O uso racional da cor

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                                    The Theory of Color Based on the Theory of Music

                                

      When a ray of light strikes a crystal, the splendor of the colors spreads around it, shattering it into a multicolored space! How many mysteries lie hidden behind this simple phenomenon, yet representing it on a canvas or in an environment is a complex task. Color has always been an inspiring source for artists of all times – an enigma not yet fully unraveled!
          Light stirs our emotions, whether on a sunny winter afternoon or during an intense summer. The power radiating from a simple glance can transform our mood as if it were its owner. Understanding these variations and their stimuli to provoke them in the viewer is one of the objectives of painting.
          Accustomed to the light of the tropics and being able to work with its vibrant colors has always fascinated me. However, I couldn't understand the logic of its harmony, realizing that there must be a system governing it . After researching and studying in vain almost all the published theories on the subject, it seemed to me that the harmonious combination of colors was a secret that artists kept to themselves –  under lock and key!
         A lover of watercolor art, where the blending of colors without losing transparency is extremely important, I embarked on my own research. I acquired all types and colors of pigments available on the market and, by mixing them together, I tried to recreate the magic of nature. But the more I tried, the more frustrated I became, as the mixture of pigments resulted only in dirty and opaque tones.
         One day , a friend who closely followed my odyssey gave me a copy of a work republished in London, about the studies of the Greek philosopher Pythagoras - The Secrets Teachings of all Ages by the Philosophica Research Society-LA. It was a very rare manuscript by the philosopher who lived in 400 BC, and among his theories of Geometry, Astronomy and Music, he also made some reference to colors.           He was a profound observer and student of nature; for him, everything began and ended in it. One fact that caught his attention was in relation to harmonic sounds: musical dissonances and consonances. He was the one who created the system of seven musical notes: do, re, mi, fa, sol, la, si, assigning each one a specific color from the solar spectrum. The primary colors: yellow, orange, red, magenta, violet, blue, and green. He also created the entire foundation of musical harmony –  the law of octaves and the diatonic scale. Because music has a very defined and proven theory ,

         Perhaps I could lean on it, drawing inspiration from its harmony. It was merely a relationship between musical notes and colors, but for me it was an enlightenment – ​​​​a new avenue of research that opened up.
        At the time, my daughter was taking piano lessons with an American conductor, Mr. Georg Byrd, based in Germany , with whom I began taking music theory lessons, but while he spoke of musical chords, I only thought of colors. I soon noticed that music was underpinned by mathematics, therefore colors should be too, and they are!
         At first, I confess, it was just curiosity to understand its mechanism, but I quickly found points of convergence between them and fell in love!... I eagerly awaited the lessons, which were like opening Pandora's box!.........                   Realizing I was on the right track, I began to look for other likely followers of this idea. The relationship between tones or sounds and a specific color already appeared in antiquity, precisely in the Middle East. During the Renaissance, Leonardo da Vinci, a creator in various branches of art, stated: "Music and painting are sisters because both depend on the same principle – that of Harmony." Pomponius Gauricus, in 1503, in his writings "De Scultura," mentions the precise harmony of the human body and its relationship with geometry and music. Michelangelo, painter and poet, wrote Madrigals, and for him, too, poetry and music walked in parallel.         According to Rudolf Wittkower in his book "Architectural Principles in the Age of Humanism," London, 1952 - " The knowledge of Pythagorean harmonic proportions passed through music to all other arts." But this relationship only appeared in Europe during the Renaissance with the development of its art and the refinement of its artists.          In Romanticism, the musical aspect is discovered with Correggio, whose work is compared to that of the musician Pergolesi, as both used high and bright tones to represent light and low and dark tones for shadows. The high point of this encounter occurred in Impressionism, when musicians and painters like Delacroix imitated nature with its tones and colors as inspiration for their works.          What are the secrets of good color? Are there rules to be followed? If there is a proven theory of music, would giving color to the notes be the solution to the problem? Would the notes of a chord transformed into colors also be harmonious? And what is the secret of the marvelous colors of the seabed? With all these questions bubbling in my head, I immersed myself in this research and with each step I felt I was on the right track!
        

        This study was conducted through in-depth research into colors, music, and their applications. The comparison between them was made intuitively, but as Pythagoras said: "
Knowledge is a cumulative process acquired by observing natural phenomena, which, when interpreted by the conscious mind, allows the unconscious to act intuitively."
        I began to apply it to my watercolors, remembering a phrase Paul Klee said when he first painted under the tropical light in Tunisia, Africa, exclaiming: "
  Now I have become a painter!"          And I thought, Eureka!


     

       PIT NOW              

                  Pythagoras was born in Greece in the 6th century BC, the son of the merchant Mnesarchus and Parthenis. They had left Syria for fear of Cambyses, a very cruel king who persecuted all who opposed him.  According to Godfrey Higgins in  "Anacalypsis," the couple decided to consult a priest at an oracle in Delphi to find out if they could safely return to their homeland – Syria !        The prophet Pythoness placed his pregnant mother on a golden tripod, prophesying that she would give birth to an exceptional boy – a predestined being!  This boy would be destined to surpass all men in the area of ​​knowledge and, through his studies, would contribute greatly to the progress of humanity.  The ages, Pythagoras has always been considered as such, with comparisons even made between his birth and that of Jesus Christ. Both were born in Sidon, later called Bethlehem in Syria, during a journey, and both mothers were warned about the importance of the children they would have.

