The light plays with our emotions likewise in a sunny winter afternoon or in an intense summer morning! The irradiation power of a simple view can change our humor as being its real owner. It has been the inspiration source to artists of all time, a puzzle not yet fully revealed. That variations and stimulus reproduction has been ever the painters' main purpose.
I'm used to the tropical light which always has fascinated me. Although I realized that the harmonious colors combinations was a secret that artists had hidden only to themselves- under seven keys!
I could not understand the color harmony believing that might have a system behind it. I had already researched almost all color theory published without any satisfactory result, then I started working on my own project. In an attempt to reproduce the nature colors combinations, I bought all painting material existing on the market, but by mixing these pigments resulted only in a dirty tones mixtures - the more I tried the more frustrated I got!
One day, a close friend of mine who joined my odyssey gave me a copy of a Pythagoras´manuscript:¨ The Secrets Teachings of all Ages¨- edited from The Philosophical Research Society-LA. It was a special publication about the philosopher who lived in 400AC. His study of geometry,music and astronomy was considered essential to a rational understanding of God and Nature. Amongst these theories there were also some references to colors.
Pythagoras was a profound studious and observer of the nature - for him, everything began and ended in it. He created all the musical harmony fundamentals, noting the harmonious sounds relations: the dissonances and the consonances. He also created the seven musical notes giving to each of them a different color - the rainbow colors - creating also the the law of the octaves and the Diatonic scale. For him this was only a relationship between the musical notes and the colors, but for me it was a new path opened - a light!
As the music has a very defined and proved theory perhaps it might be possible to apply it in colors too. As my daughter studied piano with an American maestro, who lived in Germany, Mr Georg Byrd, I also decided to have music theory classes with him. While he spoke about notes I only thought about colors.
At the beginning it was only a caprice but soon as I started finding convergence points between them, then -I felt in love! I anxiously expected for the next class, it was like opening the Pandore´s Box!
The relationship between notes and colors had already been pointed out in the ancient age, on the Middle-East. Music is based on Mathematics, so that colors must be too, and they are indeed!
When I realized that I was on the right path. I started looking for others believers in the same idea.
Pompinius Gauricus ( 1481/1530), a humanist, on his handwriting De Scultura wrote about the exact proportion among the human body, geometry, and music. For Miguelângelo Buonarroti ( 1475/1564), a painter, architect, sculptor and poet who composed Madrigals, to him, music and poetry ran together.
According to Rudolf Wittkower ( 1865/1942) in his book - ¨Principles in the Ages of Humanismus London 1952, ¨ the knowledge of Pytharogas´ harmonic proportions spread from music to all other arts and sciencie.
This relationship appeared in Europe only a long time later with the development of its artists and arts. In the Romanticism, Corregio compared the musical aspects of his work with Pergolesi´s .
The high point of the convergence between music and painting appearead in Impressionism when musicians and painters like Delacroix applied the nature colors as inspiration sources.
Would the harmonious colors combination keep a secret ? Would there exist rules to be followed? By attributing colors to the notes, would I solve the problem? Would the notes transformed in colors also be harmonious? And what about the marvelous colors in the bottom of the sea? All these questions bubbled in my head.
I researched the music theory deeply and seriously, but the comparison I have made intuitively, as Pythagoras said: - The knowledge is a cumulative process which is acquired by the observation of nature phenomenon, which interpreted by the conscious permit the unconscious to act intuitable.
I researched the music theory deeply and seriously, but the comparison I have made intuitively, as Pythagoras said: - The knowledge is a cumulative process which is acquired by the observation of nature phenomenon, which interpreted by the conscious permit the unconscious to act intuitable.
I started using these colors on my watercolors, and I remembering Paul Klee´s exclamation when was in Africa and for his first time under the tropic light – Now Ï became a painter! and I thought: - EUREKA!
PYTHAGORAS
Pythagoras was born in Greece in the VI Century AC, son of the merchant Mnesarchus and Parthenis. The couple had left Syria fearing Cambyse, a very cruel king, who used to chase everyone who was against him.
According to Godfrey Higgins on Anacalysis, they decided to consult the oracle of Delphi as to whether the fates were favorable for their return voyage to their native land Syria.
The prophet Pythoness seated Parthenis on a golden tripod, and prophesied that she would give birth to an exceptional child - a predestined being! He was destined to surpass all men in wisdom and beauty, so he would contribute to the benefit of all mankind due to the course of his life.
Pythagoras was considered through all the time as such being, even with comparisons between his birth with Jesus Christ’s. Both were born during a trip through Sídon, later called Belém in Syria, and both mothers were warned about the importance of their sons.
