The Codes of da Vinci, Bach, pi, and Co… - Sint-Lucas

The Codes of da Vinci, Bach, pi, and
Co…
… painting and music
Dirk Huylebrouck
Dep Architecture Sint-Lucas
Brussels BELGIUM
Origin talk:
"Show" of
African
music and
mathematics

1) Douglas Hofstadter: “Gödel, Escher, Bach,
an eternal golden braid”
Kunst
der Füge
1) Douglas Hofstadter: “Gödel, Escher, Bach,
an eternal golden braid”
Kunst
der Füge
1) Douglas Hofstadter: “Gödel, Escher, Bach,
an eternal golden braid”
M.C.
Escher's
"Reptiles,"
modified
for quilts
by Kay
Parker in
her
book
"Contemporary
Quilts".
Kunst
der Füge
1) Douglas Hofstadter: “Gödel, Escher, Bach,
an eternal golden braid”
Picture
of the
UN in
NY
inspired
by
Escher
Kunst
der Füge

Footprints in ash and pumice dated to 385,000 to 325,000 years
ago on the slopes of the Roccamonfina volcano in southern Italy.
France's "Grotte Chauvet" up to 32,000 years ago (horses).
2) Dawn
43000 - 82000
years old
Neanderthal
flute, Slovenia
2) Dawn
43000 - 82000
years old
Neanderthal
flute, Slovenia
Tiny 77000-years-old stone from the Lebombo
Mountains in South Africa
25000 years old
“key-pattern” from
Mezin, Ukraine
2) Dawn
43000 - 82000
years old
Neanderthal
flute, Slovenia
2) Dawn
43000 - 82000
years old
Neanderthal
flute, Slovenia

3) From Africa over the Middle East to Greece
Structural
properties
music in
Africa:
1 Hemiola
2 Additive
rhythm
3 Gestalt
Rujindiri
Rwanda
3) From Africa over the Middle East to Greece
Structural
properties
music in
Africa:
1 Hemiola
2 Additive
rhythm
3 Gestalt
Rujindiri
Rwanda
3) From Africa over the Middle East to Greece
Proportions?
Structural
properties
music in
Africa:
1 Hemiola
2 Additive
rhythm
3 Gestalt
Rujindiri
Rwanda
3) From Africa over the Middle East to Greece
“Ostrakas" in what is now called ‘Iraq’
Structural
properties
music in
Africa:
1 Hemiola
2 Additive
rhythm
3 Gestalt
Rujindiri
Rwanda

4) Greece: Euclide, Parthenon, Cithar
do
re
mi
fa
sol
la
si
do
1:1
9:8
81:64
4:3
3:2
27:16
243:128
2:1
Delphi stone
with music
notation of
the hymn.
4) Greece: Euclide, Parthenon, Cithar
do
re
mi
fa
sol
la
si
do
1:1
9:8
81:64
4:3
3:2
27:16
243:128
2:1
Delphi stone
with music
notation of
the hymn.
4) Greece: Euclide, Parthenon, Cithar
do
re
mi
fa
sol
la
si
do
1:1
9:8
81:64
4:3
3:2
27:16
243:128
2:1
Delphi stone
with music
notation of
the hymn.
4) Greece: Euclide, Parthenon, Cithar
Roger Herz-Fischler 1987; George Markowsky, 1992
do
re
mi
fa
sol
la
si
do
1:1
9:8
81:64
4:3
3:2
27:16
243:128
2:1
Delphi stone
with music
notation of
the hymn.

5) Fibonacci, cathedrals, kyries
d 1:1
e 9:8
f 32:27
fis 81:64
g 4:3
a 3:2
b 27:16
c 16:9
cis 243:128
d' 2:1
Stacking up
tones in the
medieval
tone
"system" or
… working
without it.
5) Fibonacci, cathedrals, kyries
d 1:1
e 9:8
f 32:27
fis 81:64
g 4:3
a 3:2
b 27:16
c 16:9
cis 243:128
d' 2:1
Stacking up
tones in the
medieval
‘system’ or
… working
without a
‘system’.
5) Fibonacci, cathedrals, kyries
d 1:1
e 9:8
f 32:27
fis 81:64
g 4:3
a 3:2
b 27:16
c 16:9
cis 243:128
d' 2:1
Stacking up
tones in the
medieval
‘system’ or
… working
without a
‘system’.
5) Fibonacci, cathedrals, kyries
d 1:1
e 9:8
f 32:27
fis 81:64
g 4:3
a 3:2
b 27:16
c 16:9
cis 243:128
d' 2:1
Stacking up
tones in the
medieval
‘system’ or
… working
without a
‘system’.

