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brainstormtche.blogspot.com.br/2015/01/eu-um-mendigo-edvard-grieg-um-cachorro.html
https://www.facebook.com/caetanodable/posts/10205681452058628?hc_location=ufi
https://www.facebook.com/photo.php?fbid=10204172380612785&set=a.1842353781643.108883.1324551686&type=3
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www.musicaesociedade.com.br/quem-cria-o-criador-uma-introducao-as-instancias-de-consagracao-artisticas/
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Zé Miguel Wiskik - Oceano de Harmônicos ao Piano - Arte e Ciência ...
https://www.youtube.com/watch?v=b6lpE4cQ8So
https://www.youtube.com/watch?v=b6lpE4cQ8So
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Som e consciência
https://sciart.eu/pt/09-01-2016-1201/1182/som-e-consciencia
Segundo o legado espiritual das tradições hindus, a criação do universo teria produzido um som – conhecido, nas culturas meditativas do hinduísmo, como ‘ohm’. Esse som é representado pelo símbolo ॐ.
Mas, afinal, o que é o som? Em uma das definições possíveis, ele pode ser entendido como simplesmente um conjunto de vibrações captadas por nossos ouvidos. Essa vibrações devem ter entre 20 Hz e 20.000 Hz, pois esse é o espectro de frequência que o órgão auditivo humano é capaz de perceber e que, portanto, reconhecemos como som audível.
Essa definição de som, porém, exclui completamente os sons que o ouvido humano não capta, e basicamente tudo que vibra. Então, com a licença poética, usarei a palavra 'som' pra representar a propagação de uma vibração por uma dada fonte, e sua recepção por algum sistema externo ao que a propagou, ou pela própria fonte, o que mantém a ideia de que há uma comunicação entre a emissão e a recepção.
Um som é transmitido do ouvido para o cérebro. Mas a vibração é captada pelo corpo inteiro, e, muito além do que se escuta, essa vibração pode causar mudanças fisiológicas e emocionais no indivíduo. Independente de qual língua se fale; se essa vibração é de uma pedra caindo; um tiro; um carro ou um latido de cachorro… Os sons nos afetam e nos colocam como interlocutores de um diálogo universal.
Ciência vs Espiritualidade
Há, como sabemos, muitas divergências entre as interpretações científicas e espiritualistas acerca da evolução do universo. Para a ciência, tudo é um provável fruto do acaso. Para a maioria das tradições espiritualistas, entretanto, a criação teria sido um ato intencional. Porém, ambas as correntes convergem quando assumem que, seja como for, da evolução universal resultou a consciência.
Há, como sabemos, muitas divergências entre as interpretações científicas e espiritualistas acerca da evolução do universo. Para a ciência, tudo é um provável fruto do acaso. Para a maioria das tradições espiritualistas, entretanto, a criação teria sido um ato intencional. Porém, ambas as correntes convergem quando assumem que, seja como for, da evolução universal resultou a consciência.
Segundo a ciência, apenas quando esse universo é observado é que ele de fato existe – esse é um postulado até hoje muito discutido, originado nas interpretações dos físicos Niels Bohr e Werner Heisenberg. Tal abordagem ficou conhecida como Interpretação de Copenhagen. Os antigos homens europeus judaico-cristãos entendiam o ser humano como centro da Criação. A ciência, em seguida, adotou essa cultura antropocêntrica, porém substituiu a ideia de um deus por leis naturais e acasos materialistas.
Trazendo agora o debate para nossa vida prática: somos seres conscientes e temos um órgão central de percepção, que chamamos de cérebro. Para a questão auditiva, o cérebro recebe informações de um outro órgão, nossa querida orelha. Uma curiosidade: no jargão médico, o termo ‘ouvido’ era tradicionalmente usado para se referir a essa estrutura captadora de sons, mas hoje os especialistas preferem o termo orelha, mesmo. Ela é dividida em três sistemas: orelha externa, orelha média e orelha interna.
A parte interna da orelha, também chamada de labirinto, é formada por escavações no osso da têmpora, revestida por uma membrana e embebida em um líquido. A orelha interna se divide em uma parte anterior – onde existe a cóclea, que está relacionada à audição - e a parte posterior – constituída pelo vestíbulo e pelos canais semicirculares, e é relacionada ao equilíbrio.
O som, ao chegar na orelha, é direcionado ao tímpano, uma frágil membrana que vibra e passa essa vibração para três ossículos – martelo, bigorna e estribo. Esses pequenos ossos passam a vibração externa para a parte interna da orelha, onde existe a cóclea e o vestíbulo. Essas estruturas recebem os sons e, a partir deles, produzem dois sinais nervosos, que se unem e chegam ao nervo auditivo, que enfim transmitirá os impulsos sonoros ao nosso cérebro. É assim que se forma nossa percepção sonora.
Com essa base anatômica, podemos ir adiante no entendimento efeitos causados por diferentes vibrações na consciência humana – inclusive aqueles causados por frequências abaixo ou acima do limite de percepção do ouvido.