Then, the Holy Spirit called the Sun God, appeared to his father asking him not to have any carnal relations with his wife during her pregnancy. He was so impressed that changed his wife’s name to Pythasis, like the prophet. For all this reasons Pythagoras was known as the Sun God´s son.
In 525 Ac, Pythagoras went to Egypt where he was accepted as priest on the temple of Diospolis. He’s been introduced to all the mystery of the ancient doctrines, also in Brahmins- the ancient masonary. Two years later Cambysis, the King of Pérsia, invaded Egypt where he was caught as a prisoner and he was dispatched to Babylon.
In 520AC Cambysis died and he was free to return to his town Samos. Later, he headed to Crotona in Southern Italy to study laws, where he found his school called -The Semi-círculo! He is considered the father of the esotericism, being the first one called philosopher, a name created by himself that means-¨Everyone devoted to study the mystery of nature¨.
Women could also become a philosopher and he was married with the first one, Teano, who was also a mathematician.
His school didn´t have many students, and they learned geometry, music and astronomy. The lessons always began with singing because it was considered therapeutic. One of his favorite statements was: “We must avoid with our utmost endeavor and amputate from the body, sickness; from the soul, ignorance: from the belly, luxury; from a city, sedition; from a family, discord; and from all things, excess.” “All men know what they want but few know what they need.”
The study of geometry, music, and astronomy was considered indispensable to a rational understanding of God, man, or Nature. Not all his followers could be his disciples, only if they were familiar to these sciences.
He has created all geometry, art and astronomy fundamentals, and the most important of them was his triangle- tetractys.
THE MUSIC OF PYTHAGORAS
The music of the spheres
There was speculation that Pythagoras heard the music of the planets. Saint Hildegard von Bingen,1174, who was applied as an inmated in a monastery at the age of six, wrote about it too; she had the same experience. She affirmed to hear the marvelous melody of the planets, and had visions resembling Pythagoras’.-“Alle Schönheit des Himmels”- Charlotte Herner.
NASA
( Aeronautics and Space Administration) with the use of new instruments has
recently succeeded in recording
and reproducing planets’ and stars’ electro-magnetic emited
vibrations, which produces sounds coming
from various sources: planets, their moons
and rings in their electromagnetic fields. Just as a sound wave
resonates within a musical instrument
creating a note in a much larger scale they resonate within a star or planet.
Planetary magnetospheres become radio waves
touching their surfaces producing turbulence within
it. The consequence is the appearance of the heavenly
symphonies. The
turbulence created by the
vibrations depends on the size, density
and rotation of the star.
Astronomers also see
these movements as a rhythmic change caused by the brightness or starlight
change. These sound frequencies can vary
from minute to minute in the light of the sun
- our light star.
" According to the
physicist Lee Smolin, a faculty
member at Perimeter Institute for Theoretical Physic in Waterloo, Ontario. our universe has already created many hidden universes beyond dark
horizons of black holes. "The nature laws that are perfectly tuned to the
universe may harbor life", says Smolin
Like the figure below, nowadays we know that the planets have colors, and they are the same colors that Pythagoras gave to the seven notes. He believed the universe to be an immense monochord with its single string connected its upper end to the absolute spirit and his lower end to the absolute matter.This recent picture shows the colors and sizes of the planets. How could he know about their physical characteristics?
The art of music is a well-supported science of the harmony laws having also mathematician fundament. In spite of not being a musician he was interested in its harmony- the consonance and the dissonance.
One day, while meditating about harmony he passed in front of a workshop where the locksmith hammed a piece of metal over an anvil. Perceiving the variations of the tones while he was hamming using different sizes of hammers, he had the first evidence of his diatonic scale intervals.
He came into the workshop noticing carefully the knock sound variations and the weight of the hammer. He returned to his house and made a wood frame on the wall where he seated four metal strings in regular intervals.
On the first string he suspended a twelve-pound weight, on the second, nine pounds, on the third- eight pounds, and on the fourth- six pounds. These weights corresponded to the locksmith’s hammers sizes and compositions but giving them different tensions.
With this experiment he discovered that the first and fourth strings when sounded together produced the same sound, the harmonic interval of the octave. By similar experimentation he ascertained that the first and third strings produced the harmony of the diapente, or the interval of the fifth. Pythagoras continued his investigations, discovering that the first and second strings produced the harmony of the diatessaron, or the interval of the third.
The key of the secret was contained in the tetractys or pyramid of dots, which is its proportions reveals the interval of the octave-1, 2, 3, and 4.
He went so far in his investigations about the therapeutic value of the harmonics, that Pythagoras discovered that the seven modes of the Greek system of music had the power to incite or allay the various emotions.