       The Sun God, as the Divine Spirit was then called, later appeared to his father, asking him not to have carnal relations with his wife during her pregnancy. For these reasons, he was called at the time – the son of the Sun God! His father was so impressed by this that he changed his wife's name to Pythasis, in honor of the prophet.
       In 535 BC, Pythagoras went to Egypt, where he was accepted as a priest in the temple of Diospolis. He was initiated into all the mysteries of ancient doctrines and also into Brahmins, the ancient Freemasonry. In 525 BC, the king of Persia, Cambyses, invaded Egypt, and he was taken prisoner and sent to Babylon. In 520 BC, he returned to Samos, his birthplace, the Cambyses had died, and then went to Croton in southern Italy to study law. There he founded a school that was called – "The Semicircle".         He is considered the father of Esotericism and the first to be called a "philosopher," a name he himself created, meaning : "One who dedicates himself to deciphering the mysteries of nature." Women could also become philosophers, and he married one, Theano, the first female mathematician and philosopher in history.    Pythagoras was a great scholar of the universe, of good and evil, of beauty and ugliness, stating that: "an artist is any sensitive individual who educates, interprets, and applies their perceptions derived from natural phenomena."  He also said that men know what they desire, but few know what they need , and he explained God as a  compound of substances of light and truth,  the cause and intelligence of everything.         He considered a rational understanding of the Universe essential, and one of his favorite sayings was: "We must avoid showing ourselves superior, amputating with fire and sword and by all other means the diseases of the soul – ignorance; of the belly – lust; of the city – tumult; of the family – discord; and of all other things – excesses."                       He had few disciples, to whom he taught the mysteries that had been revealed to him, the study of geometry, music, and astronomy, with classes that always began with singing, which he considered therapeutic.  Because of his teachings and discoveries, he gained many enemies who murdered him. There are different accounts of his death, in which many of his followers were also said to have been killed.         He created the current foundations of mathematics, astrology, and music, considering this triangular tripod the basis of current arts and sciences, which, thanks to his wife and disciples, have been perpetuated.

                                         

THE MUSIC OF PYTHAGORAS         

Pythagoras believed that the universe was a monochord – a single string connected at the top to the absolute spirit and at the bottom to absolute matter! The art of music, according to him, was a rigorous science with laws perfectly grounded in harmony, which in turn had mathematical foundations. He, despite not being a musician, studied its harmony – musical dissonances and consonances. One day, while meditating on it, as he passed by a blacksmith's shop where the blacksmith was hammering a piece of metal on an anvil, he noticed the variation in tones produced by the hammering.  He entered the workshop and, carefully observing the sound of the blows and the weight of the hammer,  had the first indication of the intervals of an octave and its diatonic scale. 

 
     
                          Upon returning home, he made a wooden frame on the wall, with regular intervals, where he installed four metal strings. He hung a twelve-pound weight on the first string, a nine-pound weight on the second, an eight-pound weight on the third, and a six-pound weight on the fourth. These weights correspond to the same weights, compositions, and sizes used by the blacksmith, applying different tensions to the stretched wire.          With this experiment, he discovered that the first and fourth sounds played were the same. They produced the same sound, the harmony of an octave; that is, by doubling or dividing the weight, he achieved the same effect—the same sound in a higher or lower timbre. The tension of the first string was twice that of the fourth, and so on. The note C, played in different octaves on the piano, echoes the same sound, although higher, lower, deeper, or sharper, changing only its timbre. In studying musical sounds on stretched strings under the same tension, he discovered the relationship between the pitch and timbre of the emitted note and the length of the string.         To explain further – of all the sounds of musical notes emitted, only seven can be differentiated by our ears, since the eighth is a repetition of the first – lower or higher, which he calledtheOCTAVE! Similarly, only seven colors can be distinguished by our eyes. The first note, C, on the piano has twenty-four vibrations; for a scale to be complete, it must end on the next C, which has double the vibrations, that is, forty-eight vibrations, and so on…                       He then created the seven musical notes of the octave: C, D, E, F, G, A, and B, attributing to them the seven colors of the celestial spectrum: red, orange, yellow, green, blue, and violet.

                      He went so far in his research that he could recognize the power of music over the senses and emotions. To prove how a melody affects the senses, he conducted several experiments, one of which involved placing a musician playing on a city street corner. Depending on the frequency of the melody, a man knocking on his lover's door became enraged and wanted to knock it down, but when the frequency changed ,   he calmed down and left. Upon learning of the power of music over emotions, the Catholic Church decreed that musical compositions could only be created by the Church, and disobedience could be punished even by death.
                     Confirming Pythagoras' laws, the chemist John A. Newlands (1837-1898), in London, applied the law of octaves as a model for chemical elements.  He ordered the chemical elements in ascending order of their atomic weights, as in the musical scale, and discovered that every eighth chemical element was a repetition of the properties of the first. This contributes to the creation of periodic laws, a law known as the law of octaves in modern chemistry.

                     NASA (Aeronautics and Space Administration) has recently been able, through new instruments, to record and reproduce the electromagnetic vibrations emitted by planets and stars. These sounds come from various sources, such as the electronic vibrations of the different planets, their moons, and rings in their electromagnetic fields.

                    Just as a sound wave resonates within a musical instrument to create a note, on a much larger scale they resonate within a star or planet. Planetary magnetospheres transform into radio waves upon contact with their surfaces, producing turbulence in their internal structure that causes the sound of celestial symphonies. The magnitude of these turbulences created by the vibrations depends on the size, density, and rotation of the star.