Além do audível
Sair da cidade e ir para um campo pode parecer bem relaxante e até libertador. E não apenas uma questão de ‘sair da rotina’. Os tons mais verdes e azuis, os sons de pássaros e sapos, da água corrente de rios, por exemplo, nos trazem de volta a uma realidade que parecia estar adormecida. Essa frequência vibracional do mundo natural pode ser medida, e sua frequência fundamental é de aproximadamente 432 Hz (o que corresponde à nota musical lá). Essa frequência é tida como uma frequência natural universal, e tem sido cada vez mais estudada nos dias de hoje. Ao contrário, nas cidades modernas, ondas de rádio e microondas, de televisão e celulares, além do barulho de carros, não teriam vibrações interligadas de nenhuma forma harmoniosa. Esse contexto pode causar um grande caos vibracional, confuso e ensurdecedor.
Sair da cidade e ir para um campo pode parecer bem relaxante e até libertador. E não apenas uma questão de ‘sair da rotina’. Os tons mais verdes e azuis, os sons de pássaros e sapos, da água corrente de rios, por exemplo, nos trazem de volta a uma realidade que parecia estar adormecida. Essa frequência vibracional do mundo natural pode ser medida, e sua frequência fundamental é de aproximadamente 432 Hz (o que corresponde à nota musical lá). Essa frequência é tida como uma frequência natural universal, e tem sido cada vez mais estudada nos dias de hoje. Ao contrário, nas cidades modernas, ondas de rádio e microondas, de televisão e celulares, além do barulho de carros, não teriam vibrações interligadas de nenhuma forma harmoniosa. Esse contexto pode causar um grande caos vibracional, confuso e ensurdecedor.
Essa espécie de ’frequência natural’ foi tema de infindáveis discussões ao longo do século vinte. Em resumo: acredita-se que desde tempos antigos a afinação musical era baseada na nota lá, entendida como uma vibração de 432 Hz. No entanto, conta-se que em 1939 o Ministro da Propaganda Nazista, Joseph Goebbels, teria decretado que o tom padrão de afinação da nota lá deveria ser alterado para 440 Hz. Houve polêmica. O próprio Conservatório de Paris, uma das mais respeitadas instituições musicais da época, se manifestou em contrário – reuniu 23.000 assinaturas requerendo a preservação do tom original. Mas atenção: deve-se considerar que o assunto é terreno fértil para teorias da conspiração.
O fato é que mesmo antes de Goebbels, nos Estados Unidos, já se falava em alterar o lá de 432 Hz para 440 Hz. Essa tendência vinha sendo discutida desde o final do século 19 – e mesmo o famoso compositor italiano Giuseppe Verdi tomou parte na briga. No século 19, a discussão foi influenciada pelo fisiologista Herman von Helmholtz, que publicou, em 1863, um texto intitulado A Teoria das Sensações de Tom como uma Fundação da Teoria Musical. Ele defendia a adoção do lá em 440 Hz. Mais tarde, a ideia foi aceita pela Federação Americana de Música (AFM). Em 1940, os Estados Unidos apresentaram essa afinação, em 440 Hz, como padrão. Padrão, aliás, que foi aceito mundialmente em 1953 pela Organização Internacional de Padronização (ISO 16) e permanece até os dias de hoje.
O tema ainda gera debates. Há vasto material de discussão sobre essas duas afinações, e variados experimentos de ressonância estão sendo feitos. Esse campo de estudos é conhecido como ciência cimática. Trata-se de um estudo sistemático das frequências sonoras de modo que suas vibrações possam ser visualmente reproduzidas em sistemas de membranas, superfícies metálicas ou mesmo água. Em geral, algumas frequências resultam em padrões visuais mais ‘harmoniosos’, enquanto outras resultam em padrões mais ‘caóticos’.
Vídeo: Experimento em um tonoscópio: 432 hz vs 440
Alega-se que tais efeitos podem ser percebidos tanto na matéria quanto na consciência. Mas os resultados de pesquisa desse campo de estudo têm sido polêmicos. A afinação proposta por Goebbels, por exemplo, causaria efeitos não saudáveis de desconexão entre corpo e mente – como comportamento anti-social, aumento do uso do lado esquerdo do cérebro, fazendo com que a população lentamente se tornasse mais racional, mais sujeita a ordens, menos criativa e com pensamento mais estreito e linear.
Os sons e o corpo humano
Falamos até agora de sons fora do corpo humano. Mas e nossa própria vibração? Não somos também parte da natureza? Nossa realidade não é baseada apenas em influências externas, mas em processos internos baseados nos nossos pensamentos, percepções e emoções – e isso, sim, é afetado por agentes externos, mas sempre passando por nossa própria percepção, que é produzida no cérebro. Esse mesmo órgão, aliás, produz sua própria série de vibrações, chamadas ‘ondas cerebrais'.