It is said that while observing the stars one night he encountered a young man befuddled with strong drink and mad with jealousy, who was pilling faggots about this mistress´ door. The frenzy of the youth was accentuated by a flutist a short distance away who was playing a tune. Pythagoras induced the flutist to change the rhythm, whereupon the mad man was composed and quietly returned to his home.
The Catholic Church was the only one allowed to compose music, because of its power on the main senses and emotions; the decreasing disobedience could be punished with death.
The Catholic Church was the only one allowed to compose music, because of its power on the main senses and emotions; the decreasing disobedience could be punished with death.
John Newlands, 1837-1898, a chemical, corrobored this ancient philosophical teaching with the progression of the elements according to harmonic ratios. While making a list of the elements in the ascending order of their atomic weights, he noticed a disctinct repetition of properties at every eighth element. This discovery is known as LAWN OF OCTAVES in modern chemistry.
Since it was proved that harmonic is not determined by intuition and perceptions but for mathematics reasons, Pythagoras called it as Canon. The canon principle is a motive or a musical theme which is repeated or played against himself several times, likewise textil design.
In Geometry, he added the sphere, the most perfect of them, to others geometrical forms. They are: dodecaedro, icosaedro, hub, pentagon, tetraedo, and sphere.
Qw
Qw
In 529 DC, Benedict of Nursie founded the monastery of Monte Cassino where he adopted the Gregorian calendar for the rituals that are used almost until today. The root of these songs is the modality, the proportionality or the equidistance between the tones - the diatonic range of Pythagoras. This proportion is also observed between the colors, which are also the six primary colors.
The church music, according to Julia D`Almendra in her book: - 'Les
Chants Grégoriens in Les modes l'Ouevre by Claude Debussy. '(1947-1948)
shows us how with the a simple transposition of the tonic changes the melody. The Si or H, violet, is the only note that can be changed or Bemolle Si (H), without making any difference in the diatonic system, which are the intervals that constitute the mode.
In Christianisty’s began a different way to see and understand the universe arose. The effects caused over the senses and emotions by different forms of musical compositions were already known.
The Gregorian Choir was not born in Western but it was a bridge between Western and Eastern cultures. It was a system that didn’t admit any relationship among the tones, but a real kinship. The ancient musical system corresponds to the white keys on the piano, between the first and last tones there were over 6 tones, different from the scale of eleven tones.
The Gregorians’ Songs are not just a prayer, but rather a form of a magnificent art, a perfect musical expression. Its study allows us to follow the evolutionary forms contained in the church’s ancient songs. There are different modes of tones and colors, which gives to the composer the possibility of several modulations on different tonal systems.
The diatonicism also appeared in the Greek system, the richest base of ancient and modern music, it didn’t admit changes, but also does not take into account the chromatism. Middle Age’s music consisted of tones in the ideal Do(C) -Dur which enables other unique combinations. The other scales derived from it, are differentiated only by place of halftone within the octave.Below, the song Holy Mary with colors:
THE MIDDLE-AGE MUSIC
Music in middle age was like grayscale painting, because they considered only the tonal value. The harmony happened by the degree of color in a gray and black scale called melodic - the monochromatic scale.
If you close your eyes, forcing your forehead in the direction of your nose, you can see the colors in their shades of gray, this is the tonal values of colors.
This harmony of the modal system began to change and give way to another, the chromatism, which ruled all classical music until the century X.
Julia D`Almendra studied the Gregorian modes in the compositions of Claude Debussy, in a search for the archaism in French music. She stated that there are intervals that determine the modes: Protus, Deuterus, Tritus and Tetrardus.
In any painting, song or decorating environment can be used shades of gray to achieve cadence and rhythm
Johann Sebastian Bach
Johann Sebastian Bach was a German composer (1685/1750) who didn’t get any recognition in his lifetime, but today he is known as- "The three Bs of Music -Bach, Beethoven and Brahms". He was an organist, master of the fugue art, and a counterpoint being considered as the Western music father.His greatest achievement was the tempered piano’s creation, as it is called today. He has applied in it the Pythagorean’s diatonic scale. This international scale sounds system that also served me as the convergence point for the color system.
His father, Prussia King’s master of the chaplain of the court, Great Frederico presented him to the king, who was impressed by his improvisation capacity. The Potsdam’s court was frequented by great thinkers like Voltaire and the mathematician Leonhard Euler, too.
Bach had a life plenty of personal tragedies losing his mother and father during childhood, and was raised by an older brother who didn’t give him the right to be a musician. That one was also a musician and had classes with a famous music teacher at that time - Pachebel. The young Bach, while his brother slept, in the dark, copied the lessons to study it later, but he was caught and his brother ripped everything. He got married with a cousin, but she also died early. At he end of his life he became blind.
