Jurate Macnoriute
Proportions of the Golden Ratio and Whole Numbers
Determining Character of Spirituality in Art
As I have revealed in
earlier chapter Differences
Between Sacred and Unholy Arts the golden ratio (or the golden section) and
proportions of
whole numbers take part as in spiritual as in spiritless arts. In
different quantities those proportions are noticeable in any artwork.
How does domination of one or other determine art character in aspect
of its spirituality? That
is main question of the present chapter.
I have to explain yet
that currently for pictures' research I have no software like CorelDraw
that had when worked on
my dissertation and could research the phenomenon of proportions in
highly subtle way. Now I have another software, but unfortunately for art analysis it
fits in less degree. In any case I am sure you will be persuade in
correctness of my research below.
Let us illustrate
phenomenon of proportions
of whole numbers and
the golden ratio.
In
Fig. 1 and Fig. 2 you can see equal combinations of rectangles placed
in frames of this same size. Let us call them 'pictures' and let us
call rectangles within frames 'details'.
Fig. 1 
Fig. 2
On closer inspection
you will notice that the pictures are a bit different. Its cause lies
in character of relations among details themselves and between details
and frame. You shall agree that Fig. 1 seems calmer and stable, Fig. 2
is more alive and fussy. The secret of difference is in proportions.
Fig. 1 is done using grid of equal rectangles, Fig. 2 done on the
ground of the golden ratio. Thus we groped a difference between
those two kinds of formation of sight.
As I cognized in my
earlier research, pictures of Leonardo da Vinci can be stowed in grids
of
equal rectangles. For example, lines
of grids of rectangles made by
dividing sides into 23, 24, 25, 32 equal parts and squeezed onto reproduction of his unfinished
picture Saint Jerome
successfully
touch almost all picture's details
(Fig. 3). Such grids I
called structure grids.
Fig.3
Grids on Leonardo
da Vinci's, Saint Jerome, 1480, Pinacoteca, Rome, Vatican City.
After inspection of
this same picture with grid of the golden ratio (Fig. 4 ) we
do not see many enough touches of details.
In Fig. 4 I have docket touches and did not find
more than 10 points. It needs to say that a few from these ten
coincidences are yet doubtful from aspect of accuracy of touch. Besides
that from these ten points only two (1. touching the neck and the
shoulder; 2. the right wrist of Jerome) may be called structural that
is touching main details / dabs. It follows that for Leonardo da
Vinci's Saint Jerome
the grid of the golden ratio sooner is accidental and can not be called
its structural grid. Moreover this conclusion's correctness confirms
itself in comparison Fig. 4 and Fig. 5. The lines of the grid
segmenting sides into 23 equal parts touch Jerome's head above, at the
right, score the left eye, mouth, ear, the elbow at the right, toes of
the left feet, both hands, the lion's bottom, etc. These points are
important for structure of the picture, because they marks Jerome
figure's position in picture's space.
Thus we see that
Leonardo da Vinci preferred whole numbers in his painting, though he
was the author of denomination 'the golden ratio'. Perhaps the brisk
golden ratio though divine could not satisfy throughout Leonardo's goal
intended to be attained. His mute music and poetry required proportions
of whole numbers.
Fig.4
Fig. 5
Grids on Leonardo da Vinci's, Saint
Jerome, 1480, Pinacoteca, Rome, Vatican City.
Leonardo was the greatest
experimenter and inventor, therefore perhaps he applied whole numbers
proportions for only the roughcast
Saint Jerome. But analysis of other his pictures validates my
presumption. As it is seen in examples below sooner Mona Lisa
also built on basis of whole numbers (Fig. 6), but not on the golden
ratio (Fig. 7).
On the other hand, we find the
golden ratio in Leonardo's details. Such examples can be Fig. 8 and
Fig. 9. Mona Lisa's face stows in rectangle which sides related in the
golden ratio equal 1:1.618... Details of the head are connected with
grid's of the golden ratio lines (Fig. 8). This same effect is
subsistent for Mona's
hands.
Thus we may conclude that whole
numbers are characteristic for Leonardo's composition, in details
within picture the golden ratio is noticed.
It is known that in ancient Greece
and the Roman Empire artists and architects used proportional compasses
set on different ratios, also on the golden ratio. In further epochs
like the Renaissance and classicism proportional compasses were often
used too.
Fig. 6
Fig. 7
Grids on Leonardo da Vinci's Mona Lisa,
between 1503 and 1506.
Fig.
8
Fig. 9
Grids on
details of Leonardo da Vinci's
Mona Lisa, between 1503
and 1506.
This same effect is
evidently seen in mosaic Salvator Mundi.