                   Astronomers believe that these sound frequencies may also vary because they are oscillations, like a rhythmic change caused by minute-by-minute changes in brightness or light from stars, sunlight. Cosmologists are trying to understand the enigma called "perfect harmony." According to physicist Lee Smolin, founder of the Perimeter Institute for Theoretical Physics, Waterloo, Ontario, our universe has already created many hidden universes beyond the black horizons of black holes. "The laws of nature are perfectly fine-tuned so that the Universe can harbor life," says Smolin.

         Since it was proven that harmony is not determined by intuition and perceptions, but by mathematical reasons, Pythagoras called it the Canon. The principle of the canon is that of a motif or theme repeated or played against itself. This happens when voices or the same main motif are copied several times. In music, this happens in various ways, and is also called a FUGUE, eg, in children's songs. In art, in print designs where the same motif is repeated in an orderly fashion.
         In geometry, he added the sphere to the solid forms already known in antiquity – the most perfect of them. These are: tetrahedron, cube, icosahedron, dodecahedron, pentagon, and sphere. In arithmetic, several discoveries are attributed to Pythagoras: the properties of integers and their classification into prime and composite, even and odd; the greatest and least common divisor.

         In Pythagorean philosophy, everything was numbered, a concept derived from the application of natural numbers to geometric objects, and all measurements could be based on a unit of measurement.  Among Pythagoras' discoveries, the most important is the theorem that bears its name, its statement being: "In any right-angled triangle, the square of the length of the hypotenuse is the sum of the squares of the lengths of the legs." Hypotenuse = side opposite the right angle. Leg = the two sides of the right angle.               The tetrahedral triangle is yellow in the center; the resulting squares of the sides have different areas, but they are proportional to each other. The symbol that represented the Pythagoreans was the pentagram or star pentagon, due to the properties of this figure. When we cross two pentagons, they form a new pentagon, called the golden section.

The Pythagorean theorem establishes a fundamental relationship between the sides of a right triangle. The square of the side opposite the right angle is equal to the sum of the squares of the measures of the legs. A and B are legs and C is the hypotenuse. Hypotenuse = x. x squared is equal to 6 squared + 8 squared. x = 36 + 64, equal to the square root of 100 = hypotenuse = 10 

       To continue my research and understand how harmony was used, I had to return to the beginning of music history.          

                                              Music in the Middle Ages                    

                   

     Gregorian chants                                              

                            
      At the beginning of Christianity, another way of seeing and understanding the universe emerged. Pope Gregory the Great, in the 7th century, ordered the creation of a simple and perfect melody for church rituals.  These creations bear his name – Gregorian chants, a music of clear, calm, transparent sounds and quite typical modulations, called melismas.

     The effects produced by different forms of composition were known, from which emotions such as anger, peace, passion, etc., arose. Gregorian chant was not born from the Western spirit, but it was a bridge between Eastern and Western cultures. It is a system that admits not a relationship between tones, but rather a kinship between them.                        Benedict of Nursia, who founded the monastery of Monte Cassino in 529 AD, adopted Gregorian chants for church rituals, which are still used today. Its root is modality, the proportion or equidistance between the tones of the Pythagorean diatonic scale . Modality, in the sense of the word, refers to modes or different aspects of something. There is a similarity between the ancient Greek musical modes and Gregorian chants because of modality. Modality was and always remains the richest basis of music of all time. The principle of the modality is diatonicism, which is the 7-note scale with five intervals and two semitones of Pythagoras.

    
                  Diatonicism also appeared in the Greek system, the richest basis of ancient and modern music. It does not admit alterations, but it also does not take chromaticism into account.   The musical system of antiquity corresponds to the white keys of the piano and has the form of the purest melodic nature. Gregorian music is not only a prayer, but above all a magnificent art form, a perfect musical expression. The study of Gregorian chants allows us to follow the evolution of the forms contained in the ancient chants of the church. These are different modes of color, which gives the composer the possibility of other modulations, different from the tonal system.   
            

          
              Music in the Middle Ages was like a painting in shades of gray; only its tonal value, that is, chiaroscuro, was considered.

            Musical compositions did not consider chromaticism, color in itself; harmony occurred through the degree of color on a scale from grays to black, called the melodic scale of the monochromatic scale.  If we close our eyes and compress our forehead towards our nose, when observing colors, we will see that they all have their tonal value.

                                         

                         

             The movement to abandon the old tonal system was called atonality. This system used the chromatic scale of 12 tones and semitones, respecting the equidistance between the notes of the tonal system, a movement that restored the rhythm of melody to music, as Schoenberg intended.

                        Andreas Werckmeister (1645/1706), a German organist, music theorist, and composer of the Baroque era, divided the octave.of Pythagoras (7 notes/colors)divided into 12 equal parts and ordered the number of vibrations from semitone to semitone using the multiplier 1.05946, the frequency of C/DO, a division that Bach also adopted in the construction of the piano.

                             I can only consider lemon yellow as a mid-tone when mixed with the cool greens, golden yellow towards the warm reds, purple towards the cool side, and magenta towards the warm side.Next, I can only use Prussian blue, as A/LA, which is the exact tuning reference. The difference between the semitones is that the cool semitone moves counter-clockwise and the warm semitone moves clockwise. I consider it a chord when the mixture of the colors that compose it results in black or gray.    

