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Dirk HuylebrouckDep Architecture Sint-Lucas
Brussels BELGIUM
Origin talk: "Show" of African music and mathematics
The Codes of da Vinci, Bach, pi, and Co…… painting and music
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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 herbook "Contem-porary Quilts".
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”
Kunst der Füge
Picture of the UN in NY inspired by Escher
1) Douglas Hofstadter: “Gödel, Escher, Bach, an eternal golden braid”
3
Footprints in ash and pumice dated to 385,000 to 325,000 years ago on the slopes of the Roccamonfina volcano in southern Italy.
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
2) Dawn
43000 - 82000 years old
Neanderthal flute, Slovenia
France's "Grotte Chauvet" up to 32,000 years ago (horses).
2) Dawn
43000 - 82000 years old
Neanderthal flute, Slovenia
25000 years old “key-pattern” from Mezin, Ukraine
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3) From Africa over the Middle East to Greece
Structural propertiesmusic inAfrica:1 Hemiola2 Additive rhythm3 Gestalt
RujindiriRwanda
3) From Africa over the Middle East to Greece
Structural propertiesmusic inAfrica:1 Hemiola2 Additive rhythm3 Gestalt
RujindiriRwanda
Proportions?
3) From Africa over the Middle East to Greece
Structural propertiesmusic inAfrica:1 Hemiola2 Additive rhythm3 Gestalt
RujindiriRwanda
3) From Africa over the Middle East to Greece
Structural propertiesmusic inAfrica:1 Hemiola2 Additive rhythm3 Gestalt
RujindiriRwanda
“Ostrakas" in what is now called ‘Iraq’
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Delphi stone with music notation of the hymn.
doremifasollasido
1:19:8
81:644:33:2
27:16243:128
2:1
4) Greece: Euclide, Parthenon, Cithar
Delphi stone with music notation of the hymn.
doremifasollasido
1:19:8
81:644:33:2
27:16243:128
2:1
4) Greece: Euclide, Parthenon, Cithar
Delphi stone with music notation of the hymn.
doremifasollasido
1:19:8
81:644:33:2
27:16243:128
2:1
4) Greece: Euclide, Parthenon, Cithar
Delphi stone with music notation of the hymn.
doremifasollasido
1:19:8
81:644:33:2
27:16243:128
2:1
4) Greece: Euclide, Parthenon, Cithar
Roger Herz-Fischler 1987; George Markowsky, 1992
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deffisgabccisd'
1:19:8
32:2781:64
4:33:2
27:1616:9
243:1282:1
5) Fibonacci, cathedrals, kyries
Stacking up tones in the medieval tone "system" or … working without it.
deffisgabccisd'
1:19:8
32:2781:64
4:33:2
27:1616:9
243:1282:1
5) Fibonacci, cathedrals, kyries
Stacking up tones in the medieval‘system’ or … working without a ‘system’.
deffisgabccisd'
1:19:8
32:2781:64
4:33:2
27:1616:9
243:1282:1
5) Fibonacci, cathedrals, kyries
Stacking up tones in the medieval‘system’ or … working without a ‘system’.
deffisgabccisd'
1:19:8
32:2781:64
4:33:2
27:1616:9
243:1282:1
5) Fibonacci, cathedrals, kyries
Stacking up tones in the medieval‘system’ or … working without a ‘system’.
7
doremifasollasido
1:19:85:44:33:25:3
15:82:1
6) Pacioli, Brunelleschi, simplified ratios
Simplifying ratios in tackling the Pythagorean commaproblem
Filippo Brunelleschi, San Lorenzo, 1440.
doremifasollasido
1:19:85:44:33:25:3
15:82:1
6) Pacioli, Brunelleschi, simplified ratios
Simplifying ratios in tackling the Pythagorean commaproblem
Dutch artistsVredeman de Vries ±1550
doremifasollasido
1:19:85:44:33:25:3
15:82:1
6) Pacioli, Brunelleschi, simplified ratios
Simplifying ratios in tackling the Pythagorean commaproblem
Borromini gallery, as a transportable"blow up 'play' castle"
doremifasollasido
1:19:85:44:33:25:3
15:82:1
6) Pacioli, Brunelleschi, simplified ratios
Simplifying ratios in tackling the Pythagorean commaproblem1413: Brunelleschi veroorzaakte volkstoeloop op San
Giovanniplein in Firenze met perspectieftekening
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Rembrandt, The Night Watch, 1642 (Amsterdam).
7) Newton, Vermeer, Bach
Music studies in centre of attention:mean tone scales, etcmusic geometry
doremi… ?!
11.118… = 5/2 1.25 = (5/2)2
doremi
1:19:8=1.125
5:4=1.25
Before:
Now:…
7) Newton, Vermeer, Bach
Music studies in centre of attention:mean tone scales, etcmusic geometry
doremi…
11.118… = 5/2 1.25 = (5/2)2
Aldert Mantje & Jan Maris: Night Watch Research Project
www.verbekefoundation.com/
7) Newton, Vermeer, Bach
Music studies in centre of attention:mean tone scales, etcmusic geometry
doremi…
11.118… = 5/2 1.25 = (5/2)2
Johannes Vermeer 1632 - 1675 Girl with a pearl earring
7) Newton, Vermeer, Bach
Music studies in centre of attention:mean tone scales, etcmusic geometry
doremi…
11.118… = 5/2 1.25 = (5/2)2
The Anatomy Lesson of Dr. Nicolaes Tulp (Rembrandt)
Influence science & technology:linseed (flax seed) replaces egg tempera paint; lenses and mirrors: chiaroscuro (clair obsur), geometric composition ...