He devoted a lot of his time teaching piano or organ. He was appointed as an organist in various churchs. The instrument of music at the time was the Cembalo or pianoforte, which could always play the melody with the same sounds’ height only.
Anyone who analyzes Bach fugues will be convinced that he had an approach to modulation and harmony in general . His own job required him to make a reform in piano’s keyboard of all musical intruments and also on their writings.
His insistence on correct phrasing indicated in his works show us the importance about harmony. The piano created by Bach is an instrument with a limited number of tons, if we're talking about color, it is limited to 11 colors, and the twelfth is the first, again. This system allows the sounds and colors to be mixed together.
As an organist, he created the piano inspired by the Chor’s voice- the most complete musical instrument. It has eight octaves with six white keys and four black keys, tempered by temperature and timbre as it is like the same song sung by voices on different heights.
THE MUSIC IN CLASSICISM
During the dawn of this century the French music, with Claude Debussy, started a musical movement using the chromatic modal system. He had made that emancipation appealing to modal sources of the Middle Ages, and creating a bridge between modern music and the modal system.
That very different movement from the old tonal system was called atonality because it used the chromatic scale of 12 tones and semi tones, respecting the equidistance between the notes of the tonal system. This movement was a return in order to give rhythm to the melody, as intended Schönberg.
The functional harmony was introduced in Brazil by Hans-Joachim Koellreuther, a German composer nationalized Brazilian. According to him, the main function of the agreement is the TÔNICA- that gives its name and causes the chord, its function is the same as the complementary color. The approximated function is the dominant , which has the largest area, and the removal is the sub-dominant. These functions, he said, allow us to create a temporal perspective, being able to notice the movement of music in one direction.
In classical music concerts, usually the “grand finale” gave up with the chaining of the most dominant tônica- this significant sum of two complementary colors.
THE COMPLEMENTARY COLOR
By staring at the black point in the center of the colored ball, after a few seconds, looking at the white ball or at a white paper, we will see its complementary color!
It happens because the eyes need to rest, which occurs by visualizing its complementary one. By magenta- we will see green , blue - orange, yellow – violet, turquoise - coral…
It happens because the eyes need to rest, which occurs by visualizing its complementary one. By magenta- we will see green , blue - orange, yellow – violet, turquoise - coral…
THE COUNTERPOINT AND THE COMPLEMENTARY COLOR
Counterpoint is the grammar of music like the complementary color is for painting. Everything in nature is governed by the same principle of motion: birth- death, day-night, inspiration- expiration, rest-fatigue, this also happens in music and colors.
The view is one of the most important senses of the human being, most of our life sensations are captured by our optical organ. This statement , illusion of color, is because colors do not exist in the real world, it is only caused in our brain by the rays of light. Animals see only a range of white, gray and black. Can you imagine the world without colors?
Our eyes are composed of a tissue with a huge number of light receptors, or the electro-magnetic waves, decomposing white light into a spectrum of colors, such as a prism. There are three (3) types of bastons in it, each one is sensitive to one field of color - the primary colors.The key of harmonic proportion is contained in the famous Pythagorean tetractys or pyramid of dots. It is made up of the numbers 1, 2, 3 and 4, which in their proportion reveals the intervals of the octave, the diapente, and the diatessaron.
As explained before, the octave is composed by eight notes or colors which the first ton is the same of the last one. The diapente is the interval from one point to the fifth one in the order which are the complementary colors. The diatessaron is the interval from one point to the third one in the order which are the chords or triads.
The complementary colors displayed in the exercice above are: magenta-green, blue - orange and yellow and violet.
The mixture of two complementary colors produces this rich range of tones below. At the center of this mixture it produces a range of gray to black tons which proves that those colors are really complementaries.
Mantra
Mantras are melodies produced by sounds known in the antiquity as - the seed of the sounds. They're basically Pythagorean’s fundam entals sounds of his diatonic scale, in which each sound or color corresponds to a vowel or a semivowel of the alphabet : A, E,I,O,U and Ä and Ü. The M and N is obtained by two complementary colors or sounds fusion.
They are used for meditation inspired on the cosmos, whose melodies are pointed out to human’s organs. In accord to same belief, playing upon the nerves, the spirit thus created the harmonies of normal functioning and they could be revitalized or even cured.
There are several combining possibilities using the counterpoint notes.
Mantras’ examples: sol (G)............................. DO ( C), L A(A) ............ .....................RE (D), SI
(B) ......................... MI(E) etc ........
In Antiguity, mathematic, geometry and music were developped together while the caves'man still represented humans and animals figures on the walls rocks. The fundamental reason from geometry appearances was the necessity of the objects representation in a flat and three dimensional surface.
