**ORIGINAL ARTICLE**

VIANA, Arnóbio Araújo ^{[1]}

VIANA, Arnóbio Araújo. **The harmonizing operation (H) and its inverse melody operation (M). **Revista Científica Multidisciplinar Núcleo do Conhecimento. Year. 07, Ed. 03, Vol. 03, p. 144-171. March 2022. ISSN: 2448-0959, Access link: https://www.nucleodoconhecimento.com.br/mathematical-olympiads/melody-operation

## ABSTRACT

The lack of a mathematical operation to explain the interactions of waves, especially between the sound waves of musical notes, was the problem that guided the construction of this article. In this context, the objective of this research, aiming at a better visualization of a simple sound wave, was to demonstrate operations developed by the author of this material, composed of three most important characteristics to Music: amplitude , frequency and time of duration. Thus, the form emerged and, in this way, the musical structures of a harmony and a melody formed by their harmonic and melodic groupings, respectively, are analyzed, until the operational properties of these organizations in their physical phenomena are obtained. In the grouping where these musical notes are emitted simultaneously, in space or at the same time, the sound waves are physically in Superposition, causing interference between them, thus originating a sound effect called by the musicians of Harmony. Evaluating this structure in space and time, the mathematical operation that causes this harmonic phenomenon was developed, adopting the fundamental operations that emerged, in this integrated interference, a single special operation, called Operation Harmonization or Operation H. As a result of this operation, its inverse operation was also developed, where the waves of musical notes are emitted continuously in space or one after the other in time, thus originating a sound effect called by musicians as a melody. Analyzing this structure in space and time, the mathematical operation that originates this phenomenon was also developed, called Operation Melodiation or Operation M, serving the purpose of this investigation, which aims to provide Science with a mathematical view of the musical structures of harmonies and melodies musicals, providing, in general, new mathematical operations, which can explain phenomena of Nature, making their understanding simpler to Science.

Keyword: Harmonization, Melody, Harmony, Melody.

## 1. INTRODUCTION

At the beginning of 2006, the author of this material developed Operation Harmonization for the harmonic groupings of sound waves of the harmonies of musical notes and Operação Melodiação, for the melodic groupings of sound waves of his melodies.

The problem that motivated the construction of this material and the development of these operations was the lack of a mathematical operation to explain the interactions of waves, especially between the sound waves of musical notes. In this context, the objective is to demonstrate operations developed by the author of this material, composed of three most important characteristics of Music: amplitude , frequency and duration time .

For the development of this, initially, it was considered that only for sound waves and, later, in general, for any other element with or without vibration, the physical phenomenon of “Wave Superposition” occurs, where, in the encounter between two equal waves, there is an increase in the resulting amplitude between them (SILVA, n.d.).

Using the expression, formulated in this study to represent a sound wave, with the characteristics: amplitude , frequency and duration time, it is possible to analyze in a simple way the interference between two sound waves equals.

When they meet at a common point, in this case, their amplitudes add up , remaining the same frequency, with the same duration time .

Evaluating the result of this interference phenomenon, it was observed that at the meeting point p of the superposition between these two waves, in addition to the existing algebraic sum between their amplitudes , there is also a union between their frequencies in that time, forming a single sound wave, with amplitude, frequency and duration time.

It was also concluded, in this initial analysis, that these two operations, addition between amplitudes and union between frequencies, in addition to forming the result of this phenomenon, also integrate a single mathematical operation, characterized by this Operational Duality. This explains the simultaneous emission of waves of musical notes, whose sound effect is called Harmony. Therefore, the name of Operation Harmonization or operation H was admitted, adopting a left slant bar (\) as its mathematical symbol, called the H operator. Originating, with this phenomenon, the Principle of Harmony, where the elements are harmonic, if there is a superposition between them in their space-time.

Consequently, its inverse operation was developed, in which the sound waves leave the superposition condition and pass to the uninterrupted condition, where the final time of one wave is equal to the initial time of the next wave, and so on, whose sound effect is called Melody by musicians. Therefore, the name Melodiation or M operation was adopted, with a right slash (/) as its mathematical symbol, called the M operator, originating the Melody Principle, where elements are melodic, if there is continuity between them in their space-times.