Falamos até agora de sons fora do corpo humano. Mas e nossa própria vibração? Não somos também parte da natureza? Nossa realidade não é baseada apenas em influências externas, mas em processos internos baseados nos nossos pensamentos, percepções e emoções – e isso, sim, é afetado por agentes externos, mas sempre passando por nossa própria percepção, que é produzida no cérebro. Esse mesmo órgão, aliás, produz sua própria série de vibrações, chamadas ‘ondas cerebrais'.
Nos seres humanos, existe um conjunto básico de cinco ondas cerebrais: elas são conhecidas como ondas Beta, Alpha, Theta, Delta e Gamma. Cada uma dessas frequências de onda tem um papel crítico no nosso desenvolvimento mental durante a infância, e mantém nossa saúde e vitalidade como adultos, expressando nossos estados de espírito, humor, equilíbrio, estresse… Não há um estado fixo. Oscilamos, durante nossos dias, por essa diversidade de vibrações. São nossos hábitos e práticas que determinam qual desses estados será predominante.
Essas ondas cerebrais apresentam frequências muito baixas. Uma curiosidade: para reproduzirmos essas ondas de forma audível, hoje se usa uma estratégia chamada sons binaurais. O princípio é simples: em um dos lados de um fone de ouvido, emite-se uma certa frequência (por exemplo, 432 Hz), e no outro lado do mesmo fone de ouvido emite-se uma outra frequência (por exemplo, 444 Hz). Esse processo fará com que a mente entenda a diferença entre essas duas frequências como uma terceira frequência (no caso, 444 - 432 = 12). Isto é, a frequência resultante será 12 Hz.
Vídeo: Som Alpha Binaural: 12 Hz
Voltemos ao tema das ondas cerebrais. As ondas Beta são aquelas que predominam em nosso cérebro quando estamos em estado ativo de consciência – são, de certo modo, as ondas ‘normais’ que emitimos em nosso cotidiano em vigília. Essa frequência varia entre 12 Hz e 30 Hz. É nesse estado vibracional que estamos, por exemplo, quando conversamos, praticamos atividade física, trabalhamos… Permanecer muito tempo nesse estado pode resultar em estresse, ansiedade e inquietação.
As ondas Alpha, por sua vez, se manifestam quando estamos em um estado mental mais livre e mais criativo, ligado ao relaxamento e à meditação. Mesmo o uso da Cannabis, a famosa maconha, pode induzir esse tipo de onda cerebral. As ondas Alpha vibram entre 8 Hz e 12 Hz. Crianças tendem a ter um nível de ondas Alpha bem superior ao dos adultos – são despertas, criativas, imaginativas.
Já as ondas Theta associam-se a estados prolongados de meditação. É um padrão de relaxamento ainda mais intenso – presente na prática de ioga, por exemplo. São ondas que vibram entre 4 Hz e 7 Hz. É, segundo alguns, um estado de quase transe. É comum pessoas experimentarem fenômenos psíquicos nessa condição. Assim como as ondas Alpha, as ondas Theta também podem ser mais comuns durante a infância.
E as ondas cerebrais Delta são associadas ao sono profundo. Vibram com uma frequência entre 0,5 Hz e 4 Hz. É um estado essencial para a regeneração do corpo, ativando mecanismos de auto-cura. Esse padrão costuma ser mais comum em crianças de até dois anos de idade.
Finalmente, temos as ondas Gamma. Elas são de frequências mais altas, entre 25 Hz e 100Hz. Essas ondas relacionam-se a estados de presença muito intensos, a uma sensação de “eu posso fazer tudo”, de “viver o presente momento” – o que pode ser induzido por drogas. Experimentos com monges tibetanos mostraram que, quando eles começavam a meditar e era pedido para que gerassem sentimentos de amor e compaixão, a atividade cerebral deles subia para um estado quase transcendental de consciência.
Convergência
Agora vamos juntar o conteúdo exposto sobre vibrações externas e internas. A cóclea, parte do ouvido responsável pela audição em si, se apresenta em forma de espiral – com proporções que respeitam a chamada sequência de Fibonacci. Esse padrão se repete em diversos exemplos existentes no corpo humano e na natureza. É também o mesmo padrão matemático observado na concha de um nautilus.
Agora vamos juntar o conteúdo exposto sobre vibrações externas e internas. A cóclea, parte do ouvido responsável pela audição em si, se apresenta em forma de espiral – com proporções que respeitam a chamada sequência de Fibonacci. Esse padrão se repete em diversos exemplos existentes no corpo humano e na natureza. É também o mesmo padrão matemático observado na concha de um nautilus.
Essa sequência matemática também está presente nas escalas musicais. Nosso ouvido, portanto, capta as vibrações por sequências harmônicas. Na música, as diferentes escalas estão organizadas de maneira que o som vibra de forma construtiva e harmônica – do contrário, a soma de diversos sons de diversos instrumentos, tocados simultaneamente, seria destrutiva. Uma orquestra ficaria fora de tom, e cada instrumento emitiria um som de forma isolada e não sintonizada com os demais. Se os sons não ressoam juntos, eles se destroem e a vibração some.