                           Functional harmony was introduced to Brazil by Hans-Joaquim Koellreuther, a German who became a naturalized Brazilian. According to him, the main function of the chord lies in the TONIC, which gives it its name; its function is one of rest—the same as the complementary color. The function of approach is that of the dominant—of greater area—and the function of recession is that of the subdominant. These functions, according to him, allow for the creation of a temporal perspective.   In classical music concerts, the grand finale usually occurs with the linking of the dominant plus the tonic—this means the sum of the two complementary colors—always resulting in BLACK! My intention is to use music theory to develop a new theory of colors, adapting it whenever possible. I also adopt the root tones of Andreas Weckmeister, resulting in 12 tones in colors.

      THE MUSIC OF CLASSICISM                                             

  Johann Sebastian Bach (1685-1750) was a German composer, organist, and master of fugue and counterpoint. He did not gain recognition during his lifetime, but today he is known as one of the "3 Bs" of music – Bach, Beethoven, and Brahms – and considered the father of Western music.  His greatest achievement was the creation of the tempered piano, as we know it today, where he applied Pythagoras's knowledge of the diatonic scale. This international system of musical scales also serves as a point of convergence for a color system.     His father was chaplain and court master to the King of Prussia, Frederick the Great, whose  court in Potsdam was frequented by great thinkers such as Voltaire and the mathematician Leonhard Euler. His father introduced young Bach to the king, whowas impressed by the boy's improvisational skills at the piano.
   
 

                         Bach lived a life of personal tragedies, losing his mother and father as a child and being raised by an older brother who didn't allow him to study music. This older brother, also a musician, took lessons with a famous teacher of the time – Pachelbel. So, while his brother slept in the dark, young Bach would copy the scores to study later, but when his brother discovered this, he tore them all up.              He married a cousin, but she also died young, and he became blind at the end of his life.  He spent most of his time giving piano lessons, but he was also an organist in several churches.     The musical instrument of the time was the harpsichord or pianoforte, where the melody could only be played with the sounds at the same pitch.

     Anyone who analyzes Bach's fugues can see his concern with modulation and harmony. His works required him to reform the piano keyboard and all musical instruments, and consequently also his way of composing – he placed great importance on the musical phrase!

              The tempered piano, created by Bach, is an instrument with a limited number of sounds and tones—if we speak of colors, I can say that it is restricted to 11 colors, with the twelfth being again the first. This system allows sounds and colors to mix or resonate with each other.
   The piano keyboard can also be thought of as each octave in shades of gray, starting with the lightest, the series of the highest notes F, and the darkest—the lowest notes B. This correspondence can also be represented by colors, considering their tonal value.

                     

   The organist, as he was, was inspired by a choir, which created the tempered piano, the most complete of musical instruments, which has seven octaves of six white keys and four black keys. Tempered by temperature and timbre like the voices of a choir - higher and lower, the same melody sung in different voices and at different pitches.

  Counterpoint and complementary colors                                  

               Sight is one of the most important senses for human beings, as most of our life sensations are captured by our optical organ. Color does not exist in the real world, as it is caused by stimuli in our brain through light rays; animals only see it in a sequence of white, gray, and black. 

                    

       When we stare for a long time at the black dot in the center of the colored sphere, after a few seconds, looking at the white ball on the screen, we will see its complementary color!  This happens because the eyes need rest, which occurs when seeing their complementary color.  

      The same thing happens in music; one sound needs another to complete it. This is the counterpoint, which the grammar of music plays, acting in the same way that complementary colors do in painting. Counterpoint is the tone that creates contrast, the opposite, like hot and cold, high and low, inhaling and exhaling—the movement of life! Everything in nature is  governed by the same principle of this movement .

White  is the sum of the mixture of all colors in light, but in pigments it is black, which is its complementary color. It is initially divided into 3 root colors: magenta, blue, and yellow, as in the example below, which, when mixed together, gives us the 12 colors of Andreas Weckmeister.

 In the graph below, I show how complementary colors are distributed across each octave of the piano keyboard. In music, this is called the interval of... Fair fifth. The distance between two complementary notes. These two notes/colors are considered a perfect consonance because they merge into total harmony.                 

             Only the mixing of two complementary colors or shades produces a rich range of tones, sufficient for painting a picture, decorating a corner, or an object. At the center of this mixture is always total stillness, represented by shades of gray to black, which proves that the colors are indeed complementary.

MANTRAS

       Mantras are melodies for meditation inspired by the cosmos and directed at the organs of the human body, which, according to beliefs, can be revitalized or even completely healed. There are various possible combinations of notes, but most use only the two counterpoint or complementary notes.

          Early in this blog, I recounted the saga of Pythagoras testing various frequencies in melodies and observing human reactions. He described a person who violently banged on his lover's door to one frequency of the melody, and then, by changing the frequency of the same melody, calmed down and left. The Mandras have the ancient frequency, like that of Pythagoras, who believed in the healing power of music  .

         Musical frequency is the number of times a sound wave repeats itself per second. Giuseppe Verdi (1813-1901), the opera composer, tuned his instruments to 432 Hz, which he considered to be the same frequency as nature.

Example: sun................................., do, la..................................re, si.................................mi etc.
                          

                                 TRIAD                                                                                                                                           

The ternary  triad is the pair of elements of complementary or opposing principles that find a third, intermediate, and balancing element—this is the principle of harmony.      The number three reigns throughout the Universe. Ricardo Cirenti, in his *  Manual of the Apprentice and the Great Initiators*,  states : "  All the great religious initiators were aware of the great importance of the law of the ternary; in this way, the conflict of opposites ceases and duality becomes fruitful. Example: The father and mother who generate a child."                                           
 

     The Pythagorean tetrahedron triangle is a symbol of strength and power, and its three edges represent the mystery of Unity, Duality, and Trinity. It is represented by a triangle and three squares, equivalent to a figure with four sides.