## 2. HARMONIZATION OPERATION (H)

Generally speaking, when two or more rhythmic periodic waves, with different frequencies and amplitudes, are in operation Harmonization or H , they form a harmonic grouping, called Harmony, where the resulting frequency is determined by the union operation between its frequencies and the resulting amplitude by the addition operation between their amplitudes, which can be in the same phase with equal signs, in constructive interference, or in opposite phases with opposite signs, in destructive interference.

The more waves of these types there are in this operation, the more frequencies will be joined and more amplitudes added in the result of this Harmony , as shown in the example below.

Operation Harmonization and its Harmony between three distinct and rhythmic periodic waves:

## 2.1 PROPERTIES OF OPERATION H (HARMONIZATION)

## 2.2 MUSICAL HARMONY

In the Harmonization operation between sound waves, specifically of rhythmic musical notes, where normally the harmony of a main musical chord is formed by a triad or three notes, with different frequencies, the resulting increase in amplitude is linear (MORAIS, 2020).

Assuming that these waves are equal and the fact that the sound intensity of human hearing is logarithmic with a value of * *(SANTOS, s.d.), in this case, its addition is insignificant to be noticed . If this fraction were rounded to one, mathematically, it’s as if she doesn’t exist in this harmony .

Due to this phenomenon and considering this rounding, the harmony of this operation was formed only by calculating the union operation between its frequencies . Therefore, for this simplified result, it is not necessary to know the sound intensity to be applied in a harmony with musical notes in an operation H, as this can be anyone, without prejudice to the harmony of this operation.

Some H operations with musical notes identified by their numbers are described below, where the notes of A, B, C, D, E, F and G are respectively A, B, C, D, E, F, G, taking based on the work of Guest (2020, p. 33 to 41):

1) Calculate the harmony between musical notes:**, **both with two seconds of duration and normal sound intensities.

2) Calculate the harmony between musical notes: , all three seconds long and normal sound intensities.

3) Calculate the harmony between musical notes: , all one second long and normal sound intensities.

Note: in this study, it is defined that a harmony is named with its frequencies in ascending order and tonic accent on the last frequency. For example, is the one second long Ladomisol harmony or A minor minor seventh chord .

## 2.3 UNITARY HARMONY

Unitary Harmony is the result of the H operation between two or more equal periodic waves , forming a harmonic grouping of a single frequency , with its resulting amplitude and a duration time

This type of harmony can appear, in this space-time, that there is only one periodic wave in its structure, however, two or more equal periodic waves coexist in it, occupying the same space-time, constituting a Harmonic Unitary Set capable of generating, in a its unitary structure, two or more continuous equal periodic waves in a new spacetime *. *Unlike a simple unitary set formed by a single wave, where only a single wave of its structure is generated.

In this way, two or more unitary harmonies will only be equal , if all its characteristics and quantities are the same, and when this harmony is formed only by sound waves of musical notes, it is considered as a Unison Harmony , by forming a single sound, with its frequency, amplitude and duration time , as shown in the examples below:

1) Unison harmony between four rhythmic waves, with equal frequencies and different amplitudes.

Graphic 1: Unison harmony

Graph 1 shows the time interval to , which characterizes the H operation and, in the interval from to , the result of the operation or its harmony is shown .

2) Harmony with destructive interference between two rhythmic periodic waves:

Graphic 2: Harmony with destructive interference

The time interval to, shown in the graph above, represents the result of the operation H and, in the interval from to , the result of this operation or its harmony is characterized .

3) Constructive and destructive harmony between three waves:

Graphic 3: Harmony with constructive and destructive interference

The time interval to demonstrates the H operation and, in the interval from to, the result of this operation or its harmony is represented .

4) Harmony between five waves of musical notes equal to the G note, two seconds long.