É muito provável que os sons afetem, em alguma medida, tanto a organização física da matéria quanto nosso estado psíquico. Aquele riff pesado de guitarra tocando rock tem um grande poder sobre nosso estada de consciência – assim como aquela bela melodia de bossa nova ou a inspirada harmonia da música clássica. O rosnado de um feroz leão nos assusta; o canto de um sabiá nos acalma e o som leve de uma brisa suave nos inspira. Assim é o efeito das vibrações no corpo e mente humana.
Esse é um dos motivos que nos faz intuir que músicos e artistas, de um modo geral, tendem a ser mais criativos. Eles experimentam de forma mais intensa uma conexão com o mundo ao seu redor, e, sem generalizar, apresentam uma aptidão maior na busca pela espiritualidade.
Seja através de uma ordem como “Faça-se a Luz”, ou uma grande explosão causal chamada Big Bang, o universo permanecia num estado de impossibilidades e paradoxos – até que surgiu um movimento, uma vibração. De lá para cá, tudo tem seguido esse imperativo, da menor das partículas até os estados puros de energia. Tudo está em permanente vibração, e a propagação desse movimento afeta o mundo ao redor, que retribui essa onda em um estado eterno de efeito dominó, que foi se organizando harmonicamente e criando o mundo qual o conhecemos. O homem, enfim, viu-se diante da escolha entre continuar o “ohm” original ou criar o próprio. Independente de qual for o destino escolhido e construído por nós, seres humanos, o fato é que no princípio era o som, e, que tudo indica, continuará sendo.
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Interference Theory of Music Perception
By Richard Merrick
http://www.tokenrock.com/music_theory/interference_theory.php
Harmonic Interference Theory
'It occurred to me by intuition and music was the driving force behind that intuition. My discovery was the result of music perception.' - Albert Einstein
The central question in music education and theory is how do musical scales, intervals and chords combine to create a sense of anticipation and resolution, or tension and release. Parallel to this discussion is what causes some intervals to sound pleasingly concordant while others are perceived as gratingly dissonant. These are the fundamental questions of our perception of music that Harmonic Interference Theory was developed to help answer.
We begin by analyzing the pattern of two tones diverging at a constant rate from unison to an octave using what is called a 'Blackman Spectral Analysis' in Adobe Audition.
In this illustration, naturally concordant intervals are identified by vertical gaps in the overall pattern. These intervals correspond to simply harmonic proportions, such as 5:3 for a major sixth and 3:2 for a perfect fifth. Thinner gaps or regions with no gaps then identify dissonant intervals.
The question is then how can we describe the pattern of consonant gaps and what might this have to do with music perception.
As it happens, the distribution of gaps created by two standing waves as they interfere over a frequency-doubled octave can be described mathematically by an equation known as a Gaussian first derivative distribution. Most would recognize this as a the change in velocity along a Gaussian curve, popularly known as a 'Bell curve.'
This first derivative Gaussian curve is very important in the study of human perception. Recent studies have found that the distribution of photoreceptors around the fovea centralis (or blind spot) in the eye follows a Gaussian derivative distribution. The Basilar membrane in the inner ear has also been found to focus itself according to a Gaussian first derivative. Even in the brain itself, neurons always fire in a Gaussian derivative wave.
It would seem that this harmonic interference curve is the one key pattern behind human perception. But its equation looks oddly complex and incomprehensible. Why would something so fundamental to perception and nature be so complex and ungraceful, even as it is clearly related to harmonic formation?
Fortunately, there is another way to describe this organic curve using something called a 'Harmonic Interference Function.'
The same distribution of concordant gaps can be found by simply dividing the square of the harmonic series by the Fibonacci series. Since resonance can always be represented by squaring a round number and damping can be approximated by a Fibonacci spiral, the harmonic interference function helps us understand how nature balances itself between a close circle and infinite spiral.
This can be visualized geometrically using a resonating surface and a Fibonacci spiral. As the spiral pushing into the resonating surface, the geometric mean between the two forms a Gaussian first derivative curve.
This many seem abstract and far removed from the subject of perception and harmonics - that is, until we recognize this geometry acts as a natural focusing function in the formation of life.
Since life too is a standing wave, oscillating in place with every heartbeat, the organic geometry of the body is the reason we developed senses that can perceive and recognize the world? And beneath this, it is the resonance of carbon and water under pressure that made it possible to focus on the world long enough so that Darwinian evolution could help us adapt to our environment. But as it concerns music, the harmonic interference function is the 'built-in' harmonic pattern that enables each one of us to instantly recognize music by focusing on melodies, anticipating harmonic resolutions and feeling the emotion of music simply by listening to it with our Fibonacci double spiral ears.
Between our two ears sits the mysterious brain. But, given that we have two ears mirror images of the other, would not one side of our brain also be a reflection of the other? Further to the point, wouldn't our brain represent a reflection of the same harmonic interference function found in an embryo, just wound around a polar axis?
And, wouldn't this interference geometry be found elsewhere in the body and all nature?