                

            The colors indicated by the hexahedron form a family, just as people are related to each other. Since the colors are at the same temperature, they also have an obligatory kinship, and rotating the polyhedron will reveal a new family.

          Ternary chords give personality and richness to colors, and they are:

           Remember that the three colors only form a consonant chord when their mixture results in a neutral shade of gray to black. The difficulty in reproducing colors on a computer screen is also due to the fact that their tone changes when printed. We can observe this fact when visiting a museum with the catalog of paintings exhibited in hand; some of them are completely different in their tonality.

           In his self-portrait Vincent Van Gogh used the following accord: bordeaux, turquoise and golden yellow or yellowish orange and mixtures between them.

In the watercolor below, which I created – depicting a custard apple – I used only purple, green, and orange.

                  Renoir's  painting

COMBINATION OF FOUR COLORS

The square shape within an octagon, almost the opposite of a circle, is a flat shape. It means stability, solidity, and stillness, and for many cultures, it represents two cardinal points.

In terms of color, one can think of two complementary colors.

MODULATION

   An interval is understood as the distance between two simultaneous or successive tones. This topic encompasses various aspects – interval, counterpoint, dissonant tones, and tempo. Pythagoras believed in the existence of a proportion between cosmology and interval.

     In color theory, we can call this interval modulation; it's the transition from one color to another in nature or in painting. A given color projects its complementary color onto the next, adding to it. 

The same phenomenon is observed in nature, as seen in the parrot below.

     In the example of the parrot : the turquoise blue casts the reddish-orange color, its complement, onto the edge of the next color, which in turn casts its turquoise-blue complement onto it, and the sum of these results in a moss green, which are the feathers between the two colors of the body and tail.

 Modulation in the Painting of Paul Gauguin              

     Paul Gauguin, 1848-1903, was born in Paris but spent the first 7 years of his life in Lima, Peru, where he fell in love with the vibrant colors of the tropics. He returned to Paris, where until the age of 38 he lived a married life with children and a bureaucratic job.

      The dream of becoming a painter burned within him, and it finally materialized when he met Van Gogh and Cézanne, the driving forces behind Impressionism. Self-taught, like his friends, he received little or no recognition during his lifetime, which is why, at the end of his life, he moved to Tahiti. The colors of his childhood memories then exploded onto his canvases, and his most famous works were born there.

 

  IMPRESSIONISM IN MUSIC AND PAINTING 

CLAUDE DEBUSSY

       At the dawn of this century, French music, with Claude Debussy, initiated a musical movement using the chromatic modal system. It was he who achieved this emancipation by appealing to the modal sources of the Middle Ages, creating a bridge between modern music and the modal system.

          Debussy was born in Saint-Germain-en-Laye in 1862, but spent his childhood in Cannes with a very religious aunt who raised him. In church, through songs and hymns imbued with the religious sentiment of past centuries, he received his first notions of art and music.

      He began his piano studies at the age of six and at eleven he was enrolled and accepted into the Paris Conservatory, where he was considered a rebellious student. He did not accept the teachers' instruction on harmony and had a horror of conventional cadence forms.      In 1884, at the age of 22, Debussy created the prelude "The Prodigal Son" and won the Prix de Rome. He then spent almost three years at the Villa Medici, where he studied and played the works of the composer Palestrina on the piano during masses.       It was then that the feelings already manifested in the conservatory's harmony classes reappeared, leading him to seek new paths and new forms of composition.

Art in Europe was linked to instinctive feelings rather than spiritual ones and needed renewal. Music had exhausted its sources of inspiration, and this need resonated with the spirit of Debussy. He, who from the beginning had perceived the difference in structure and rhythm between music considered secular and church music, due to its modality, then sought new forms of composition in the spirituality of Gregorian chant.

      A similar reaction occurred among painters like Monet and Pissarro, who freed their landscapes from the intellectual conceptions of the classical school, renouncing the earthy tones of the Romantic era and dedicating themselves to the exploration of color in a subtle interpretation of light. The outlines of their paintings were merely colored patches, and according to Corot: "Beauty in art is the truth of Nature."

http://www.youtube.com/watch?v=wtI4AYxNCH0

     In this composition, Debussy reveals his preference for a richer and more positive language: that of the ancient modes. The theme of the Prelude has a completely Gregorian character, that is, of the Greek lower tetrachord – deuterus. From the first chords of the Prelude, we still feel an unexpected impression; something intangible, of a rather religious gentleness and peace.

      Back in Paris, he wanted the emancipation of music, just as he had sought it in other artistic expressions like painting and poetry, and thus "Impressionism" was born!

      In Paris, Debussy became an avid listener of Saint-Gervais singers, where he could observe the freedom of rhythm in relation to the flexibility of the Latin accent. Sisley, Monet, Bazille, Cezanne, and Pissarro formed the group of Impressionist painters.

   While artists imbued their paintings and poems with color and light, Debussy, on his own, attempted to color his musical compositions. While everyone else used chords from the diatonic scale, he maintained his own style.