## 2.4 EMPTY HARMONY

Empty harmony is the result of the operation H between a wave and its opposite wave or the operation between several waves and their opposite waves , forming a harmonic grouping of a single frequency , with its zero amplitude and a duration time

This kind of harmony , it may appear, in this space-time, that there is no periodic wave in its structure. However, it coexists with a resulting frequency, with null amplitude , in an infinitely small state of vibration, in the dimension of time, called Harmonic Primordial Vibration (HPV), represented by a negated zero , constituting, therefore, a Harmonic Empty Set, called by Science of “Quantum Vacuum”, capable of generating in its structure, more than one vibration in a space-time , unlike a simple empty set, where nothing exists and nothing can be generated.

In this way, two empty harmonies will only be equal if their characteristics and quantities are equal. Whatever the empty harmony , it is considered the Neutral Element of the Harmonization operation *,* due to being only an active duration time, which hides one or more inactive vibrations or unable to interact with any active element.

Therefore, the result of the harmony between any neutral element and an active element is the active element itself , no matter what the origin of this neutral element is, if it is with equal frequencies or with equal frequencies, regardless of their duration

, for these vibrations coexist only in the Dimension of Time.

When this harmony is formed by sound waves from opposite musical notes, the sound amplitude is completely eliminated from its frequency

, originating in its place a silence in time, forming a Harmony of Silence. In this case, its silence time is perceived by the human being, due to its duration being equal to or greater than one tenth of a second , this harmony being known as Musical Pause , which will be demonstrated in the examples below.

When this harmony is formed by luminous vibrations, the luminosity of the amplitude of its frequency is totally eliminated

, giving rise, in its place, to a darkness in time, being called the Harmony of Dark Energy and, probably, the darkness that inhabits the Universe, is originated by this harmony implicit in its immense Harmonic Void.

1) Harmony between two waves: , with its graph in the Cartesian system.

Graphic 4: Empty harmony of

The time interval to , shown in the graph above, represents the H operation and, the range from to , is the result of this operation or its harmony .

2) Harmony between musical notes: C, one second long, with equal and inverse amplitudes .

Note: Empty Harmony is a place in space-time where there is a thought that nothing exists in it, however it may be filled with non-perceivable vibrations.

## 2.5 UNSTABLE HARMONY

Unstable Harmony is the result of the H operation between two or more arrhythmic periodic waves or with different durations , where the one with the shortest duration forms the harmony of this operation , due to the property of the rhythm matching the durations of this wave to the smallest, leaving a part of the duration of the longest one , where the formed harmony remains (/) .

The greater the number of these arrhythmic waves in this operation , greater will be the instability of the formed harmony , with degradations in secondary harmonies , with or without a continuous remainder of the wave of longer duration , according to the examples listed below.

1) Unstable harmony between two arrhythmic waves: , with its line graph in Cartesian coordinates.

Graphic 5: Unstable harmony of

The time interval to, shows the graph of the operation H and, in the interval from to , the result of this operation or its harmony is represented .

2) Harmony between two arrhythmic musical notes: , respectively with their durations of threeseconds.

3) Unstable harmony between three arrhythmic musical notes: , respectively with durations of four, three and two seconds, with its graph in the system of Cartesian axes.

Graphic 6: Unstable harmony of

The time interval to , represents the graph of the operation H and, in the interval from t5 to t13, the result of this operation or its harmony is shown .

4) Unstable harmony between three arrhythmic musical notes with equal frequencies:

5) Unstable harmony with empty harmony between two waves: *,* one being triple the duration of the other .

Graphic 7: Unstable Harmony with empty harmony of

The time interval to depicts the operation H and, in the interval from to , the result of this operation or its harmony is shown .

6) Harmony between two G musical notes with equal amplitudes in opposite phases, one lasting three seconds and the other lasting two seconds .

## 2.6 NUMERIC HARMONY

When two or more numeric constants, are in Harmonization or H operation, they are considered rhythmic vibrations and, as they have only one parameter, which can be either frequency or amplitude, they are at the same time joined as frequencies and added as amplitudes , forming the harmony of this operation

Any cluster formed by a combination of Combinatorial Analysis is considered the result of an H operation between these elements ,with the result of their amplitude implied in the union between them, as demonstrated in the examples below.

