR ' . . . . . . . osrng the Goldett Se:tiot1

In 1942 , Le corbUs·,er begat1 his study and publis11ed the ·' Modular "
a Harmo11ious Measure iD the 11umaM scale u11ivers21lly applicable

+o Architecture at1d Mecha11.1CS. He tkerefore t:ased his measuri11g

-tool , the Modt.Jior. or both mathematics (The aesthetic di111e11siotts
of tHe 6oldet1 Sectiot1 a11d the Fitx:mace1 Series) . and the pruFXJrtiol1s

Of tl1e f1uma11 oody ( FU11ctiot1al dimel15i011S). These sysiEm of
meDsurement governs leHgtl1, surfaces. at1d volumes , a11d '' Mairrtai11

-the huma11 scz:tle everywhere ." It coo!d lend itself to a11 infj11ity of

comPina-tio~s.

-lt--u'3~ 5ecot1d step Third step

First step take the ce111ter 1ransfer tl1e diagonal
a11d draw a diago11al to the b:15e
con5truct a square

.The ooldet1 I
Section ~
l
(perfect rectemgle)
[

I

Fourth I step

complete ·the rectat1gie

-70

Note : This is a formull! using 1-93m Fift11 step : from the center

or ~>-o " average Height ofa per5011 line draw a 90° Jit1e

for any neigl1t Ofa ~rso11 , use his corres~r~d1119

"avel 11eigl1t to s-tart tt1e sqJare.

109

2.26 -1.83= .4'5
1.83 - 1.40 : .43

1.40 -1.13 =.2.7
1.1'3 - .96::.27

.80 -.70:::.16

. 70 - .54 =.16

. 54 -.4'5:: .II
.4'?> - .1'>2::; .II
.'32 - .27= .OS
.2.7 - . 22~ .OS

0 - -·- - - - · -

.22 - .19: .03
_ _ _. I~J~ =.0'3

The "MODU LOR " (le corbus1ers )

.16 +.II : .'27
.27t.l6 =--43
.4'3 t.'Z7::. .70
.?ot.\6 =-.86
OO+.'Z7"' 1.1:3

1./3 tzr: r.-.o

1.40 t .27t .16:: I.93

I. 83 t .4'?l -:?28

BASED ON
1.11:5 HEIGHT

110

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ANTHROPOMETRJCS (Human Dimensicwr)

"IFURNICUBe" A Formula Discovered by tHe Auttlor as based from

Le corbus·lers MODULOR

a height of any per~ il1 Meter-5 divided by t~e Ho. 7.8'5

will give tl1e d!me11~iot1 of +11e 11ead or H.

111

SALVANS • FURN ICUBE •......... .. using Head Dimet1sio11

(as resed on Le corbusiers MODULOR)

This autl1or coi.-1ed tHe word Fur11icube from " Furniture~ a11d cube. which

is formed by perfect squares. The .9Jidet1 sectio11 is based 011 SQUARE.

As the modulor uses LS3 ( ~.'-o" ) r!eight of a pgrso11 , mostly all

furl1iture it1 tke market is ba6ed 011 th.,s standards. 1l1e author deems

it nece5sary tnen io 5eek a For-mula 1o produce a com fortatJie HEIGHTS

for a11 irtdividual person, from midget to gia11t5. attd t1ot nece55arily t:>e

forced io use 'Hte staHdard ne·lghts fbr 6 Footers.

After a serie5 of mathematical co11versio11s, trials at1d measurementG.
It is found out that huma11 bei~ is composed of 7.85 t imes hi511ead srze.
At1d so iu get your f1ead aime11sior1, measure your ban:~foot height it1
meters next divide your height by 7.8'5 this will give your head si1B
or"H:" by usi11q tl1e table below , multiply your· H'' witl1 tHe corresp?r~dil1g
fOrmula givet1 for eacl1 Fur11iture de5ired this is your most comfortable

11eigl1ts.