                 Medieval music was composed using this tonal system, the ideal C-Dur, which allows for other original combinations. The other scales derived from it differ only in the placement of the semitone within the octave.     Julia D'Almendra, who studied Gregorian modes in the compositions of Claude Debussy, in an investigation into the archaism of French musical art, states that it is the intervals that determine the modes: Protus, Deuterus, Tritus, and Tetrardus.
    

                   Church music, according to Julia D'Almendra in her book  "Les Modes Grégoriens dans l'Ouevre de Claude Debussy" (1947/48), shows how simple transposition of the third note forward is possible, since this melody has nothing to do with pitch. 
          B or H is the only note that can be altered or flattened without making any difference to the diatonic system. They are always read ascending, while the Greek modus are read descending, and these are the intervals that constitute the mode. 
        Transposition is done by modulation on the fourth or fifth note, counting from its tonic. Thus we have protus in D, A and G with B flat. Deuturus in E, A flat, and B or H sharp. Tritus in F, B flat and C. Gregorio) – hexa-chord of six notes – had a fixed interval pattern.

 THE GEOMETRIC SHAPE OF SOLIDS          

    In antiquity, mathematics, geometry, and music developed in parallel while cavemen still represented human and animal figures on rock walls. The fundamental reason for geometry arises from the need for the planar representation of three-dimensional objects.    According to the Greek historian Herodotus (5th century BC), geometry took its first steps in the construction of the Egyptian pyramids. The Greeks inherited all the experimentation, intuition, and empiricism of the Babylonians.

           It was through Thales of Miletus (624 – 546 BC), with the use of the ruler and compass,  that geometry established itself as a science. He was its great promoter, and one of his main propositions was   the demonstration of the height of the pyramid through his own shadow.    The geometry of the Greeks was strongly influenced by philosophical, aesthetic, and religious considerations, which saw  perfection in everything that was circular. The word Polygon meant "many knees," and Isosceles meant "equal legs."
 

https://youtu.be/SUSyRUkFKHY?si=VwxKHRwzE6siBiHt

Escher and plane geometry

In the works of Escher (1898-1972), a Dutch graphic artist, one observes a composition where there is no negative space; the positive figures are repeated in the negative.

 

 

 

 

 Painting of my own creation, depicting 2 couples enjoying the positive and negative aspects of space.

                                                 Textile Design Made by Me

 JAZZ - JOHN COLTRANE

 John Coltrane (1926-1967) was an American jazz saxophonist and composer who brought great innovation to contemporary music. Like Debussy, he spent his early years playing clarinet in the Catholic church choir, and like him, was greatly influenced by sacred music and its harmony. He studied music at the Ornstein School of Music in New Jersey and harmony at the Granoff School of Music in Philadelphia.

He frequented other churches and religions, such as Islam and occultism, a neo-pagan belief predating Christianity that affirms the existence of the supernatural and of physical and spiritual principles. The symbol of this belief was the pentagram, which for esotericists and pagans represents the five elements: earth, air, water, fire, and spirit.

In geometry, the pentagram is the name given to the regular star pentagon, used as a talisman by the Pythagoreans, which is, followed in the rules of life attributed to Pythagoras.

Leonardo da Vinci's illustration for the book "The Divine Proportion," by the Italian Franciscan monk and mathematician Luca Pacioli, shows the geometric relationships between man and the universe. The so-called "Vitruvian Man" represents the pentagram beneath a human figure.

Although the pentagram has always been associated with beauty and goodness, in the 19th century the inverted pentagram took on a connotation related to "evil." Éliphas Lévi (1810 – 1875) claimed that the lower point of the pentagram towards hell, indicating the "kingdom of Satan."    

The pentagram is a five-pointed star derived from the pentagon and was used as a symbol in esoteric doctrines, while the musical staff is a musical stave formed by five parallel horizontal lines, which form four spaces between them, where musical notes are written.

The Coltrane cycle, as his harmony is called, according to theorists and researchers, is a circle with a pentagram inside. His interest in the chromatic relationships of thirds with musical symmetries and geometry is said to have been inspired by religion and spirituality,   but the   division into five fifths of Pythagoras  , "die Pythagoräische Komma," was already used in Baroque music, with the last tone of the fifth being chosen randomly. 

This makes it possible to change from one tonal system to another, the famous descending fifth progressions. Giants Steps has 3 equidistant tonal centers.

This rosette is from a tonal system he created, in which I simply added the colors of the notes; we can see the staff ordering the musical notes.

Harmony in the Use of Five Colors - The Pythagorean Pentagram

While researching the musical structure of jazz and bossa nova, I noticed that both somehow made use of five colors or notes, which brings me back to the concept of the staff.

The pentagram is a five-pointed star, to which magical and mystical interpretations are attributed. It is always considered a force of energy that represents the five elements: earth, air, fire, and spirit.

In geometry, it's a regular star shape, known as the Pythagorean pentagon, but in reality, it's the Star of David. The Pythagorean star has six points.

It was also used by the mathematician Luca Pacioli to represent the geometric relationships between man and the universe. Leonardo da Vinci's Vitruvian Man is an example of this.

The tonal system is not simply a set of distinct notes or colors, but a system that possesses a relationship, almost a familial kinship (DNA); because the notes that make up the chromatic scale are under...the same temperature..

With this, we return to the teachings of Pythagoras and the Gregorian modes.

COLOR MODULATION

I started this blog, almost as a draft, researching ancient artwork, the use of two colors or two notes (mantras), three colors or three notes (chords), four colors or notes (tetrachords), and I stopped at the fifth chord, researching the jazz music of John Coltrane. Besides using Pythagorean fifths, already used in Baroque music where the fifth note or color is random, capable of changing from one system to another, called modulation, in a harmonic and new way... His system changed the entire conception of music theory, even serving as inspiration for bossa nova.