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doremifasollasido
11.122…=22/12
1.259…=24/12
1.334…=25/12
1.498…=27/12
1.681…=29/12
1.887…=211/12
2
8) Gauss, J-F Millet, 21/12 relation.
One mathematical rule explains all music notesJohn Constable, Dedham Vale 1802
doremi… ???
1:11.118 = 5/2
1.25 = 5/2)2
Before:
Now:
doremifasollasido
11.122…=22/12
1.259…=24/12
1.334…=25/12
1.498…=27/12
1.681…=29/12
1.887…=211/12
2
8) Gauss, J-F Millet, 21/12 relation.
One mathematical rule explains all music notes
Jacques-Louis David, La mort de Socrate 1787
doremifasollasido
11.122…=22/12
1.259…=24/12
1.334…=25/12
1.498…=27/12
1.681…=29/12
1.887…=211/12
2
8) Gauss, J-F Millet, 21/12 relation.
One mathematical rule explains all music notes
Adolph von Menzel, Flötenkonzert 1850-52
doremifasollasido
11.122…=22/12
1.259…=24/12
1.334…=25/12
1.498…=27/12
1.681…=29/12
1.887…=211/12
2
8) Gauss, J-F Millet, 21/12 relation.
One mathematical rule explains all music notes
Jean-François Millet, The Gleaners (1857), a realistic painting, applying all known techniques before photography.
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1830: Belgische stelling, Dandelin‐Quételet
Doorsnede kegel vlak = ellips.
Brandpunten = raakpunten ingeschreven bollen.
IJsje verkocht in 2006 in Casino Oostende
Een smaakmaker; wat is de wiskunde?
Ziet u de ‘Belgische’ stelling?
↑ J.-M. Dendoncker
10) Einstein, Picasso, Grisey.
Pablo Picasso, The Bull lithographies, 1945.
Helmholtz: consonance = overlap overtones,in ear of observer.
Applied by composer Gérard Grisey founder of spectralism.
10) Einstein, Picasso, Grisey.
Pablo Picasso,, Les Demoiselles d'Avignon, 1907
Helmholtz: consonance = overlap overtones,in ear of observer.
Applied by composer Gérard Grisey founder of spectralism.
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10) Einstein, Picasso, Grisey.
Georges Braque, Violin and Candlestick, 1910.
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.
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.
Uit “Aldo Van Eyck”: […] Hieruit hoeft echter niet geconcludeerd te worden dat het kubisme beïnvloed werd door de relativiteitstheorie.
Greg Frederikson, Perdue University, USA
Frederique TombeurMuziek Selah Sue,
met expliciete toelating, ‘omdat het voor de wiskunde is’.
Inspiratie = ‘amateur’- wiskunde Dynamische wiskundige vormen
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15) Impressionism
In Claude Debussy's time, nocturnes, arabesques and preludes became fashionable.
Edgar Degas, La Classe de Danse, 1874
15) Impressionism
In Claude Debussy's time, nocturnes, arabesques and preludes became fashionable.Pierre-Auguste Renoir, Le Moulin de la
Galette, 1876
15) Impressionism
In Claude Debussy's time, nocturnes, arabesques and preludes became fashionable.Claude Monet, Impression, soleil levant, 1872
15) Impressionism
In Claude Debussy's time, nocturnes, arabesques and preludes became fashionable.
Monet’s Sunset changed to grey values: the disk of the sun disappears.
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Lissajous T shirt Fibonacci-mouwen
Pi-jasje
A. Van Neer en Renée Verhulst
Zijn er modes in de wiskunde?
17) Expressionism
Schoenberg’ s opera “Erwartung” (1909) is called expressionist because of “screaming emotions” of the main character.Constant Permeke, The Daily Bread
17) Expressionism
Schoenberg’ s opera “Erwartung” (1909) is called expressionist because of “screaming emotions” of the main character.
Edvard Munch, The Scream, 1893; forerunner of expressi-onism.
17) Expressionism
Schoenberg’ s opera “Erwartung” (1909) is called expressionist because of “screaming emotions” of the main character.El Greco, View of Toledo, 1595-1610 resembles 20th
cent. expressionism (art-historically: “mannerism”).
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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.
20ste eeuw: topologie: fles van Klein
Rode rits sluiten Omdraaien
Rode rits sluiten Donkerblauw
Lichtblauw
Alle rode openen 2 Möbius Groene rits open
2 twists Witte ritsen open Elk 4 twists
20ste eeuw: topologie:fles van Klein
‘Versnijden’ = ritsen openen
2 Möbiusringen, loodrecht op elkaar
Beide ritsen open
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18) Continued?* Gödel Escher Bach in recent times?
Popular music?
J. Cage, 1952:4’33”
… of silence
Victor ServranckxLe rectangle le plus carré, 1924
new realism Luc Tuymans The Perfect Table Setting, 2004
* education?
Going by the books?
Or learning intuitively, as
if it were a game?
18) Continued?
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