1) Harmony between numerical constants 1 and 1

2) Harmony between numeric constants 1 and -1

3) Harmonies between numeric constants

4) Harmonies between numeric constants

5) Harmonies between numeric constants

6) Harmonies between a numeric constant and any neutral element

Note: the harmony of the operation H between any numerical constant “n” and any neutral element , is the numerical constant itself with amplitude equal to its value . In this operation, we know that the amplitude of the neutral element is zero , but its frequency is undetermined and, even if it were known , she would be in the dimension of time, unable to interact with any active element of any dimension.

## 3. OPERATION MELODIATION OR OPERATION M

The Melody operation or M, is the inverse operation of Harmonization, because after the end of the duration of a harmony, the periodic vibrations that were in superposition, pass the condition of Uninterruption, that is, they form a continuity between their spaces-times, where the end time of one duration is equal to the start time of the next duration , This phenomenon is called the Melody Principle.

Therefore, when two or more periodic vibrations stay in operation M , the result is a melodic grouping, which if they are waves of musical notes, the sound effect results in a Melody and, if these elements are numerical constants in operation M, they will also form a continuous grouping between them, forming the numerical melody of that operation . Thus, any grouping formed by an Array of the mathematics of Combinatorial Analysis is the result of an operation M, which is not a commutative property.

## 3.1 MELODY WITH EQUAL FREQUENCIES AND OPPOSITE AMPLITUDES

Normally, musical notes in an M operation have amplitudes in positive phases, however, if there is a note with amplitude in negative phase, it can be modulated to positive phase, as the frequency remains the same, producing the same sound effect in the formed melody

.

However, this negative sign can remain in the musical note cipher and in the melody result with a dot over it . If this element is a negative numeric constant in this operation , it can also be modulated to positive or identified a point on the constant in the resulting melody.

## 3.2 THE MUSIC PAUSE (*p*)

The Musical Pause is a musical note with zero sound frequency amplitude, represented by a negated zero . In other words, it is the neutral element of the H operation, and its main function in a melody is to provide a sound discontinuity between melodic musical notes or to leave a soundless space between them . It can also be implied only at the beginning of the first bar of a rhythm and at the end of the last bar of that rhythm, completing its periods.

## 3.3 EXAMPLES OF OPERATION BETWEEN WAVES OF MUSIC NOTES

The Binary Rhythmic Module in has been added to organize musical notes grouped into measures every two seconds.

## 3.4 APPLICATION OF THE DISTRIBUTIVE PROPERTY OF OPERATION H

When a musical note starts in one measure and ends in another without losing its sound continuity, its continued cipher receives an apostrophe in the next measure, for example, .

1) Rhythmic Distribution:

2) Major Arrhythmic Distribution

3) Minor Arrhythmic Distribution

## 3.5 EXAMPLES OF OPERATION M WITH NUMERIC CONSTANTS

## 4. ALGEBRA OF VIBRATIONS

The Algebra of Vibrations is nothing more than Algebra with at least one of the Harmonization or Melody operations in its expression.

Even if it does not present any of these operations, it can be modulated for the Algebra of Vibrations, through the available wave modules, such as: the Melodic Module , that turns an algebraic expression into a melody; the Harmonic Module , that transforms an algebraic expression into a harmony; the Composite Module , which transforms an algebraic expression into a melody with harmony, whose normally arrhythmic results are modulated to any rhythm.

Through the standard rhythm modules , that organize the musical cells into rhythmic sound groups, adding their durations in equal periods, in measures: Binary , Ternary or Quaternary . In this case, the first and last measures of any rhythm may be incomplete with musical notes, as shown in the example below.

given to the expression: and the numeric constants and sonorous . Values are calculated, numeric , melodic , harmonic it’s composed .

## 4.1 CALCULATION OF THE NUMERICAL VALUE OF *E=x+3y−2z*

Replacing the variables in the expression E

## 4.2 CALCULATION OF THE MELODIC SOUND VALUE OF* E=x+3y−2z*

the melodic module transforms a numeric algebraic expression into a melodic algebraic expression, replacing all existing operations with M operations (/).

The normally arrhythmic result is modulated to any rhythm , to organize the musical notes in a simple performance.

Note: The operation M between a numerical constant “n” and a sound constant “x”, is equal to the melody of the sound constant “n” times .