U R~- .. -· . I HEIGHTSOF!NDIVIDUAL

Comfortable Is'-J6'-6'-' l6'-o'' s'-e" 6'' s-,:-_-4-,:;-rs'~-o"'"4-,_-8-::-~.,
lI
1.9S~_i!.S3M f.72M p.67M 1.62M_ l.SZM 1.42M

r-- SIZE _o~~DS or' H" itt meter

1 Heights Formula 0.252 0.233 0.219 0.213 0.200 0.193 Q.IM
t - - - - · ·- . ···--!--
' Foot - -~t. - - 1- - DIS 0-16 0.15 o.1s 0.14 0 .13 0.12

stool i o.70{H) ·.. :o 29 ~- <J25 o.24 o23 o.22 0.20
11 lBoewda~tttocoflckair- ·- I 1. 158 (H)
--- ·- o 46 o.43 o.40 o.::e o.ze o.:;s a.:;;
1. ss (H)

Din{~g table- --··· _3.. (H) - ·-. 0.7? '?-70 !0.6S . 0.:~:~2_:~1 .a.s7 0.54

Office table 3.1S(H) .0.79 o.733!0.69 o.67 o.04 o.ro o.~

Coffee taole ---==--..j__-~~fH) ···-· ··ro.54 ~ 047- OAS. 0.44 o.~l o.~
: 2.95(H)
. c.art:J-fable ~-71 0.66 0.62 OW 0-=8 0.'::5 ~.51

yar . · _3.!0(H} o:~3. 0.90 o.e1· 0.78 0.70 o.2!_ ~
0.64 o.sg o.ss o.s3 to.~z 0.43 0.45
; Bar stool 2.53fH) . r-·- +---t-- -+--=->'---=.-t---i
1 - - - - - - - +-·- ......:,...-::---- --
lavaiory -·-- 0.91 .0.75 0 .70 O.GB O.f.G jO.ef 0/57
3 .22 (H)

Kitchef1 cabinet -·· -3.8S1H) 0.97 0.90 ·o.84 0.82 0.73 0.74 0.09

Railit1 - --- -- . - 3.-io(H) 0.93 0.86 0.91 0.78 O.?fi> 0.11 Q.~

Shoulder- re~t 4.Ss (H) 1.22 l.f3 l.cxo 1.03 o.gg 0.93 o.B7 ·

Anttpit ~t ___ . 6.0(H) 1.51 1.40 1.31 lt.z7·1.23iJ.J5 lOS

Height of persot1 7.8S(H) 1.98 1.83 I.B:J l!iJ7 1.61 LSI 1.41
1 9.70 (H) 244 2.26 1.99 !.972.12 ~ - 00 1.74 ,· t---·,~...,..------+---:-7"t-:--+--;--::-:-t--:-~ --::-=--t-:-::~
Vertical reac~-

112

Z. 11COAU!::> 1-70H

~- ----1

~~1 ~ () () ~
f) ~ ~EAO"--\ ~5~~ ~I - " /
p · : _.I--+--t---i-+--+-+---t-+-+--\-··- ;:
I\ I I I \ ~o- JI
.?~-:I \ It- ....
I r--..

.,1/ 'e' • •I ) 1~ ) ~II)
L
\. I !~\\ \ :% -
~ :x:
\J ' o,;v V ~ u V • -·· ---P~o\IH \ I zH ··-~\ ' \ '
';) \ lVJ ...
) .\ )J ' 1 --:;:;.

\I \ \ . : h'l\\ I~
I ;EAA ,( ~~ WJ J \~, \ JVL') ~T
\!)
I v
- - - ----~=+~....... ·-+---·· .. --\----tt---+-~---+t-<,...-- -~,...---tt---1--t----
J \' ' I ~. - . .. - ·- --f---t--+---+---
~AS-f :I:

)I .-

- - - -- -----;,..!="'V+-+.-:IM"-:i- · - . -

9YEARS }j :r

!J \ \\ \ ....