6) Pacioli, Brunelleschi, simplified ratios
Filippo Brunelleschi, San Lorenzo, 1440.
do
re
mi
fa
sol
la
si
do
1:1
9:8
5:4
4:3
3:2
5:3
15:8
2:1
Simplifying
ratios in
tackling the
Pythagorean
comma
problem
6) Pacioli, Brunelleschi, simplified ratios
Borromini gallery,
as a transportable
"blow up 'play'
castle"
do
re
mi
fa
sol
la
si
do
1:1
9:8
5:4
4:3
3:2
5:3
15:8
2:1
Simplifying
ratios in
tackling the
Pythagorean
comma
problem
Dutch artists
Vredeman de Vries
±1550
6) Pacioli, Brunelleschi, simplified ratios
do
re
mi
fa
sol
la
si
do
1:1
9:8
5:4
4:3
3:2
5:3
15:8
2:1
Simplifying
ratios in
tackling the
Pythagorean
comma
problem
6) Pacioli, Brunelleschi, simplified ratios
1413: Brunelleschi veroorzaakte volkstoeloop op San
Giovanniplein in Firenze met perspectieftekening
do
re
mi
fa
sol
la
si
do
1:1
9:8
5:4
4:3
3:2
5:3
15:8
2:1
Simplifying
ratios in
tackling the
Pythagorean
comma
problem

Rembrandt, The Night Watch,
1642 (Amsterdam).
Johannes
Vermeer
1632 - 1675
Girl with a
pearl earring
7) Newton, Vermeer, Bach
do
1
re 1.118… = √5/2
mi 1.25 = (√5/2)
… ?!
Music studies in
centre of attention:
mean tone scales, etc
music geometry
2
Before:
1:1
do
9:8=1.125
re
5:4=1.25
…
mi
Now:
7) Newton, Vermeer, Bach
do
re
mi
…
1
1.118… = √5/2
1.25 = (√5/2) 2
Music studies in
centre of attention:
mean tone scales, etc
music geometry
Aldert Mantje & Jan Maris:
Night Watch Research Project
www.verbekefoundation.com/
Influence science & technology:
linseed (flax seed) replaces egg
tempera paint; lenses and
mirrors: chiaroscuro (clair
obsur), geometric composition ...
The Anatomy Lesson
of Dr. Nicolaes Tulp
(Rembrandt)
7) Newton, Vermeer, Bach
do
re
mi
…
1
1.118… = √5/2
1.25 = (√5/2) 2
Music studies in
centre of attention:
mean tone scales, etc
music geometry
7) Newton, Vermeer, Bach
do
re
mi
…
1
1.118… = √5/2
1.25 = (√5/2) 2
Music studies in
centre of attention:
mean tone scales, etc
music geometry

John Constable, Dedham Vale 1802
Adolph von Menzel, Flötenkonzert 1850-52
8) Gauss, J-F Millet, 2 1/12 relation.
do
1:1
re 1.118 = √5/2
mi 1.25 = (√ (√5/2) (√
… ???
2
Before:
Now:
do
re
mi
fa
sol
la
si
do
1
1.122…=2 2/12
1.259…=2 4/12
1.334…=2 5/12
1.498…=2 7/12
1.681…=2 9/12
1.887…=2 11/12
One mathematical
rule explains all
music notes
8) Gauss, J-F Millet, 2 1/12 relation.
do
re
mi
fa
sol
la
si
do
2
1
1.122…=2 2/12
1.259…=2 4/12
1.334…=2 5/12
1.498…=2 7/12
1.681…=2 9/12
1.887…=2 11/12
2
One mathematical
rule explains all
music notes
Jacques-Louis David, La mort de Socrate 1787
8) Gauss, J-F Millet, 2 1/12 relation.
do
re
mi
fa
sol
la
si
do
1
1.122…=2 2/12
1.259…=2 4/12
1.334…=2 5/12
1.498…=2 7/12
1.681…=2 9/12
1.887…=2 11/12
2
One mathematical
rule explains all
music notes
8) Gauss, J-F Millet, 2 1/12 relation.
Jean-François
Millet, The
Gleaners
(1857), a
realistic
painting,
applying all
known
techniques
before
photography.
do
re
mi
fa
sol
la
si
do
1
1.122…=2 2/12
1.259…=2 4/12
1.334…=2 5/12
1.498…=2 7/12
1.681…=2 9/12
1.887…=2 11/12
2
One mathematical
rule explains all
music notes