Melodic expression module

Comment: choosing a rhythm is optional and, if the ternary rhythm module was chosen, the last note would be divided with a part in the penultimate measure and another continuous in the last measure, identified with an apostrophe in its cipher.

## 4.3 INTERACTIVE MELODIC VALUE OF *E=x+3y−2z *

When substitution occurs in the melodic module, both of sound and numerical constants, the resulting melodic expression is called interactive, as it includes a physical dynamics as a function of the numerical constant, as shown in the example below.

given to the expression and the constants Its melodic value is calculated.

Note: the numerical value three (3) in the first bar represents any physical action, for example: counting from one to three in triple time and then playing the indicated melody in the following measures . This counting in binary or quaternary rhythm makes the execution of this complex dynamic difficult to fulfill, therefore, it is important to choose a suitable rhythm for an interactive melodic expression.

## 4.4 MELODIC NUMERIC VALUE OF *E=x+3y−2z *

When in the melodic module the constants are all numeric, the result is a numeric melodic grouping, as shown in the example below.

## 4.5 HARMONIC SOUND VALUE OF *E=x+3y−2z*

The harmonic sound module transforms a numerical algebraic expression into a harmonic sound algebraic expression, replacing all existing operations with H operations (\). The result is usually arrhythmic modulated to any rhythm for its easy execution.

Note: the operation H between a numerical constant “n” and a sound constant “x” is equal to the unison harmony of the sound constant .

## 4.6 INTERACTIVE HARMONIC VALUE OF *E=x+3y−2z *

When the replacement of both sound and numerical constants occurs in the harmonic module, the resulting harmonic expression is called interactive, as it includes a physical dynamics as a function of the numerical constant, as shown in the example below.

The harmonic sound value of the expression is calculated , given the constants .

Note: the numerical value three (3) in the single bar represents any physical action, for example: counting from one to three in triple time while performing the indicated harmony . This counting in other rhythms makes the execution of this dynamic complex and difficult to fulfill, therefore, it is very important to choose a rhythm for an interactive harmonic expression.

## 4.7 HARMONIC NUMERIC VALUE OF *E=x+3y−2z *

When in the harmonic module the constants are all numerical, the result is a numerical harmonic grouping, as shown in the example below.

## 4.8 COMPOUND SOUND VALUE OF *E=x+3y−2z*

The composite module transforms a numerical algebraic expression into sound expressions with melodies and harmonies, replacing all existing operations with M and H operations. The result is usually arrhythmic modulated to any rhythm for its simple execution. In this case, there will be the option of which operations will be replaced by the voiced ones, and with each choice a different composite sound expression will be formed, as shown in the example below.

The composite sound value of the expression is calculated , replacing the first two operations by H operations and the last two by M operations, for the sound constants

## 4.9 INTERACTIVE COMPOUND VALUE OF *E=x+3y−2z*

When the substitution of both sound and numerical constants occurs in the composite module, the resulting composite sound expression is interactive, as it includes a physical dynamics through the numerical constant, as shown in the example below.

The composite sound value of the expression is calculated , replacing the first two operations by H operations and the last two by M operations, for numerical constants and sonorous .

## 4.10 NUMERIC VALUE COMPOSED OF *E=x+3y−2z *

When in the composite module only numerical constants are replaced, the result is a numerical composite grouping, as shown in the example below.

## 5. SCIENTIFIC HYPOTHESES OF THE AUTHOR

With the development of the Harmonization operation, some scientific hypotheses raised by the author of this material emerged, in this study, for some natural phenomena.

## 5.1 WAVE-PARTICLE DUALITY OF LIGHT

The phenomenon of wave-particle duality of light, where light has the characteristic of either a wave or a particle, can be explained by the Operational Duality property of the Harmonization operation.

It is known that light is a harmony formed by several shades of light vibrations in operation Harmonization or H , where the resulting amplitude has as a function the addition operation between the amplitudes of these vibrations.

The greater the number of vibrations in this operation, the greater the resulting luminous amplitude , influencing, with this amount of light energy, its particle side, while its waveform is maintained as a function of the Union operation between the frequencies of these light vibrations

, that form the harmonic grouping of the harmony of this operation , influencing its wave side.