Indeed, reflective interference forms across frequency doubled domains can be found everywhere - from the leaves on trees to the fruit they bear to the animals that eat the fruit. The natural world is built out of interference patterns resonating up from the atomic level into an environment that is built out of the same interference patterns resonating down from the cosmic level. It is here where we meet in the middle between the closed circle and the open spiral.
Even our eardrums twist out of an open spiral to form a closed polar reflective interference pattern.
From the very first moment sound touches our Fibonacci ears, they begin focusing on harmonic proportions. They do this by first using a spiral to cancel out unwanted wave reflection, creating an environment for the recognition of coherent sound.
As they drill further inward, they blossom into the same pattern in our brain, which is repeated like puzzle pieces at different scales in the head.
What we find is that our head is really a fifth appendage that has curled around itself like a clenched fist. In the process, it opens up the sinus cavity and pushes cell growth forward to form the peculiar geometry of a nose.
The spiral of polar reflective interference patterns eventually break through the cranial eggshell at the base of the brain and shoot down into a wave-like spine to create the music of the body. All of this ends in perception, cognition and consciousness - a direct result of the architecture of our nervous system and a harmonically structured body.
From Harmonic Interference Theory, we can use the reflective interference distribution as simple metrics to measure fundamental perceptual qualities in music. Tension and resolution can be measured as a dynamic and temporal differential function gauging the velocity of energy currents (resonance).
Similarly, consonance and dissonance can be measured as a static and spatial integral function gauging the combined area occupied by energy currents (damping). Thus the perceptual qualities of tension and dissonance can be considered separately, one in time and the other in space - yet, both part of the same physical model.
Perception is first and foremost a result of the geometry of the body and Gaussian distribution of cells resulting from the bonding patterns of water and carbon. This distribution is driven from the atomic level up, manifesting step-wise in stages to create the basic shape and taxonomy of each organism.
As evidenced by our conscious self-awareness, we human beings are among the most resonant and harmonically balanced organisms on Earth. For this reason, our most primordial perceptions and emotional responses can be measured and predicted using a spectral harmonic function.
But while the reflective interference model can be used to measure the perceptual qualities of music, we might wonder if scales, chords and intervals inherit this from a pattern deeper in sound. Could the spectral interference pattern of two tones diverging over an octave simply be the visualization of a pattern already existing inside the harmonic series of a single tone? That is, could the single tone produced by a plucked guitar string have this same Gaussian distribution pattern inside of it?
The answer is YES, it does. We can prove this by measuring the proximity of each harmonic to the points of maximum resonance and damping in a standing wave.
To measure maximum resonance, we must identify the point where a Fourier wave adds together to create the standing wave's maximum amplitude. This is marked by a yellow square in the diagram.
For maximum damping, we identify both the frequency and amplitude damping locations that are golden sections (and its inverse) of the waveform. These are marked by 16 dots and 2 vertical lines in the diagram, but due to periodicity just 4 dots can be used to measure proximity.
In this way, this Timbral Proximity Method can be used to order harmonics according to their resonance and damping qualities. This can then be compared to the tension and consonance metrics to see if they agree or not.
Using this diagram as a master template, each harmonic frequency is superimposed to measure its proximity to one or several of these points. Each harmonic is unique in how it aligns near these different locations. However, only the 9th harmonic partial aligns with ALL of the points of maximum resonance and damping. Coloring the intersections with red and green, Partial 9 lights up the proximity plot like a Christmas tree.
This perfect alignment in the plot means Partial 9 acts as a kind of surrogate or twin for the prime resonant frequency of the fundamental wave. More than this, it acts as a polar axis with the fundamental frequency around which all of the other harmonics balance and ‘orbit.' For this reason, Partial 9 can be designated as the Harmonic Center in any standing wave while the axis formed with Partial 1 becomes a Harmonic Axis.
Taken as a numerical proportion, 1 : 9 equals 0.1111111111… while squaring it into the proportion 1 : 81 reduces to 0.012345679…
In these simple proportions we find the synchronization exhibited in the physical intersections of the 9th partial to the fundamental period reproduced in the behavior of numeric division. The number 9 splits out Unity (or singularity) into an infinite number of copies of itself while resonating it into a 9 x 9 square splits (or refracts) Unity into the harmonic series (sans octave 8).
This simple correspondence of physical wave intersections to mathematical proportions appears to be at the bottom of the many legends surrounding 8 and 9.
The Chinese consider 8 to be an auspicious and very lucky number. Things repeat in frequency-doubled octaves. The center ball in a game of billiards is 8. In mathematics, square-free 'sphenic numbers' used to describe periodic functions like Möbius strips and cyclotomic polynomials always have 8 divisors. This means that periodicity in nature is a function of 8, emerging from the cube of 2 (expressed as 23).
At the same time, multiples of 9 are used in the symbolisms of ancient temples to represent heaven and eternal life, translated into modern times as the legendary nine lives of a cat and the bliss of living on ‘cloud nine.' Nine is a harmonic twin or reflection of Unity in the harmonic series of a standing wave, conjuring up the idea of an invisible parallel reality. Thus, scalar recursion in nature is a function of 9 or 3-squared (expressed as 32).