In examples Fig. 10 and
Fig. 11 sooner the golden
ratio is accidental, but figure of Christ fits very well in a grid of
whole numbers. The head of Christ together with halo also shows
existence of the golden ratio in details
(Fig. 12). In the mosaic
Christ looks grand and angry. It is clear that he came to judge. Thus
in the Middle Ages developed by ancient Egyptians effect of proportions
of whole numbers was forwarded by Christian church and secular power for keeping
their power over the poor.
Fig.
10
Fig. 11
Fig. 12
Grids on Salvator Mundi.
74.5 x 52.5 cm, the 12th century, Gemäldegalerie, Berlin
For sighting yet one
side of proportions we have to return briefly to epoch of the
Renaissance, to art of Michelangelo, to his trust in simple whole
numbers. For example, Michelangelo's fresco Temptation and Fall is build on its division into nine parts (Fig. 13).
The third part of fresco is committed to Adam and Eve tempted
themselves to eat an apple, the third part to heaven's tree with
Serpent and angel, the third part to Adam and Eve expelled from heaven,
about the third part to earth. Adam and Eve's hands protruding from the
left part of fresco to the middle one seems symbolical enough. The
angel flogging first human beings also protrudes his arm from the
central part to the right one.
In that way
Michelangelo's division of surface into small number of equal
rectangles helped him to arrange highly complicated multi-figurative
compositions. We must also remember extreme hard working conditions on
ceiling of Sistine chapel.
Fig. 13
Grid on Michelangelo's Temptation and Fall
from the Sistine Chapel Ceiling,
(1508-1512).
My research turns to
conclusion that in Europe proportions of whole numbers were used in art
knowingly and effect of their domination is characteristic for
substantial part of European art. It appears in formation of majesty,
sublimity, gravitas of old European masterpieces.
European artists had
far roots in Ancient Egypt with Egyptian square grids and strong
determination of proportions of human body.
Secret teaching of Egyptian oracles and architects was intercepted
through influential Greek mathematician and philosopher Pythagoras, the
greatest votary of numbers. Together with proportions of whole numbers
in details of European art we notice manifestation of the golden ratio,
reached using tools like proportional compasses.
I have to add that
proportions of whole numbers together with the golden ratio are reached
by human beings also intuitively. They are tracing in drawings of all
artists from prehistoric times to today. In various quantities
invisible proportions of irrational and whole numbers are distributed
in works of art and like genes they determine characters of art styles.
Let us throw a glance
to an artwork of Oriental type. As
I showed in earlier
chapter Differences
Between Sacred and Unholy Arts, analyzing an
example from the Ten
Oxherding Pictures of The Manual of Zen Buddhism, main details of that
example were touched by lines of grids as of the golden ratio as whole
numbers. If we review another Oriental representative like Japanese
Buddha's image Shaka Nyorai (Fig.
14 and Fig. 15), we see this same.
Grid of the golden
ratio placed onto reproduction of Shaka Nyorai shows that main
bright dabs are as if squeezed between verticals of the grid. Variance
in case of horizontals may be explained by cutting off the underneath
of the picture in this reproduction (Fig.
16). Such opinion is nearer
to truth, because I saw another photograph of this sacred image with
larger footer.
Fig.14
Fig.15
Fig.16
Grids on
Shaka Nyorai (Enlightened Buddha), color on silk, 12th century, Japan,
the Kyoto National Museum.
We may think that
perfect proportions are achievable by artists of the Far East
intuitively, because we know great role of meditation helping to open
and balance inner movements of spirit of artist and to forget any
concern.
Besides meditation
Eastern calligraphy plays tremendous role. It is possible that any
person acquiring to write hieroglyphs using brush and ink becomes
together an artist.
Thus we can conclude
that in Europe proportions of whole numbers were used in art knowingly.
In the East proportions
of whole numbers together with the golden ratio are detected in perfect
unity.
All articles
on theme spirituality of art
-
Introduction
to Spirituality of Art
-
Characteristics
of Spirituality
-
Differences
Between Sacred and Unholy Arts
-
Spirituality
in Various Art Styles
-
Goodness
and Evil in Art
- Halo in European Art.
Recognition of Picture Figures. Semantic Level of Art Analysis
-
Proportions
of the Golden Ratio and Whole Numbers Determining Character of
Spirituality in Art
-
National Spirituality
-
Particularities
of Spirituality of Women Art
-
Spirituality
and Mental Illness
-
Abstract
Art and
Spirituality.
-
Gallery of parodies of modern art creation
- The Closing Section of Research Into
Spirituality Of Art
Copyright
© Jurate Macnoriute
THE SECRETS OF PERFECTION