I~EARS J \~ )( ~
- - ... .. . . . --·- -- .-· -----~~ .. -- · f ' '
f - '\. r----

'/ '- ;,)'i ~ "'' / '\.. , <ih l.
~ ·~
v -- _.) •/.? H_~ Hi:EL_ALLDW~CE..J 1
, 3D HEAD ALLOWANCE FOR ~HOE:~

5

BODY SHAPE OF A
MAN AND WOMAN
1-"

"-"
(JJ

+-,-:_~~-'~,I , __ _D1"'-, ----- ---b c ',

l ......, 1', \
\
I ', ''''''''
\ 4
I ', \
\
1 a', \

I '-, \
I ' -....
\

-'

I ',.... '''''' \
\
I ~'-.... ~ f"" __ '_ \ 6
I \
\
I ,
\
I
I '3 '' 1',
I ' ' '.....
' ':5.:::~1<-.-..-.....- \
I : .... \
'
I ' '

I ~---- ' \

I \

I ---~'~ '..,. ''\

I
:
JI
c1...-- - - - ---- ' ,\'.,
8

A recta11gie wl1ose £ide.5 are proportionoo

accordi11g to the 6oJde11 s~tio11 k11owt1 .?JG a

Go!de11 rectangle

', d-1 ' , d - .2 2

" 'I"'::-- ------- - "-;1,..,,-----+- -------,

I' '
'II ' ' , '"
II ' ' , ' ',
\.

'I
'' , 1 ' 2.

II ' ' ' ,

': ",,
", ', from the goldel'1 sectio11

',, ',, draw a diagonal d-1
'" , ' ,........
:L - ---- - ----· ' ''~~ 0 at1d di;~w'w:t7:":·~-f d-2 to

-L-----~---...lt FOit1t o. tHe itttef13eeti011
of d·l witl1 tke vertical

I ' "d1 - - - - - - - - - d2. d3 edge of tl1e squa~ is
~'-,
1', point 1 . draw a
\
"': ......... \ horizontal line to

" ' '1 ' '' ' \ it1rersect d- z from
ihe p?itrt 2 draw a
\
'" ' ,' ' ""', vertical line .
' "" " "' ' ~" , \

\. \
\
"
\

\

' '' ' ' \
\!

' ' ',\
.------ ----. L_···--·---·- :1~s
· -.. -~---- L . ._

114

2

from poi~t 1, draw a horizontal li11e to it1t~

at point 2. from PJittt 2.con5truct a vertical line

1o i11ter~a:.:t at ?Jil1t ~' c<Jt145truct a horizontal

10 it1ter5eet at poitrt -'f, from p:?il1t 4- , a

115

as diagonal c. repeat tne proce~ u11til you create a

serie~ of 6q{JareG getti119 smaller proporti011ate!y

;~--------~-----­

frott1 this ?quare draw the goldet1 5a:;tiol1 io give ?Ji11tC

A B C D E F GH

1. witl1 8 at a ~ter a11d AS as the radiu5, co11~tru~t

a semi- circle to give tl1e p:>il1t D.
2. with C aG a ce11ter a11d BC aG tne radius, conEtruct

a semi- circle io give tHe poi11t E.

3. witl1 D as a ce11ter a11d CD a~ tne radius, c011struct

a semi - circle to give tHe poi11t F, at1d ~o 01'1

AB:: BC +CD

BC =CD t DE

CD~ DE t EF
DE= EF t FG

EF = FG +6H

FG = GH t HI

GH = HI + IJ

116

PROPORTIONING StST&MS

~o cp beyOHd · tke fuHctiOf1a/ attd technical determit1aHts oF

z:m:;J-trtec,tural form at1d 5pace io pruvide at1 a€ilCPthetJC, rcrl'io11i3le

for iiieir dimerr~ion6. They am vi~ally uHifY tke multiplic.lty
of erernetrt~ in 8rf architectural deGign l?y navirtg arl of it.G part;
belottg to #1e ~me family of prq:xJrtioHG.