Georges Seurat, Sunday Afternoon on the Island of La
Grande Jatte 1886
Georges Seurat, Sunday Afternoon on the Island of La
Grande Jatte 1886
Georges Seurat, La Parade, 1889
9) Cantor, Seurat, Hertz.
do 261.63 Hz
re 293.66 Hz
mi 329.63 Hz
fa 349.23 Hz
sol 392 Hz
la 440 Hz
si 493.88 Hz
do 523.25 Hz
Some label
Anton
Webern’s
“Concerto for
Nine
Instruments”
pointillist.
9) Cantor, Seurat, Hertz.
do 261.63 Hz
re 293.66 Hz
mi 329.63 Hz
fa 349.23 Hz
sol 392 Hz
la 440 Hz
si 493.88 Hz
do 523.25 Hz
Some label
Anton
Webern’s
“Concerto for
Nine
Instruments”
pointillist.
Theodoor van
Rysselberghe,
Portrait of Alice
Sethe, 1888
After Georges Seurat, La Parade, 1889
9) Cantor, Seurat, Hertz.
do 261.63 Hz
re 293.66 Hz
mi 329.63 Hz
fa 349.23 Hz
sol 392 Hz
la 440 Hz
si 493.88 Hz
do 523.25 Hz
Some label
Anton
Webern’s
“Concerto for
Nine
Instruments”
pointillist.
9) Cantor, Seurat, Hertz.
do 261.63 Hz
re 293.66 Hz
mi 329.63 Hz
fa 349.23 Hz
sol 392 Hz
la 440 Hz
si 493.88 Hz
do 523.25 Hz
Some label
Anton
Webern’s
“Concerto for
Nine
Instruments”
pointillist.

Pablo Picasso, The Bull lithographies, 1945.
Georges Braque, Violin and Candlestick, 1910.
10) Einstein, Picasso, Grisey.
Helmholtz:
consonance
= overlap
overtones,
in ear of
observer.
Applied by
composer
Gérard
Grisey
founder of
spectralism.
10) Einstein, Picasso, Grisey.
Helmholtz:
consonance
= overlap
overtones,
in ear of
observer.
Applied by
composer
Gérard
Grisey
founder of
spectralism.
Pablo Picasso,, Les Demoiselles d'Avignon, 1907
10) Einstein, Picasso, Grisey.
Helmholtz:
consonance
= overlap
overtones,
in ear of
observer.
Applied by
composer
Gérard
Grisey
founder of
spectralism.
10) Einstein, Picasso, Grisey.
Uit “Aldo Van Eyck”:
[…] Hieruit hoeft
echter niet
geconcludeerd te
worden dat het
kubisme beïnvloed
werd door de
relativiteitstheorie.
Einstein formuleerde de bijzondere relativiteitstheorie (1905)
weliswaar vóór het kubisme tot bloei kwam (1910-11), maar deze
bloei werd uiteraard voorafgegaan door een ontluiking. De
nieuwe, relativistische wijze van zien tekent zich in de
schilderkunst reeds twintig jaar eerder af, met name in het werk
van Cézanne. Bovendien maakt de bijzondere relativiteitstheorie
de werkelijkheid nog niet kenbaar als een complex energetisch
veld. Deze opvatting van de werkelijkheid, die in het kubisme van
1910 gestalte krijgt, vindt haar wetenschappelijke formulering pas
in de algemene relativiteitstheorie, die Einstein in 1916 voltooide.
Helmholtz:
consonance
= overlap
overtones,
in ear of
observer.
Applied by
composer
Gérard
Grisey
founder of
spectralism.

Vasarely, Stri
Neu. Some speak
of colloïdal art,
and make
comparisons with
chemical topics
11) Russell, Vasarelly, sound illusion.
perception
11) Russell, Vasarelly, sound illusion.
perception
Sound illusions
Sound illusions
Bridget Riley,
Movement in
Squares, 1961.
11) Russell, Vasarelly, sound illusion.
perception
11) Russell, Vasarelly, sound illusion.
perception
Sound illusions
Sound illusions

12) Schrödinger, Pollock, Xenakis.
Jack The Dripper.
12) Schrödinger, Pollock, Xenakis.
CD collection jazz Pollock
allegedly listened to while
painting. Is it art?
Xenakis’
musical
pavilion in
Brussels
(1958) and
stochastic
music.
Xenakis’
musical
pavilion in
Brussels
(1958) and
stochastic
music.
12) Schrödinger, Pollock, Xenakis.
Jackson Pollock, Lavender Mist 1950.
12) Schrödinger, Pollock, Xenakis.
Xenakis’
musical
pavilion in
Brussels
(1958) and
stochastic
music.
Xenakis’
musical
pavilion in
Brussels
(1958) and
stochastic
music.

