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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”

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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’.

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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

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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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