They caH provide a §~e of order i11, at1d heignte11 the

COt1tinuity of a s-equet1ce of ~~ . They caH e£fabfi~h

refatio11ships t:Jet"\M9en -Hie extericr at1d inrenor elemeHts of a

buildil1q.
r--------------- -----------------------
1I
II

II
I1

1l

II

II
I I
I ~ 1
~--------------- ·-----------
I
II

II

I <? I
I ~I

II .,n:;r) I:

1-------- ---- ---- ---- I
11
I
1I
1 I I
I I
IIr.-Jl-' ------------ 1 I
I I

I ,_,~ I I I

I vI I I
I II
I
II
I
II I
I
II
I
II 1
I1

Il

d·3 d-4

~quaf'l? ~~tem JT, J2

J3,J4,JS

D'fNAMIC AND HARMONIC SERIES

a. DYNAMIC RECTANGLES- Wk811 GP atd AP are combit1ed ro

cot1ceive a myria::i variatioH~ . They cat1 ~ comtJit18d to

117

sit 0t1e a top tHe attfer, tkey ca11 be ~et ~~ ~it1ot1 so

that 0t1e diverges ~ tke other cotfYerge:;. They can
alternate at1d they cart ~llate . A cammot1 difr!u1:mce

or rafu cat1 be programmed oo that it i5 no longer carrmon, or

eot1$ta11t, but ~ at1 AP or 6P it1 ·rts OWM rigtft:

Exampte 1

fr()tf a ~uare 1, Y2 of tke diago11al ig tke widtn cf -tHe 11ext

square 2. Then Y2 of -Hie diag1Hal of ~re 2 will ~ the
widtH of tke next GQJa~ 3 and t;O ott

~quare-s

square-~

square-2.

square -1

b. SQUARE SYSTEM

a square of side 1 kas a dia_gonal let1gff1 =j i
-two para/lei sides cf the ~are are extended

il1definitely. Rota+i0t1 of GUc~ive diagot1al$

formG a dyttattnc GerieG of rect311gles

front a 5ka~ datum .

118

C. This dyHamic seri~ , projected itt two dimet1~ions of(e~ eJ ~rie~

of~~ witH ar~ of I,Z,3.+.!i'.~.7.... $quare unit~.

1

5ubdivisiot1 Manager

Office ~r .L.. Security office

Toilet·- t.

TL

,J"'t

5ecunty

d~1 is the fir5t diagottal with o as i+fs ceHter draw at1 arc uM+il it

re;:;c~es the diaQQ1al 1 with 1tte iJ1tersectiol1 draw a horizontal litte.
COmpleting tke Gecmd ~Uc'1m, usi11g tHe ~de ~ -tke diag::Jtfal d-z draw c3f

an:: till it readteG diag~al line e at1d complete o ~are ~ witk tke ~ide
of 50qua~ 3 as d~l, draw a11 an: till rt reach~ diag:mal ~~ complete

ttte GqUal!'.

D AI tert1atit1g ~tiv~ <md n~ive rotatiotf, to t11e x attd y ax~,

produce:; a1 1t1term1ttef1t ~eri~ of dyt1amic re~arrgles.
1?earra11gement t7.rittg5 tke cet1tr~ of energy to t~ c.eHtre of
pattern.

119

rotatiHg ect;/1 diaq;nal i_~to itfe rtext quadrant pnxtuetJS a
~~ralli: g Gerit* of dy11arnrc. rectangle~ ,

g

/ +

II 15
73

z

6

e. Diago11al $y#em giviHg a dimi11ishing 9radation of li~ u5i~g tl1e

'7GUARE

120

A ~ .6eri~ ~H ~generated ftom a regular pentagott.