Due to the length of these waves, this balance is maintained between these two characteristics wave and particle, which does not occur with a sound wave, due to its large wavelength in relation to the light wave, with this, its side prevailing preponderantly waveform, relative to the insignificance of its particle side.

## 5.2 ORIGIN OF DARK ENERGY

The phenomenon of Dark Energy existing in the Universe may be a consequence of Empty Harmony, the result of the Harmonization operation between vibrations of opposing luminous particles ,that eliminate the luminosities of these vibrations, originating in its place the Darkness that constitutes the Dark Energy, where the resulting frequency of this harmony coexists in a state of Harmonic Primordial Vibration (HPV) in a Harmonic Void, also called Quantum Vacuum.

## 5.3 THE STRUCTURE OF TIME AND ITS EXPANSION FORCE

A time interval consists of a period , formed by an initial time and an end time , whose difference between them measures their duration . These periods are seamlessly linked, where the end time of one period is equal to the start time of the next period and so on, constituting a closed time interval from a past period, to a present period, and open at the beginning of a future period, forming its Space-Time , which by the Melody Principle is equal to the operation M between these past periods , present and future .

It is also known that the initial time of each period is characterized by a Beat , caused by an intrinsic impulse, given by a force with an instantaneous duration , remaining a time of silence until the end of that period , given by the difference between the end time of this period by the time beating of this impulse .

Therefore, a period can be defined by the operation M, between its beat and its silence time . Replacing the periods with your beats in Space-Time *,* The Rhythmic Cadence of Space-Time is formed , whose beat speed, called Rhythmic Tempo , is inversely proportional to its period , scaled in heartbeat per unit of time.

The shorter this period , the greater your rhythmic tempo . This phenomenon also promotes, with its influence on Space-Time, two movements in physical bodies located in its field of action, one of which is called Rhythmic Regency , where a body without leaving its resting position accompanies the beats of the rhythmic tempo, and another called Rhythmic Dance , where a body moves from its resting position to other distinct positions, also depending on the Rhythmic Tempo of this rhythmic cadence.

Considering a period , where the silence time is null , the instantaneous pulse time will constitute its shortest duration , there is, therefore, a repulsion force implicit in its structure, considered weak in its rhythmic cadence in Space-Time , however capable of moving away any celestial body in the Universe and promoting with its Rhythmic Tempo, the Rhythmic Conducting and Rhythmic Dance movements.

It is known that the Universe is expanding and that its galaxies are moving away from each other, which can be explained through the Time Expansion Force of its Rhythmic Cadence and, considering that the orbits of galaxies around the center of the Universe are approximately elliptical, therefore, their accelerated expansion is not yet explained due to this approach to their center of gravity, where there is probably a harmony of black holes, with their force of attraction.

However, this acceleration should cease to exist after the galaxies move away from this center, with a deceleration and, those that reach the largest orbits, will form the unstable edge of the Universe, like an unstable liquid bubble, as they would be changing shape as a function of the infinities of maximum afcenters of these galaxies in all directions, relative to the center of the Universe.

## 5.4 THE SINGULARITY OF THE BIG BANG AND THE DARKNESS OF RELIGIOUS THEORY

It is known that all matter is formed by atoms, which are in constant vibration, which in turn are formed by smaller and smaller particles until we reach the smallest of all particles of matter, called the Elementary or Primordial Particle (ANJOS, n.d.) , represented, in this study, by a simple vibration , with its frequency , amplitude and continuous time . Likewise, there is its primordial antiparticle of antimatter, with the same frequency , opposite amplitude and opposite time or harmonic, that is, instead of time going from the present to the future in a melodic cadence, it comes from the future to the present, in a harmonic cadence.

These luminous vibrations in Operation H , will form the Primordial Unitary Harmony of Dark Energy, capable of originating all the energy of matter and antimatter, contained in its structure in a state of Primordial Harmonic Vibration or in a Harmonic Void, also called by the Science of Quantum Vacuum *.*

Therefore, for any Theory of the Origin of the Universe, it is always admitted the existence of a point of origin of everything, such as the Big Bang Singularity, the Darkness of the Religious Theory (Bible) or any other, which always leads to Primal Unitary Harmony of Dark Energy *,* capable of generating all the energy for the formation of both the Universe of Matter in the Rhythmic Cadence of Continuous Time, with its Expansion Force , as well as all energy in the formation of the Antimatter or Immaterial Universe in the Rhythmic Cadence of Harmonic Time, called “God’s Time”, with its Force of infinite attraction.