 The world we live in is colorless; it's in shades of gray and black. This is because the colors of matter, objects, etc., are produced in our brain through three rods—yellow, red, and blue—that connect to another part of it: the macula. The macula is the central part of the retina, containing photoreceptors that receive light rays and transform them into electrical impulses.

 Some time passed, and although I didn't add anything to it, my head continued to ask me questions, always   trying to understand and explain the path to the harmonious use of colors... While sunbathing, almost daily, even with my eyes closed, I saw colors moving in my mind. I always knew that there is light and color in the brain, many blind people affirm this, so I decided to paint these colors, always remembering that it is difficult to reproduce colors on a computer.

I noticed that it always starts with a strong color in a small area, increases with another color, then another slightly larger one, and then another, but it never goes beyond five colors, starting all over again with new colors. The most interesting thing is that the color of the smallest area, which would be the tonic color, always has its complement in the fourth color, and the fifth serves as a modulation for another system... I realized that this is a natural connection of our brain, since I had my eyes closed and wasn't looking at anything...

Scientists claim that we have a little-known gray matter area in the brain called the zona incerta, which plays an important role in learning and memory. It functions like a network of traffic lights that optimizes brain traffic, not by exciting neurons, but by inhibiting them. This inhibition creates an optimization of the flow of connections to other areas.

I tried using this color harmony system in a self-portrait and I liked it; it was a different and new way of thinking, but it seemed harmonious to me.

Since it deals with light rays in their various applications, I was drawn to the 2023 Nobel Prize awarded to scientists Alain Aspect, John Clauser, and Anton Zellinger for their experiments on the entanglement of subatomic particles, known as the quantum dot, which gave them color.

We know that matter filters light rays according to its density, like a kitchen filter, either finer or very closed. The color of the object or matter is the one that is emitted, as the others are absorbed. Light rays were considered straight and direct, but scientists discovered that they form a tangle and mix, like colors on a palette in new colors or in the case of connections. They were able to observe how this connection operates and also how the system repeats itself.

BOSSA NOVA

The new musical movement called Bossa Nova emerged in Brazil in the late 1950s, a period known as the golden years, created by brilliant and idealistic young musicians.

  At that time, Brazilian popular music was going through a dark phase, in which American and Caribbean rhythms dominated the music market. Then a cultural and economic elite of musicians rediscovered the samba of the favelas and peripheries of Rio de Janeiro, created and played by popular musicians.

Since this audience also enjoyed jazz, it had a decisive influence on the scope of work of these composers. They, like Debussy, in search of new ways of composing music, returned to the past to the lost roots of a very melodic music: Gregorian chants. 

   It was a natural melody with a syncopated rhythm like the ticking of a clock and the beating of a heart, but always accompanied by sophisticated musical arrangements. Syncopated rhythm is a feature of church and worship music, in which weak beats extend into strong ones.

Some music critics also highlight the influence of classical impressionist rhythms from Debussy and Ravel on this new rhythm due to its syncopated elements. 

 This rhythm is very important because it changes the standard rhythm by shifting the beat accents from strong to weak, thus opening the mind to another dimension and knowledge beyond the body. Syncopation symbolically reproduces a cyclical action linked to the concept of reversibility of time and space. But it is not just an act of emotion because it brings a physical effect on the human body, its breathing and movements. This "obligation to move" is like returning to the natural standard rhythm.

 Syncopated rhythms accentuate the tempo, never the off-beats or the syncopation itself. But there is always a very strong rhythmic accompaniment, with strong beats seeking exactly the same effect.

 Bossa Nova also uses notes of vivid and vibrant colors, but instead of a feeling of serenity, it brings a rather intimate and sensual appeal.

THEME OF THE GIRL FROM IPANEMA

Off-beat occurs when notes sound on a weak beat, preceded by a rest before the strong beat.

Which leads me to add the colors white and black. In the drawing below, I outlined the figure with white and black.

Painting created by me using the colors of the theme above.

NOBODY -- PAINTING USING MY COLOR THEORY

                       

 Harmonious Spaces

          The arrangement of colors in the spectrum and musical notes requires a different system to preserve their proper tone and color analogies. Certain differences were observed between ancient and classical music. The main difference relates to the number of light and dark tonal notes in a musical composition.

 The concept of the golden ratio determines how to divide a given area into harmonic proportions between the larger and smaller areas, applying the knowledge of pi (pi). It describes the perfectly symmetrical relationship between two proportions, a shape with a ratio of approximately 1 to 1.618.

I've already talked about the famous PI and the golden cut on this blog, so I'll just show the results without going into the mathematical calculations.

 According to Fibonacci, at the end of the 12th century, a succession of numbers in a numerical sequence began with 0 and 1 and is infinite. They can also be used to calculate quantities or spaces.

 It is present in various natural phenomena, living organisms, and events in our daily lives. The following numbers are always the sum of the two preceding numbers, like an arithmetic progression.

 Fn = Fn - 1 + Fn - 2            

 1 + 1 = 2

 2 + 1 = 3

 3 + 2 = 5

 5 + 3 = 8

 By transforming these numbers into squares and arranging them geometrically, one can construct a rectangle with specific characteristics, called the Golden Rectangle. This is a geometric shape with the following property: If we divide it into a square and a rectangle, the new rectangle will have an appearance similar to the original.