-ceilil1 ''

9 \

s '\ ' ~parallel

1 '' ' ' ' ' '\ \ \ \ \ \ \ \ \ ''''\ '''' ''' \ line~
& \ \ \ \
' '' ''' \ '\ \ ' ' '' ' \ \ '\
5 '\ '\ '\
4f \ '' \ \ ''\ ''\ \
'\ '\ ''\ '\ \
'5 '\ ''' '\ \ \
2 '\ ''' \
1 \ ''\ \ '\ '\ '
' '
floor 0 '' \ \ \ ' '\
\ \
' '\ \ '\
\
''\ \

\

' \

'''\ \\ \

'\ \
\\
\\ \
'

121

a vertical liHe am be divided to equal p3rt~. (or example into 10

by u~ittg a diagol1.31 mea~unmret1t- equaling 10, ju5t con;truct a
horizontal line. iff1~ is done for rnea~rement· of ~l'i:iit? . Con~t~ring

parallel line~ will make the equ:al part~ /CMger but agaiH i11 equal

part~ . Thi~ i5 c.31lea AritHmetic Progre~iort or AP. The ~Me~ oF

numl/er7 l.i?,3,4,S,G.7.8.9,IO IG art AP witk a~ of1 and a
commort differeYice of

II

At1 AP grow~ tJy ~{mp/e il1tere?t. It-s rate of c~ange 1~ a:t~~t:mt

t11ro0311out the 5erie;;. Arcf1itect~ u~ AP for ae7111etic a11d ph~ical

ecettomy i11 the duplildtion of moaule7 frum their brick~, tna~mry,
t imber? , COl'lcrete forrnwork etc. Arithmetic mean i~ tht Wtal

?Um divided by 2, therefore ?.7 and .3=E -= IS the aritHmetic
2
mean and thu5 AP i~ ~. 1s, at1d 27

W~ett 111e arc ~ diviMd into ~ert (more or I~) equal pa-t~ an4
tne dia~::mal<? a~ cot1~tnJCted to 1oucl1 tne vertical line, It will
prOOllce a proFtJrtianate dirni.,y~hi11g diStance;; -so that tHe 11igher

portiat1 IS biggsr- ifa1 tfte lower portiOH. Thi~ w~ ~ t:>y -Hte

122

Greeks wnere1n +he figure~ ItT tke Higl1er fOr tiot1~ are m~e bigger

fJ(J that it appear? t1te ~me when ~e11 from below.

NATURE tends 1n grow oy compound interest or 6eometric
Progression or GP. lt i~ explai11ed as a doubli~g prvce~$

-GaY frot11 1 I t I =Z

2i2:"4 al1d ~ fortff

4+4 =a

ate=~

ICP t l(j: 7J2

3Z t~t= ~

at.go from 1 J)C'~:~ mul+ipliarti0t1
-,.x~:::rg

9 :x~-.=z7
27 X~-= 9l

01 ')C' ~ ..- Z4~ at't:t ~ [t>rtk

z ')(3=~

lP)(~-=18

18 X 3:: _?f
$4 )(~:: Jf>Z.

'~ )(~:4~

A GP c.att t:7e produced frvm an AP by radiatiott~ from a p:1i11t. tke angle

~ the AP at1d GP Bi~ at1d -H18 ~lati'r'6 ~itia1 of 1ke (l'int contn:JI
1118 c.ommon ratio in the 6P

123

Whirling triangles
Whirling triangle help our understanding of spirals.

Considering similar triangles, programmed so that the longest side of

one triangle becomes the shortest side of the next, they subtend
similar angles at the origin, the centre of rotation.
The whirling equilateral triangle is the simplest, completing a regular
hexagon in one revolution.
In any two similar triangles, the ratio of areas equals the square of the
ratios of corresponding sides. Therefore, when whirling a 3, 4, 5
triangle, the correspondidng sides of adjacent triangles are in ratio of
5:3. Their areas are in ration of 25:9.
Whirling a right angled triangle so that the medium side of one
becomes the shortest side of the next produces a spiral sitting neatly

on the x andy axes.

A whirling isosceles triangle generates a

logarithmic spiral. An approx.imation is
described by using circular arcs, triangle by
triangle.