According to the Greek historian Herodotus, the geometry first steps happened on the Egypt's pyramids constructions. The Greeks inherited from the Babylonians all theirs experimentations, intuitions and empiricisms.
But it was through Thales of Miletus(624-546 B.C), with the ruler and compass finding, that geometry was stablished as a science. He was its great booster and one of his main proposition was the demonstration of the pyramid height constructions through its own shadow.
Geometry was strongly influenced by aesthetic, religious and philophical conceptions considering perfect everything in a circular form
Greeks’ geometry was strongly influenced by philosophical, aesthetic and religious considerations, which saw perfection in everything that was circular. The Polygon word meant "many knees" and Isosceles mean "equal legs."
But it was through Thales of Miletus(624-546 B.C), with the ruler and compass finding, that geometry was stablished as a science. He was its great booster and one of his main proposition was the demonstration of the pyramid height constructions through its own shadow.
Geometry was strongly influenced by aesthetic, religious and philophical conceptions considering perfect everything in a circular form
Greeks’ geometry was strongly influenced by philosophical, aesthetic and religious considerations, which saw perfection in everything that was circular. The Polygon word meant "many knees" and Isosceles mean "equal legs."
The pointeds colors by the hexahedral dots constitute a family, having like a kinship, because they are under the same temperature. A new color family is constitued only by the hexahedron rotation.
THE TRIAD
Ternary is the complementary pair of opposed principles which in addition of a third element, the intermediary and balancing one produces harmony. Ricardo Cirenti, in his Manual for Apprentices and Great Initiates says: "All great religious initiators were aware of the great importance of the ternary laws." Thus ends the conflict of opposites and the duality becomes fruitful, as the father and the mother generating their child. Ternary chords gives personality and richness to colors and they are:
Pythagoras's tetrahedron, has four equilateral triangles as faces, and it is the universal symbol of strength and power. Its three points summarizes all the mysteries of: Unity, Duality and Trinity!
The consonant chord is got when the colors mixture results in a neutral ton- from gray to black. Vicent Van Gogh, painted his self portrait this chord below;
Below, my watercolor - A fruta do Conde- 1989- which was painted with the following chord:
Interval or Modulation
Interval is the distance between two simultaneous or successives tones. To this theme belongs many aspects, like: interval, counterpoint, dissonants tones and speed. Pythagoras believed in the existence of a ratio between cosmology and interval.
In color, the interval is called modulation, which means the passage from one color to another. Every color projects its complementary color over the next one by mixing them.
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In the above example: the turquoise color projects its complementary color- red-orange on the border. On the other hand the red-orange color also projects its complementary color -turquoise on its border, that two colors mixture results in the feathers green- moss ton.
GAUGUIN'S PAINTING MODULATION
GAUGUIN'S PAINTING MODULATION
Paul Gauguin, 1848-1903, was born in Paris spending his first seven years of life in Lima, Peru, where he fell in love with the vibrant colors of the tropics. He returning to Paris when he was 38 years old, he had a bureaucratic job and was married with children .
The dream of becoming a painter seethed within him was finally materialized by meeting Van- Gogh and Cezanne- the boosters of Impressionism. He was an autodidactic as well his friends, he had a little or no recognition during his life-time, the reason he moved to Tahiti. Once there, the colors of his childhood’s memories exploded on the screens , creating his most famous works.
CLAUDE DEBUSSY
Debussy was born in Saint-German-en-Laye in 1862, but he spent his childhood in Cannes, with a very pious aunt. At the church, through the songs and hymns imbued with the religious feeling of centuries past, he received his first notions of Art and Music.
He began his studies of piano at the age of six, and with eleven he was already accepted at the Conservatoire of Paris. He was considered a very rebellious student, because he didn’t accept the teachings of harmony and loathed the conventional rhythmic forms. ((Maurice Emmanuel)
At the age of twenty-two, thanks to the Prix of Rome, he stayed three years at the Villa Medici, where he had the opportunity to study and play the Palestrina’s old masterpieces in the masses. That feeling he had already manifested on the conservatory’s harmony classes reappeared, and it should bring him to seek new composition forms.
Backing to Paris, he wanted to emancipate the music like to other manifestations of art, such as painting and poetry.
This Prelude’s theme has a Gregorian character - the Greek inférier Dorian tetrachord, therefore - the deuterus. In this composition Debussy reveals his preference for a richer and positiver language, like the old modes.Since the Prelude’s first chords, we feel even an unexpected feeling; something intangible, a gentleness and peace quite religious.