 The Golden Ratio is illustrated in the image using a Golden Rectangle: a large rectangle consisting of a square (with sides equal in length to the shorter length of the rectangle) and a rectangle.                

               A sphere for studying curved space as described by Einstein.

The geometry of the hyperbolic plane is the geometry of curved surfaces; although the heptagons are distorted, they are all the same size.

He showed us that our three-dimensional space curves, which makes time relative, creating an architecture in which the two things merge: space and time.

I added the colors because this sphere reminds me of Pythagoras's sphere.

The heptagon is a polygon with seven sides and seven vertebrae. Its area is the same as that of pi. The sum of its interior angles is 360 degrees, and the number of triangles formed within it is 7. It has all the elements studied so far; it is the most complete of them.

Today, I'm touching on quantum physics, because what caught my attention was the 2023 Nobel Prize awarded to Alain Asect, John Clauser, and Anton Zellinger for their experiments on the connections and entanglements of subatomic particles, the quantum dot, and which gave them color.

The beam of light was considered straight and direct, but they discovered that it forms a tangle and mixes with itself, a rainbow of the nanoworld. Like the colors on a palette? I wonder...

Electrons are the unit of matter, while the unit of light is called photons. The result of the encounter and entanglement of both produces what is now called quantum mechanics. 

Can you imagine the field of research that opens up? Even Newton's sphere is a step beyond those that came before it.

Size of the area of ​​each color in a work of art.

I've been studying the golden ratio rule, used since the beginning of time by artists and scholars. Although I can use and understand it, when it comes to the proportion of color areas in a work of art, I get lost.

I studied Pythagoras' tetrahedron triangle, Einstein's color wheel, and also compared it to the musical staff of John Coltrane, the creator of jazz.

In all mathematical studies on these rules, we use the sphere as a starting point, representing the perfect form, that of planet Earth. I used musical theory to understand the harmonious combination of colors, since each musical note corresponds to a color, and I managed to create a system that works, at least for me. From the beginning, I mentioned that in addition to research, I allowed my thoughts to be free to draw my own conclusions.

Since everything in art works with proportions, to use a set of colors that are not only harmonious with each other, we have to consider the amount of area each color occupies in a visual field. I used the famous Pi (pi), did calculations, and didn't arrive at any satisfactory results. Then the idea of ​​the colors contained in the rainbow came to me, which are 7, like musical notes. I tried to verify their areas, although in nanometers.

Red: 750/620 Orange 620/590 Yellow 590/570 Green 570/520 Turquoise 520/450 Indigo 450/420 Violet 420/400. Some say 750 or 780.

Subtracting the values ​​we have: - Red 130, orange 30, yellow 20, green 50, turquoise 70, indigo 30, violet 20. It's clear that this is where the mathematical progression comes from - 30+20=50, 50+20=70 and then it decreases in the same proportion.

In working with colors, their complementary colors are fundamental, so I decided to add them: orange 30 + indigo 30, yellow 20 + violet 20, but turquoise 70 doesn't match, since its complementary color is red, which should be 70 and not 130, and the complementary color of green 50 is still missing, which is magenta, an eighth color.

I've always heard and read that human eyes don't have the capacity to see all colors or hear all sounds, and I believe it. I've always heard complaints from composers and artists about the semitone F/B - yellow/violet. Nobody gets along with that...

Well, for me, thinking about working with colors and not wanting to create any controversy, magenta is missing. The value of red cannot be 130, but 70 as its complement. Therefore, magenta can only be 50 like green. So in terms of colors, everything matches up...

Going back to the time of Pythagoras, they only had the rainbow to study, could it be that everything started there? In that case, studying the rainbow with its colors, the one that connects the increasing and decreasing parts is magenta. Perhaps because of its intensity, human eyes cannot see it... (nor can machines?) I don't know...

The Dome of the Rock - Jerusalem

                                                                                                                                            

The eight-pointed star formed by the octagon is part of Islamic tradition, two superimposed squares symbolizing the union between the material and spiritual worlds. The dome of the Dome of the Rock in Jerusalem is one of the oldest examples of its use. Known as the Star of Solomon and mentioned in the Quran, it occupies a central place in the art, architecture, and cosmology of Islamic tradition. It was also widely used in the Iberian Peninsula during the Arab occupation.

Until now, I have followed everyone who has studied the subject, but now I need to deviate a little from them, whether I am right or not.   I have adopted the 8-pointed star or octagon as a standard for color selection. Following the colors of the rainbow, plus magenta, which exists but our eyes can distinguish in the sky, but is necessary to neutralize green as its complementary color.

So I rotate the 8-pointed star inside a 12-pointed star, following the musical genius Johann Sebastian Bach, who placed the 12 notes in each octave of the piano keyboard. For a very simple reason, also in colors, this number allows us to differentiate one color from another, just as one sound from another. The other notes are repetitions of the same notes.

Anyone who has had the opportunity to read this work must have noticed that for a large part of my research I did it directly online and published it immediately afterwards. In fact, I almost always used my notebook as a draft.

I tried combining 2 complementary colors between 3, 4, 5, 6, 7 and now I'm stopped at 8 colors. Although these combinations are valid, if we use an arithmetic progression, if we get closer to the combinations used in different eras and styles of music. For example, Jazz and Bossa Nova, which is where I wanted to get to from the beginning.

I'll go even further: Bach's famous fugues—we take a progression like 3-5-8-12 and return to the 11-7-4 and 2 colors. Could that be it?