124

SCALE ........... size

Scale is a fixed proportion used in determining measurements and dimensions.

Scale has reference to proportions which are good for humans. Scale deals with the relation
of architectural motifs, such as doors, windows or mouldings, to each other and the human
figure. Architecture must be adapted to human needs. Doors should be large enough to
walk through in comfort but not so gigantic that they require an almost impossible physical
effort to close them.

Steps should be of such a size as to permit easy ascent and descent. Ceiling heights must be
properly proportioned to the size and function of the room. In order to prevent one from fall-
ing from one level to the next, a balustrade should be related to the human figure in such a
way that safety is secured. Thus, design is a matter of the adjustment of architectural ele-
ments to meet the needs of the human race, and proper scale should be present when this
adaptation is made.

While proportion refers to the mathematical relationships among the real dimensions of a
form or space, scale refers to how we perceive the size of a building element or space rela-
tive to other forms. In visually measuring the size of an element we tend to use other ele-
ments of known-size in their context as measuring devices. These are known as scale-giving
elements, and tall into two general categories.

a. building elements whose size and characteristics are familiar to us through experi-
ence like doors, windows, tables, chairs, stairs, etc.

b. human figure.

In architecture, therefore, we are concerned with two types of scale:

1. GENERIC SCALE- the size of a building element relative to other forms in its context;
(three windows indicate three stories, the small window indicate a small room
inside).

[[[]

~~ 110 scale

- 125

-~ ~......__

2. HUMAN SCALE- the size of a building element or space relative to the dimensions and
proportionl) of the human body.

In this figure, there is an area which represents the facade of a building but it has no
scale. There are no details of any kind which might tell whether the building is thirty or
one hundred fifty meters long. The structure lacks doors, windows. and steps-all of
those elements which might give some hint as to its size-the human element is
missing, the figure of a man.

,n)

lli

a orte ~storey buildil1g

a model of a building a two- storey !Mldittg

In the above figures, a man has been introduced and immediately we are in a posi-
tion to estimate the size of the structure,whether it is a one or a two storey building.
Scale is thereby established.

126

1111 IIII

IIII

One must always remember that a small building must necessarily contain few win-
dows, but t hat of a large structure may have many openings. The above figures
show how the number of doors and windows give a definite clue to the comprative
sizes of the other . If the top figure is about 15 meters long then the figure below
is about 30 meters long.

Correct scale is then to bring all parts of the bu ilding and landscape into proper rela·
tion with each other. The various elements should be correctly related to human
uses. A door should be of such a size that they may be entered without fear of dis-
comfort. While, the windows should have a better relationship to the floor levels,
wall areas and functions of the interior.

Factors that effect SCALE:

1. Normal requirements of human beings.

s1ze of doors height of height of stair risers
a11d S.ze of stair tre~
window sill
127
Oi f:alcot1i~

2. Sizes of familiar materials and those of nature. Example, the size of bricks or hol-
low blocks which is usually 0.20 height and 0.40 length or the common plywood
which is four feet (1.20 m} wide and eight feet long (2.40 m).

0
f
~
()

Normal <t: E
6 f t. ~
1.som. ()

tl/

0 C)
io

3·. Beauty or appearance.
Scale is so subtle that it affects even the smallest things that its mastery
must be acquired through cultivation of good taste and an instinct for har-
mony in Architecture.

4. Character
whether it is monumental, residential, rustic or formal.

5. Functi on or purpose
usually, classroom areas or theatre areas affect the design of a room.

6. Location or visual distance
mouldings , bas reliefs and statues outside the building should be bigger than
that is viewed from the inside.

- ----m{

7. Economics
depends upon the budget of the owner. A limited budget will provide a
smaller building, a lower ceiling height.

A building maybe in proper scale but is entirely out of proportion. Proportions are
only referrable to one another, and therefore, a building may have good proportions
and yet be entirely out of scale or vise versa.

aEx. A well-proportioned door for a residence may be out of scale
for" huge cathedral.