Below a Debussy's composition excerpt of Proses Lyriques-1893- De Soir, showing how he tried to paint it. His scores over a recited text.
DE SOIR- CLAUDE DEBUSSY
THE IMPRESSIONISM IN MUSIC AND PAINTING
The music in Europe had exhausted its inspirations sources that found resonance in Debussys' mind. From the beginning he had noticed the structure and rhythm differences between the profane and church music, then he looked for the Gregorian song'spirituality as an inspiration for a new composition form.
A similar reaction occurred with painters like Monet and Pissarro, who released his landscapes classical style, leaving aside the Romantic era earth tones.The contours of the paintings became only colored spots, and according to Corot: "The beauty in art is the truth of nature."
The music in Europe had exhausted its inspirations sources that found resonance in Debussys' mind. From the beginning he had noticed the structure and rhythm differences between the profane and church music, then he looked for the Gregorian song'spirituality as an inspiration for a new composition form.
A similar reaction occurred with painters like Monet and Pissarro, who released his landscapes classical style, leaving aside the Romantic era earth tones.The contours of the paintings became only colored spots, and according to Corot: "The beauty in art is the truth of nature."
In Paris, Debussy became an avid listener of Saint-Gervais singers, where he could feel the rhythm freedom of the Latin accent flexibility.
Sisley, Monet, Bazille, Cezanne and Pissarro, formed the impressionist painters' group.
While artists pervaded his paintings and poems with color and light, Debussy tried alone to do the same with his compositions.
Music combines sounds and silences according to a time organization. Painting, especially textil design, repeats a motif according to a background proportion, it is called canon. The canon principle is a motif or theme repeated or played against itself. It happens when voices or motifs are copied several times, thus many sounds or motifs harmonize with each other and become part of the melody.
The first attempt to
translate words into music happened in the church’s choir with natural, soft and curves intonations called melismas. It would be easier to understand it while listening to a Debussy’s composition on a
Stéphane Mallarmé’s poem: Prélude
l’àprés-midi d’un Faune played by Leonard Bernstein.
The melody runs in a monologue form, as someone reciting and alternating slowly and-sadly almost tearful passages with other exalted and fast. Just by listening to the melody we can notice all the emotions contained in the text.
Music notes are like colors since both have a saturation degree. The mixture of two complementary colors results in black, which corresponds to 100% of the total saturation. That saturation degree is divided among complementary colors: violet has 86% of saturation and yellow has 14% , blue has 71% and orange, 29%, green would have 57%
and magenta 43%, and so on ........
The figure and their background
The senses like seeing and hearing are sensations captured by our brain through the optic nerves and audio system. They are physically and external ones because only the human being sees in colors while animals see in black and white. If the color caused by solar rays only exists in our brains, the sound caused by air vibrations exists outside it? If the color is an illusion, should the sound also be?
According to the neuroscientist Francisco J. Rubia in his book -What you know about the brain? -"The brain is a closed world translating external stimuli into the language provided by the brain structures, giving an internal version or representation of an external reality." "From what we understand that the human being is closed in itself! As the computer has its own language, the brain also has its, the harmony is the accepted way to its perfect understanding.
On many above-named compositions there is an
analogy between the figure, its background, as the musical theme and its accompaniment. In all musical or artistic compositions
forms, the figure, the musical theme as their background have the same
influence on our brain.
On Bach’s baroque
compositions can be noticed the musical accompaniment coming along the melody
theme which is repeated several times but
in a higher or lower voice, called recursive- the famous Bach’s fugues!
The video below shows it perfectly:
Maurits C. Escher was a mathematician and a Dutch graphic artist who especially worked in two- dimensional plans. He used the figure and its ground in a very special way.
In the Escher's graphic designs, the same motif is repeated several times, in a positive and negative form.
Douglas R. Hofstadter in his book- “Gödel,
Escher, Bach” asserts that the figure is the positive form while the background
is the negative one. The melody is the music’s most important part and the accompaniment is its background.
Above is a painting of mine attempting to play with the positive and negative backgrounds by mixing their
outlines. In the ballroom
there are just two
couples, but it gives us the impression of seeing a room full
of people.
JOHN COLTRAME - JAZZ
John Coltrane (1926/1967), was a saxophonist and composer of American jazz who brought great innovation to contemporary music. Like Debussy, he spent his early years playing the clarinet in the choir of the Catholic Church, and like him he was 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 in Philadelphia.
He attended also other churches and religions such as Islam and the occult, a neo-pagan belief prior to Christianity that affirms the existence of the supernatural and the physical and spiritual principles. The symbol of this belief was the pentagram which, for esoteric and pagans, represents the five elements: earth, air, water, fire and spirit.