So we have 23 and 32 as the two basic powers describing how harmonics cycle in space and nest in time.
Returning now to Partial 9, we can see it acting as a Harmonic Center once the harmonics surrounding it are mapped out in table form.
Here we see two group symmetries of 13 harmonics each balanced around Partial 9, forming a Harmonic Axis with the fundamental Partial 1 to induce coherent resonance. At the same time, we find another group symmetry of 9 harmonic partials balanced around Partial 5, forming an anti-harmonic damping axis with the center of another near-symmetry group of 6 harmonics.
In this way, we can begin to see how the harmonic series in a standing wave unfolds and balances around its Harmonic Center much like the planets balance around our Sun. We can also see how the timbral components in a single vibrating string correspond to the symmetry and unfolding of intervals in an octave.
For instance, the Super Tonic or 'ninth' in music harmony corresponds directly to Partial 9 in the harmonic series of a single tone. In this way, the Super Tonic acts as the Harmonic Center of a diatonic scale and traditional music harmony. You can prove this to yourself on a piano keyboard by finding the point of symmetry in a C major scale. You will find it to be the Super Tonic D - the same tone corresponding to Partial 9 in the harmonic series of tonic C and commonly known as the ‘ninth.'
Perception of musical scales appears to be directly connected to the physiological recognition of symmetry induced in the brain's neural patterns by sensory input. The brain's symmetrical reflective interference geometry, a product of carbon-water standing wave patterns crystallized into brain tissue, are able to instantly pattern match and measure incoming sound patterns that employ an identical interference pattern. More significantly, the same sensory apparatus is used to pattern match at different scales in sound, simultaneously recognizing timbre and harmony at two different resolutions of harmonic interference.
From this timbre-harmony equivalence principle, we can deduce a 5-level hierarchy that unifies these scales across the entire human spectral auditory range as follows.
This hierarchy is really a continuation of the earlier discussion concerning Phi-recursive heterodyning of harmonics. Each cognitive level is equivalent in its geometry and general emotional effect, even while perceived distinctly at each resolution. Overall, the structure can be modeled as a 3D projection screen organized as 2 to powers of 12 divided into 5 discrete scales of resolution. This bubbles up from inside the narrow proportion 22/3456 that forms around the Phi-eigenvector of a standing wave.
In summary, Harmonic Interference Theory explains music perception as the simple organic process of comparing sonic geometric patterns against the body's own physiological geometry, more specifically that in the auditory system. The key principles are:
1. The brain and senses are a harmonic focusing system based on the model of a standing wave,
2. Perception occurs by matching interference patterns in the environment with a standardized reflective harmonic pattern in the brain,
3. Emotional responses in music are triggered by the direction and velocity of energy transferred between harmonics at Phi-damping locations,
4. Dissonance is a static, spatial and integral perceptive quality while tension is a dynamic, temporal and differential quality, and
5. Emotions can be measured and predicted by weighting and averaging the proposed interference metrics over time.
These findings can be extrapolated to explain all sensory perception. This, however, is an ongoing line of investigation.
Interference - A Grand Scientific Musical Theory, By Richard Merrick
Content courtesy of Richard Merrick
Copyright (c) 2011. All Rights Reserved.
http://www.interferencetheory.com/
Harmonic Interference Theory
'It occurred to me by intuition and music was the driving force behind that intuition. My discovery was the result of music perception.' - Albert Einstein
The central question in music education and theory is how do musical scales, intervals and chords combine to create a sense of anticipation and resolution, or tension and release. Parallel to this discussion is what causes some intervals to sound pleasingly concordant while others are perceived as gratingly dissonant. These are the fundamental questions of our perception of music that Harmonic Interference Theory was developed to help answer.
We begin by analyzing the pattern of two tones diverging at a constant rate from unison to an octave using what is called a 'Blackman Spectral Analysis' in Adobe Audition.
In this illustration, naturally concordant intervals are identified by vertical gaps in the overall pattern. These intervals correspond to simply harmonic proportions, such as 5:3 for a major sixth and 3:2 for a perfect fifth. Thinner gaps or regions with no gaps then identify dissonant intervals.
The question is then how can we describe the pattern of consonant gaps and what might this have to do with music perception.
As it happens, the distribution of gaps created by two standing waves as they interfere over a frequency-doubled octave can be described mathematically by an equation known as a Gaussian first derivative distribution. Most would recognize this as a the change in velocity along a Gaussian curve, popularly known as a 'Bell curve.'
This first derivative Gaussian curve is very important in the study of human perception. Recent studies have found that the distribution of photoreceptors around the fovea centralis (or blind spot) in the eye follows a Gaussian derivative distribution. The Basilar membrane in the inner ear has also been found to focus itself according to a Gaussian first derivative. Even in the brain itself, neurons always fire in a Gaussian derivative wave.
It would seem that this harmonic interference curve is the one key pattern behind human perception. But its equation looks oddly complex and incomprehensible. Why would something so fundamental to perception and nature be so complex and ungraceful, even as it is clearly related to harmonic formation?