128

SCALE TYPES

SCALAR SEQUENCE
Simple A'ug"ession
Prsparati<M - Surprise

COifstriction --Relief

129

BALANCE and
GRAVITATIONAL CURVES

Gravitational-natural tendency toward some point or object of influence. The gravitation
of people towards suburbs.

BALANCE or equalization ......... equilibrium

In the temperate zone, the climatic changes tend to balance each other. However, nature is
variable. If there is marked lack of rain , a drought results. If there are too many people for the
food supply, there is famine. The proper balance between supply and demand has not been
maintained. A person should also have a balanced diet in order not to be thin or stout or get
sick. Furthermore, the books of accounts of an office or business establishment is balanced
so as to have a clear view of the assets and liabilities.
If balance does not exist, there must necessarily be lack of balance or inequality. Balance is
equality. It is composition. It is the foundation upon which arrangement, harmony and
adjustment of weights, tones , values, etc. are developed. Proper balance satisfies the eye
w ith reference to the relative importance of the various parts of the desig'1 .

AXIS

The most elementary means of organizing forms and spaces in architecture. It is a line estab-
lished by two points in space and about which forms and spaces can be arranged in a regular
or irregular manner.
Although imaginary and not visible, an axis is a powerful, dominating, regulating device.
Although it implies symmetry. It demands BALANCE .
The specific disposition of elements about an axis will determine whether the v.isual force of
an axial organization is subtle or overpowering, loosely structured or formal, picturesque Of
monotonous.

130

An axis has qualities of length and direction, and induces movement and views along its
path. An axis must be terminated at both of its ends and can be reinforced by defining edges
along its length.

I --[-·-·1

,

---- ·\ ------·

I

I

I

The terminating elements of an axis serve to both send and receive its visual thrust. These
terminating elements can be any of the following :

Inequality, balance is equality. It is composition. It is the foundation upon which arrange-
ment harmony and adjustment of weights, tones, values etc. are developed. Proper balance
satisfies the eye with reference to the relative importance of ·the various parts of the design.

The notion of an axis can be reinforced by defining edges along its length. Tbose edges can
be simply lines on the ground plan, or vertical planes that define a linear space coincidental
with the axis.

I

*'---:

131

There are three {3) types of BALANCE in the study of composition .

1. SYMMETRICAL BALANCE .. .... .... . .. ....... .. ... .... ..... .... ... .. .... . monumental effect
centralized
formal

radial

2. UNSYMMETRICAL BALANCE ......... . informal

3. GRAVITATIONAL BALANCE picturesqueness of
surroundings.

1. SYMMETRlCAL

a. Central axis-the easiest and simplest kind of balance in which the elements are
arranged in precisely the same manner on either side of a central axis or line.

Not only is the arrangement similar but each object is exactly like the one occupy·
ing the corresponding position on the opposite side. In this kind of balance the
eye catches at a glance the equality of attraction on each side of the centre of the
composition.

All elements are duplicated -shape for shape, size for size, and tone for tone.
The left half of the composition is identical with the right half. This type of
balance gives a feeling of repose and order. It is straight forward and direct. The
effect of monumentality is more readily secured by the use of a symmetrical com-
position than by an informal grouping of units.

i9

r ·..-...____... .
!

T'r1e Saguio Cafl'lf?dral . Baguio Gty, Prlilippi11es
132

I
I

.•f

b. Formal
There is another type of balance which approaches absolute symmetry but which
lacks some of the essentials of this kind of composition. At first glance the
elements on one side of the central axis appear to be identical with those on the
opposite side, but upon closer examination it is found that such is Aot the case .
The general mass and grouping of parts may be similar, but there are dissimilar-
ities in plan, elevation, or details. The volumes of the balancing units may corres-
pond, but there may exist a difference in their shapes and surface treatments.
This type of composition is called 'Formal Balance.'

Formal Bnlance

.)