13) Finite geometry, minimal art, discrete-tones
Jean-Marie Dendoncker (Belgium) is a
carpenter – mathematician, who makes wooden
models, for, for instance, an arrangement of 7
points on 7 lines, 3 by 3.
Twelve tone symmetry
Xenakis's Bohor layout
13) Finite geometry, minimal art, discrete-tones
Carlo Sequin's (Berkeley) Minimal Trefoil
Twelve tone symmetry
Xenakis's Bohor layout
13) Finite geometry, minimal art, discrete-tones
ISIS
Tihany
2004
Bukowsky
Twelve tone symmetry
Xenakis's Bohor layout
13) Finite geometry, minimal art, discrete-tones
Twelve tone symmetry
Xenakis's Bohor layout

J.M.W. Turner, The fighting Téméraire tugged
to her last Berth to be broken, 1839.
Francisco de Goya y Lucientes, The Third of
May, 1808.
14) Romanticism
Young van Beethoven;
Beethoven's third
symphony = “good
romantic style”
14) Romanticism
Young van Beethoven;
Beethoven's third
symphony = “good
romantic style”
Egide Charles Gustave Wappers, Episode of the
Belgian Revolution of 1830, painted in 1834.
Francisco de Goya y Lucientes, The Third of
May, 1808.
Théodore Géricault, Raft of the Medusa, 1839.
14) Romanticism
Young van Beethoven;
Beethoven's third
symphony = “good
romantic style”
14) Romanticism
Young van Beethoven;
Beethoven's third
symphony = “good
romantic style”

Edgar Degas, La Classe de Danse, 1874
Claude Monet, Impression, soleil levant, 1872
15) Impressionism
In Claude Debussy's
time, nocturnes,
arabesques and preludes
became fashionable.
15) Impressionism
In Claude Debussy's
time, nocturnes,
arabesques and preludes
became fashionable.
Pierre-Auguste Renoir, Le Moulin de la
Galette, 1876
Monet’s Sunset changed to grey values: the
disk of the sun disappears.
15) Impressionism
In Claude Debussy's
time, nocturnes,
arabesques and preludes
became fashionable.
15) Impressionism
In Claude Debussy's
time, nocturnes,
arabesques and preludes
became fashionable.

Tatlin
Tower.
Model of
the
Monument
to the Third
International
Construct
ivists
designed
of posters
for everything
from film
to propaganda;
here:
photomontage
by Gustav
Klutsis.
16) Constructivism
Alexander Mosolov’s
“Steel Foundry”
introduced mechanical
sounds.
16) Constructivism
Alexander Mosolov’s
“Steel Foundry”
introduced mechanical
sounds.
Rodchenko, Stairway, 1930.
Tatlin’s
tribute to the
working
class.
16) Constructivism
Alexander Mosolov’s
“Steel Foundry”
introduced mechanical
sounds.
16) Constructivism
Alexander Mosolov’s
“Steel Foundry”
introduced mechanical
sounds.

Constant Permeke, The Daily Bread
El Greco, View of Toledo, 1595-1610 resembles 20th
cent. expressionism (art-historically: “mannerism”).
17) Expressionism
Schoenberg’ s opera
“Erwartung” (1909) is
called expressionist
because of “screaming
emotions” of the main
character.
17) Expressionism
Schoenberg’ s opera
“Erwartung” (1909) is
called expressionist
because of “screaming
emotions” of the main
character.
Above: painting by Schoenberg’s friend
Kandinsky; left: painting by the composer
Schoenberg.
Edvard
Munch,
The
Scream,
1893;
forerunner
of
expressionism.
17) Expressionism
Schoenberg’ s opera
“Erwartung” (1909) is
called expressionist
because of “screaming
emotions” of the main
character.
17) Expressionism
Schoenberg’ s opera
“Erwartung” (1909) is
called expressionist
because of “screaming
emotions” of the main
character.

* Gödel Escher Bach in recent times?
Victor Servranckx
Le rectangle le plus
carré, 1924
new realism
Luc Tuymans
The Perfect Table
Setting, 2004
18) Continued?
J. Cage, 1952:
4’33”
… of silence
Popular
music?
* education?
Going by
the books?
Or learning
intuitively, as
if it were a
game?
18) Continued?