Fortunately, there is another way to describe this organic curve using something called a 'Harmonic Interference Function.'
The same distribution of concordant gaps can be found by simply dividing the square of the harmonic series by the Fibonacci series. Since resonance can always be represented by squaring a round number and damping can be approximated by a Fibonacci spiral, the harmonic interference function helps us understand how nature balances itself between a close circle and infinite spiral.
This can be visualized geometrically using a resonating surface and a Fibonacci spiral. As the spiral pushing into the resonating surface, the geometric mean between the two forms a Gaussian first derivative curve.
This many seem abstract and far removed from the subject of perception and harmonics - that is, until we recognize this geometry acts as a natural focusing function in the formation of life.
Since life too is a standing wave, oscillating in place with every heartbeat, the organic geometry of the body is the reason we developed senses that can perceive and recognize the world? And beneath this, it is the resonance of carbon and water under pressure that made it possible to focus on the world long enough so that Darwinian evolution could help us adapt to our environment. But as it concerns music, the harmonic interference function is the 'built-in' harmonic pattern that enables each one of us to instantly recognize music by focusing on melodies, anticipating harmonic resolutions and feeling the emotion of music simply by listening to it with our Fibonacci double spiral ears.
Between our two ears sits the mysterious brain. But, given that we have two ears mirror images of the other, would not one side of our brain also be a reflection of the other? Further to the point, wouldn't our brain represent a reflection of the same harmonic interference function found in an embryo, just wound around a polar axis?
And, wouldn't this interference geometry be found elsewhere in the body and all nature?
Indeed, reflective interference forms across frequency doubled domains can be found everywhere - from the leaves on trees to the fruit they bear to the animals that eat the fruit. The natural world is built out of interference patterns resonating up from the atomic level into an environment that is built out of the same interference patterns resonating down from the cosmic level. It is here where we meet in the middle between the closed circle and the open spiral.
Even our eardrums twist out of an open spiral to form a closed polar reflective interference pattern.
From the very first moment sound touches our Fibonacci ears, they begin focusing on harmonic proportions. They do this by first using a spiral to cancel out unwanted wave reflection, creating an environment for the recognition of coherent sound.
As they drill further inward, they blossom into the same pattern in our brain, which is repeated like puzzle pieces at different scales in the head.
What we find is that our head is really a fifth appendage that has curled around itself like a clenched fist. In the process, it opens up the sinus cavity and pushes cell growth forward to form the peculiar geometry of a nose.
The spiral of polar reflective interference patterns eventually break through the cranial eggshell at the base of the brain and shoot down into a wave-like spine to create the music of the body. All of this ends in perception, cognition and consciousness - a direct result of the architecture of our nervous system and a harmonically structured body.
From Harmonic Interference Theory, we can use the reflective interference distribution as simple metrics to measure fundamental perceptual qualities in music. Tension and resolution can be measured as a dynamic and temporal differential function gauging the velocity of energy currents (resonance).
Similarly, consonance and dissonance can be measured as a static and spatial integral function gauging the combined area occupied by energy currents (damping). Thus the perceptual qualities of tension and dissonance can be considered separately, one in time and the other in space - yet, both part of the same physical model.
Perception is first and foremost a result of the geometry of the body and Gaussian distribution of cells resulting from the bonding patterns of water and carbon. This distribution is driven from the atomic level up, manifesting step-wise in stages to create the basic shape and taxonomy of each organism.
As evidenced by our conscious self-awareness, we human beings are among the most resonant and harmonically balanced organisms on Earth. For this reason, our most primordial perceptions and emotional responses can be measured and predicted using a spectral harmonic function.
But while the reflective interference model can be used to measure the perceptual qualities of music, we might wonder if scales, chords and intervals inherit this from a pattern deeper in sound. Could the spectral interference pattern of two tones diverging over an octave simply be the visualization of a pattern already existing inside the harmonic series of a single tone? That is, could the single tone produced by a plucked guitar string have this same Gaussian distribution pattern inside of it?
The answer is YES, it does. We can prove this by measuring the proximity of each harmonic to the points of maximum resonance and damping in a standing wave.
To measure maximum resonance, we must identify the point where a Fourier wave adds together to create the standing wave's maximum amplitude. This is marked by a yellow square in the diagram.
For maximum damping, we identify both the frequency and amplitude damping locations that are golden sections (and its inverse) of the waveform. These are marked by 16 dots and 2 vertical lines in the diagram, but due to periodicity just 4 dots can be used to measure proximity.
In this way, this Timbral Proximity Method can be used to order harmonics according to their resonance and damping qualities. This can then be compared to the tension and consonance metrics to see if they agree or not.
Using this diagram as a master template, each harmonic frequency is superimposed to measure its proximity to one or several of these points. Each harmonic is unique in how it aligns near these different locations. However, only the 9th harmonic partial aligns with ALL of the points of maximum resonance and damping. Coloring the intersections with red and green, Partial 9 lights up the proximity plot like a Christmas tree.