133

l

fl I llllll~

different in texture

Here the two units are located at equal distances from the central shaft and are
similar in mass or bulk. However, they are unlike in plan and in elevation , though
the general eff ect is still one of simple balance.

c. Radial

Is characterized by an arrangement where all the parts radiate from a center like
the spokes in a wheel.

2. UNSYMMETRICAL (Informal)

Unsymmetrical or occult balance is more subtle and elusive, and is more difficult to attain. It
attempts to satisfy the eye without any effort to place equal masses at similar distances from
the center of the composition. It is the grouping, in an informal manner, of elements of vary-
ing sizes and shapes .

134

1~lllililoiiiiiii.o.o.. _ - - 91__.....
0
DD(JD
t --4

The eye must be satisfied when one is working for unsymmetrical balance. But the eye must
be trained to perceive the accomplishment of this result. A see-saw is used as an example
wherein a lighter weight is farther from the fulcrum and a heavier one nearer. In an informal
arrangement the larger and heavier masses should be nearer the centre of the group , while
the lighter, lower and more horizontal elements may constitute the long arm.

I l0t1ger- dista11ce

I l
.a

In this unsymmetrical diagram, the room on the left carries up higher and thus forms a more
important exterior mass. The centre of gravity of the composition is near the main entrance,
and one feels that the long, low mass to the right is balanced about this fulcrum by the
heavier, more compact portion at the left.

135

r.~..._.-- ··---..·---------··----------·--------·-··--·------ ----·---· ________,...__,:.·.),

I~

3. GRAVITATIONAl or PICTURESQUE
This kind of composition is the complete adaptation to its surroundings. This type of com-
position is often far removed from conscious composition. Picturesqueness is the opposite
of symmetrical composition. Essentially, it is a quality which is not composed but freely
results from time and the forces of nature.
One sense. rather than sees, a state of equilibrium . The gravitational is typical arrangement
of nature, in wh ich a landscape is in form al in its disposition of parts. Its arrangement is ac-
cidental, and it may be good in its composition or it may be lacking in this quality. Nature
works in an unconscious manner with no attempt to meet man-made rules.
The artist puts upon canvas his interpretation of the scene before him, modifying it to suit
his own particular fan cy. He moved trees, houses and even mountains about so that they
will conform to a pattern which embodies the principles of good design. He secu res informal
balance in a number of ways. He n:-ilY use small areas of bright colors on one side of the
painting to balance a large area of neutral tone on the other, or he may create a feeling of
movement in order to equalize a static quality in another part of the composition.

r---· ................_.....-.... ...- ....- ~ ...__....... ... .""!

·I

.....-.Jit1'14u~{" -' -- i

~ · ~- ;~:i
. ·I

T~is 15 !Jetter

136

t i....- .................._ .... . ··-··'"'''''""'"''_j
.i

I. .. ..····-·· ........ ......__ .... -~·.. -:.~.... ........._...=...... ..._]

better

··------·· ·---·-------·.-::·;-:.·:~-. .~~

-' ... .. ':
..<.".....~ ......

~"

better

Balance suggests a gravitational equilibrium of a single unit in space, or of pairs symmetrical-
ly arranged with respect to a central axis or point.

In picture-making, balance refers to a "felt" optical equilibrium between all parts of the
work. The artist balances forces horizontally, vertically, radially, diagonally in all directions
and positions.

00 There are several factors which, when combined with the ele-
ments to balance in a work of art. These factors or variables
are position or placement, size, proportion, quality and direc-
tion of the elements of these factors, position plays the lead
role. If two shapes of equal physical qualities are placed near
the bottom of a picture frame, the work will appear bottom·
heavy or out of balance with the large upper space. Such
shapes should be placed in positions which will contribute to
the total balance of all the involved picture parts.

In seeking balance, it should be recognized that the elements of art represent " moments of
force". The eye, as it travels over the picture surface, pauses momentarily for significant pic-
ture parts which are contrasting in character. These contrast represent moving and direc-
tional forc es which must counterbalance one anoth er sc that a controlled tension results.

137