## 5.5 THE ZERO TIME OF CREATION OF THE UNIVERSE

A period of time, however short its duration, will always be formed by an initial time with a beat , formed by a force F, and a beat duration time greater than zero .

Considering this initial time, it can be said that the Universe had its beginning in an instantaneous beat , but before this beat happened, there was a null or zero time and, For this to be true, there must first be an Empty Primordial Harmony , formed by infinite waves-particles of matter in harmony with infinite waves-particles of antimatter .

In this case, the time continuum of the material Universe was in harmony, too, with its opposite or anti continuous time of the Antimatter Universe, resulting in Null Time or Zero Time in this harmony, full of energy accumulated in a single frequency in Harmonic Primordial Vibration.

Considering the shortest possible time to exist in a harmony, with its beat, formed by a force F with a certain intensity , it turns out that time is a wave-particle, where F is its amplitude and the inverse of your beat time is your frequency , that in Harmony with its opposite wave-particle, also, with its opposite amplitude and its frequency , results in an empty harmony of Time Zero of the Beginning of the Universe.

## 5.6 OMNIPOTENT UNITARY HARMONY

In the formation of the Material Universe, continuous time with its expansion force, was forming the innumerable distinct particles of matter, through their combinations, with a single primordial particle *.*

In the case of the formation of the Antimatter Universe, the anti continuous or harmonic time, with its force of attraction, formed the Primordial Unitary Harmony

, attracting all primordial anti-vibrations in a single harmony, capable of originating all of its structure, forming the Immaterial or Antimatter Universe , hence called Omnipotent Unitarian Harmony (God).

## 6. FINAL CONSIDERATIONS

With the development of the Harmonization operation and its inverse Melodiation operation, it was possible to create a mathematical structure for the evaluation of the musical characteristics of a melody, as well as a harmony, making Music not only an art, but also part of Science.

It also became possible to use Algebra with not only numerical expressions, but also sound ones, forming the Algebra of Vibrations, with interaction between numerical and sound values in the result of an algebraic expression, allowing a physical act to be accompanied by a melody or of a harmony, or even of a melody accompanied by a harmony

A new way of looking at the Universe was also proposed, through a macro and micro perspective, through the conception of the structures of harmonic and melodic vibrations, since everything is vibration. Therefore, some of the hypotheses raised by the author of this material were demonstrated for some questions still unanswered for Science, such as the existence of God.

## REFERENCES

ANJOS, Talita Alves dos. Partículas elementares. **Brasil Escola.** Disponível em: https://brasilescola.uol.com.br/fisica/particulas-elementares.htm. Acesso em 21/03/2022.

GUEST, Ian. **Harmonia – Método Prático.** Editora Luminar. Vol. 1, p. 33 a 41, 2020.

MORAIS, Gustavo. Teoria musical para iniciantes: você sabe o que são os acordes? **Terra**, julho de 2020. Disponível em: https://www.terra.com.br/diversao/musica/teoria-musical-pra-iniciantes-voce-sabe-o-que-sao-os-acordes,7c62b1fa5e0fe37c8e0180310bc04200tnys05tj.html Acesso em: 20/03/2022.

SILVA, Domiciano Correa Marques da. Interferência de ondas. **Brasil Escola. **s.d. Disponível em: https://brasilescola.uol.com.br/fisica/interferencia-ondas.htm. Acesso em 17/03/2022.

SANTOS. Marco Aurélio da Silva. A Sensibilidade Auditiva. **Mundo da educação. **Disponível em: https://mundoeducacao.uol.com.br/fisica/a-sensibilidade-auditiva.htm. Acesso em: 20/03/2022.

^{[1]} Graduated in Electrical Engineering, op. Electronics from the Federal University of Pará-UFPA. ORCID: 0000-0001-7010-9114.

Sent: February, 2022.

Approved: March, 2022.