This perfect alignment in the plot means Partial 9 acts as a kind of surrogate or twin for the prime resonant frequency of the fundamental wave. More than this, it acts as a polar axis with the fundamental frequency around which all of the other harmonics balance and ‘orbit.' For this reason, Partial 9 can be designated as the Harmonic Center in any standing wave while the axis formed with Partial 1 becomes a Harmonic Axis.
Taken as a numerical proportion, 1 : 9 equals 0.1111111111… while squaring it into the proportion 1 : 81 reduces to 0.012345679…
In these simple proportions we find the synchronization exhibited in the physical intersections of the 9th partial to the fundamental period reproduced in the behavior of numeric division. The number 9 splits out Unity (or singularity) into an infinite number of copies of itself while resonating it into a 9 x 9 square splits (or refracts) Unity into the harmonic series (sans octave 8).
This simple correspondence of physical wave intersections to mathematical proportions appears to be at the bottom of the many legends surrounding 8 and 9.
The Chinese consider 8 to be an auspicious and very lucky number. Things repeat in frequency-doubled octaves. The center ball in a game of billiards is 8. In mathematics, square-free 'sphenic numbers' used to describe periodic functions like Möbius strips and cyclotomic polynomials always have 8 divisors. This means that periodicity in nature is a function of 8, emerging from the cube of 2 (expressed as 23).
At the same time, multiples of 9 are used in the symbolisms of ancient temples to represent heaven and eternal life, translated into modern times as the legendary nine lives of a cat and the bliss of living on ‘cloud nine.' Nine is a harmonic twin or reflection of Unity in the harmonic series of a standing wave, conjuring up the idea of an invisible parallel reality. Thus, scalar recursion in nature is a function of 9 or 3-squared (expressed as 32).
So we have 23 and 32 as the two basic powers describing how harmonics cycle in space and nest in time.
Returning now to Partial 9, we can see it acting as a Harmonic Center once the harmonics surrounding it are mapped out in table form.
Here we see two group symmetries of 13 harmonics each balanced around Partial 9, forming a Harmonic Axis with the fundamental Partial 1 to induce coherent resonance. At the same time, we find another group symmetry of 9 harmonic partials balanced around Partial 5, forming an anti-harmonic damping axis with the center of another near-symmetry group of 6 harmonics.
In this way, we can begin to see how the harmonic series in a standing wave unfolds and balances around its Harmonic Center much like the planets balance around our Sun. We can also see how the timbral components in a single vibrating string correspond to the symmetry and unfolding of intervals in an octave.
For instance, the Super Tonic or 'ninth' in music harmony corresponds directly to Partial 9 in the harmonic series of a single tone. In this way, the Super Tonic acts as the Harmonic Center of a diatonic scale and traditional music harmony. You can prove this to yourself on a piano keyboard by finding the point of symmetry in a C major scale. You will find it to be the Super Tonic D - the same tone corresponding to Partial 9 in the harmonic series of tonic C and commonly known as the ‘ninth.'
Perception of musical scales appears to be directly connected to the physiological recognition of symmetry induced in the brain's neural patterns by sensory input. The brain's symmetrical reflective interference geometry, a product of carbon-water standing wave patterns crystallized into brain tissue, are able to instantly pattern match and measure incoming sound patterns that employ an identical interference pattern. More significantly, the same sensory apparatus is used to pattern match at different scales in sound, simultaneously recognizing timbre and harmony at two different resolutions of harmonic interference.
From this timbre-harmony equivalence principle, we can deduce a 5-level hierarchy that unifies these scales across the entire human spectral auditory range as follows.
This hierarchy is really a continuation of the earlier discussion concerning Phi-recursive heterodyning of harmonics. Each cognitive level is equivalent in its geometry and general emotional effect, even while perceived distinctly at each resolution. Overall, the structure can be modeled as a 3D projection screen organized as 2 to powers of 12 divided into 5 discrete scales of resolution. This bubbles up from inside the narrow proportion 22/3456 that forms around the Phi-eigenvector of a standing wave.
In summary, Harmonic Interference Theory explains music perception as the simple organic process of comparing sonic geometric patterns against the body's own physiological geometry, more specifically that in the auditory system. The key principles are:
1. The brain and senses are a harmonic focusing system based on the model of a standing wave,
2. Perception occurs by matching interference patterns in the environment with a standardized reflective harmonic pattern in the brain,
3. Emotional responses in music are triggered by the direction and velocity of energy transferred between harmonics at Phi-damping locations,
4. Dissonance is a static, spatial and integral perceptive quality while tension is a dynamic, temporal and differential quality, and
5. Emotions can be measured and predicted by weighting and averaging the proposed interference metrics over time.
These findings can be extrapolated to explain all sensory perception. This, however, is an ongoing line of investigation.
Interference - A Grand Scientific Musical Theory, By Richard Merrick
Content courtesy of Richard Merrick
Copyright (c) 2011. All Rights Reserved.
http://www.interferencetheory.com/
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