In geometry, the pentagram is the name given to the regular starry pentagon, used as a talisman by the Pythagoreans, that is, followed in the rules of life attributed to Pythagoras.
Leonardo da Vinci's illustration for the book “A Divina Proporção”, by the Franciscan monk and Italian mathematician Luca Pacioli, shows the geometric relations of man with the universe. The so-called "Vitruvian Man" represents the pentagram under a human figure.
He attended also other churches and religions such as Islam and the occult, a neo-pagan belief prior to Christianity that affirms the existence of the supernatural and the physical and spiritual principles. The symbol of this belief was the pentagram which, for esoteric and pagans, represents the five elements: earth, air, water, fire and spirit.
In geometry, the pentagram is the name given to the regular starry pentagon, used as a talisman by the Pythagoreans, that is, followed in the rules of life attributed to Pythagoras.
Leonardo da Vinci's illustration for the book “A Divina Proporção”, by the Franciscan monk and Italian mathematician Luca Pacioli, shows the geometric relations of man with the universe. The so-called "Vitruvian Man" represents the pentagram under a human figure.
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Musical frequency is the number of times a sound wave is repeated per second. Giuseppe Verdi (1813/1901), opera composer, tuned his instruments at 432 Hz, as he considered it to be the same frequency as nature. His first application of the new harmony was in Giants Steps.
COLOR MODULATION
I started this blog researching ancient art works from painters and musicians on the use of 2 colors or two notes (mantras), three colors or 3 notes (chord), four colors or notes. John Coltrane used the fifths of Pythagoras in his jazz compositions, which was already been used in baroque one. The fifth note, passively changes from one musical system to another one, what´s called modulation. It was a new way of composing, that changed the entire conception of music theory, serving as inspiration even for bossa nova.
The world we live has no colors, it is in shades of gray and black, because the color we see is are produced into our brain through three rods: yellow, red and blue. It´s connected with another part of it, the macula, the central part of the retina, with photoreceptors, which receive rays light and transform them in colors
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I didn't add anything to my blog for a long time, but my head continued to ask me questions, trying to understand and explain the path in the harmonious on use of colors... When taking my daily sunbath, with closed eyes, I see colors moving on my mind, so I decided to paint them, but always remembering how idifficult it' s
to reproduce colors on the computer.
I noticed lit starts with a strong color in a small area, that increases to another color to a slightly larger and then another one, but it doesn't go beyond five colors, starting all over again.The color of the smallest area, which would be the tonic, has its complement color in the fourth area and the fifth one serves as a modulation to another system. I believe it's a natural connection of our brain. Scientists claim that we have a gray matter in our the brain, called the uncertain zone, which plays an important role in learning and memory. It works like a traffic light network 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 portrait of myself and I liked , it's was a new way of thinking, it looks harmonious.
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A ray of light has different applications, the 2023 Nobel Prize for scientists ALAIN ASPECT, JOHN CLAUSER AND ANTON ZELLINGER caught my attention about the connections experiments between the entanglements of subatomic particles, the quantum dot, which they gave colors.
The matter filters the ray of light according to its density, like a kitchen filter, thinner or very closed. The color of the object or matter is the one that is expelled, because the others are absorbed. The ray of light was considered straight and direct, but scientists discovered that they form a tangle and mix, like the colors on a palette creating new color, in that case of news connections. It was possible for them to see how this connection operates and also how the system repeats itself.
BOSSA NOVA
The new musical movement called Bossa Nova appeared in
Brazil in the late 50's, at a period known as the golden years – it was
attended by brilliant-young and idealist musicians, such as Debussy was
in his lifetime, trying to find new way of composing music.
And again they turned to the past to the lost roots of a very melodic
music:
the Gregorian choirs
At that time, Brazilian popular music lived in a dark
turning point, in which the American and Caribbean rhythms were dominating the
music market. Then, a cultural and economic audience elite rediscovered the
samba of the Rio de Janeiro’s slums and suburbs, which was created and played
by popular musicians.
As that public also enjoyed the jazz, it had a decisive
influence on the composers’ scope work. Some music critics also highlight the
influence of Debussy and Ravel classical impressionism pace on this new rhythm due
to its syncopated elements. It was a natural melody with a syncopated rhythm as tic tac
clock and the heartbeats, but always accompanied by sophisticated musical arrangements.
The syncopated rhythm is the church and worship music feature, in which weak
beats extended to the strong one.
This syncopated rhythm is very important for the ritual because it
changes the standard rhythm by moving the forte beat accents to the
faint one, thus, opens the mind to another dimension and knowledge
beyond the
body. The syncope symbolically reproduces a cyclic action
linked to the concept of reversibility of time and space. But it is not
only an
act of emotion because it brings a physical effect over the human body,
its
breath and movements. This "obligation to movement" is like coming to
the natural standard rhythm back.
The syncopated rhythms accentuates the temps never the contretemps or the syncope itself.
But it always has a very strong rhythmic accompaniment, with strong
beats looking for exactly the same effect. Bossa Nova also uses vivid and vibrant colors, but instead of a feeling of serenity, it brings an appeal quite intimist and sensual.
= HARMONIC SPACE
The arrangement of the spectrum colors and the musical notes needs a different system to preserve their proper tone and color analogies. It was possible to notice certain particularities between the old music and the classical music. The main one refers to the tone notes amount in a musical composition.
The golden ratio concept determine how to divide a certain area in harmonics proportions between the largest and the smallest ones, applying the IP knowledge. It describes the perfectly symmetrical relationship between two proportions, it´s a shape with a proportion of 1 to 1.618 approximately.
In this blog I have already dealt about the famous PI and the gold cut, because of that I just will demonstrate the results without going into the mathematics calculations.
According to Fibonacci, at the end of the 12th century, who elaborated a succession of numbers in a numerical sequence starting with 0 and 1 and It is infinite . Those can also be used in order to calculate the quantities or spaces.
It`s present in various phenomena of nature, living organisms and facts of our daily lives. The following numbers are always the sum of the previous two numbers, as an arithmetic progression.
Fn = Fn - 1 + Fn - 2
1 + 1 = 2
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8.
By turning these numbers into squares and arranging them geometrically, a rectangle with specific characteristics can be constructed, called the Golden Rectangle. This is a geometric shape with the following property: If we divide it into a square and another rectangle, the new rectangle will look similar to the original.
The Golden Ratio is illustrated behind using a Golden Rectangle: a large rectangle consisting of a square (with sides equal in length to the shortest length of the rectangle) and a smaller rectangle.
Cezanne´s picture
As already mentioned, music and mathematic are governed by laws and systems. Modus is the system used to order a musical composition or an artistic creation. It is formed by colors or notes from the same family in an ascending or descending order. It always begins with the dominant one which appears in greater quantity, and the followings in a mathematical progressive proportion. The color which makes the contrast gives balance to all is called Tonic, and it is always the dominant complementary one.
The Egyptians, 3500 years ago, started with an 8-sided polygon, inscribed in a circle to get the Pi's value. Then they have found the ratio of the circle dividing its length by its diameter that is always the same for any circle and its value was a number about 3.16.
The Pi is an irrational and transcendental number having an infinite decimal sequence, which is used to measure the diameter and volume of the circle. But it calculates much more than that: the rolling of the waves on a beach, the apparent daily path of the stars in the sky, the compass of the music, the movement of the gears and bearings, the propagation of electromagnetic fields and a very large number of the natural and mathematics phenomenas, which are associated to the circular and spherical symmetries. But the most impressive calculation was made by the Dutch mathematician Ludolph van Ceulen (1540-1610), starting with a polygon of 15 sides and doubling the number of sides 37 times, Ceulen obtained a value for Pi with 20, and later with 35 decimal sequences.
The 1-meter-diameter circle in order to roll back to its initial position runs 3,1415... meters -the Pi's value.
The amount of colors or tons in the melody follows Pythagoras’ Golden Ratio calculation The color or the note which occupies the largest area is called dominant, it is followed by the sub-dominant and the tonic which in spite of occupying the smallest part in the melody, gives its name.
Sphere to study the curved space described by Einstein.
The geometry of the hyperbolic plane is the curved surfaces geometry, although the heptagons are distorted, they all have the same size.
He showed us the space is three-dimensional and curved space, which makes this term relative, creating an architecture in which the two things merge, space and time.
I added the colors, because this sphere reminds me Pythagoras´s. That Sphere open the study of curved space described by Einstein. 
The heptagon is a polygon with seven sides and seven vertebrae which area is the same as that of the PI. The sum of the internal angles is 360 degrees and the number of triangles formed in it is 7. It has all the elements studied so far, it is the most complete of them.
Today Iwe came across the quantum physics, because was Nobel Prize 2023 Nobel Prize was given to Alain Asect, John Clauser and Anton Zellinger for experiments on the connections and intertwining of subatomic particles. The quantum point, and which gave them colors to each of them.
The ray of light was considered straight and direct, but they discovered that they form a tangle and mix with each other, as a nanoworld rainbow. Like colors on a palette? ....
Electrons are the unit of matter while the unit of light is called photons. The result of the meeting and intertwining of both produces is called quantum mechanics.
Can you imagine the research field that opens up? Even Newton's sphere is a step beyond those before it.
