A scale method in which music note frequencies are composed of natural numbers

Abstract

The invention relates to a method for scaling the note frequency scale describing tonal frequencies between two octaves in musical systems to scale intervals that are more harmonious than the scale system intervals used today, and for defining note frequencies in the scaling as frequency values consisting of natural numbers.

Description

[0001] A SCALE METHOD IN WHICH MUSIC NOTE FREQUENCIES ARE COMPOSED OF NATURAL NUMBERS

[0002] TECHNICAL FIELD

[0003] The invention relates to a method for scaling the note frequency scale describing tonal frequencies between two octaves in musical systems to scale intervals that are more harmonious than the scale system intervals used today, and for defining note frequencies in the scaling as frequency values consisting of natural numbers.

[0004] PRIOR ART

[0005] Sound can be described as the wave motion generated by any vibrating object and propagated in the material environment in which it is located. The vibration of sound is described in terms of frequency and its loudness in terms of amplitude. Music, on the other hand, can be defined as the art of shaping sounds by dividing the formal properties of sounds into specific frequency (pitch) regions called 'notes', presenting them in a harmonious sound sequence and thus stimulating an emotional response in listeners. In music, the scaling (intonation) system is the scaling system between the frequencies of notes defined in a frequency range (octave frequency range) where frequencies increase by a factor of 2, and the same scale system is used in all octave frequency layers. In music, the intonation system is the creation of notes of a certain scale between two octaves to create music.

[0006] Music is made up of notes, rhythms, parts and meters. It is important that the note frequencies that make up the music are chosen to best reflect the harmony between the sounds [1]. The first of the musical sequences was introduced by the Greek philosopher Pythagoras in the 6th century BC. Pythagoras discovered that a single string with two fixed ends produces different sounds when stretched. Suppose we get the Do sound when a stretched 1 m long wire vibrates. According to the Pythagorean theorem, if the length of the string is shortened to 8 / 9, the Do sound is taken from 64 / 81 , Mi from 64 / 81 , Fa (interval of 4) from 3 / 4, Sol (interval of 5) from 2 / 3, La from 16 / 27, Si from 128 / 243, and Do, the treble octave of the first Do, from 1 / 2 of the string. Pythagoras also observed that a harmonious sound is produced when the length difference between the strings is 2 / 1 , 3 / 2, 4 / 3, 5 / 4. In other words, he discovered the importance of numbers such as 1 ,2, 3, 4, 5 in the proportional relationship between note frequencies and created the so-called 'pentatonic scale'. The distance between two notes with a ratio of 3 / 2 is called a 'perfect fifth'. For example, in Table- 3 created with the invention, there is a perfect fifth ratio between the do and sol note frequencies. Even if the Pythagorean scale is not used in the chromatic scale of Western music today, it is seen that the Pythagorean scale is taken into account when constructing a proportional relationship of integers between the frequencies of notes (do, re, mi, fa, sol, la, si). As you move towards the end of the octave band in the Pythagorean scale, or as you move towards microtonal notes, you fall into intervals called "wolf intervals", which sound quite uncomfortable. If it is a generally accepted fact today that the necessity of frequency scale harmony with good reflection in the ear within an octave range, it is better to turn to scaling systems where both the harmony in scaling is achieved and the scaling harmony does not deteriorate rapidly as you move along the octave band or towards microtonal notes.

[0007] When a wire with two fixed ends is pulled in the middle and released, the vibrations on the wire create a sinusoidal wave motion. In this wave motion, a main wave with a fundamental frequency and harmonic waves with frequency values at integer multiples of this main wave frequency (Figure-1). During all this movement, with the interference of vibrating waves, a pattern called 'standing waves' is observed, and standing waves are a very important concept for all musical instruments. Standing waves on a guitar string, for example, are resonant waves that, as they move in different directions due to the vibration of the strings, gather together and become stronger, thus reaching large energy levels. When the string is struck, it causes vibration depending on the angle and speed of the strike, and the vibration mode of the string, i.e. the resonant frequency, is formed on each of the standing waves formed on the string. The other waves generated on the wire by the effect of this mode of vibration are harmonics (also called spontaneities or selenics). In air, this vibration travels perpendicular to the length of the wire.

[0008] A sine signal, taken by itself, has a single frequency (fundamental frequency). The harmonics of a sine signal, as mentioned above, progress as integer multiples of the fundamental frequency. If the fundamental frequency is F0, the 1st harmonic F0 (fundamental component), 2nd harmonic frequency 2 x F0, 3rd harmonic frequency 3 x F0. If we express the signal function in Figure-1 as y(t), the total y(t) function including the fundamental component sin(2TrF0t) and 4 different harmonic components can be expressed as follows: y(t)=Y1 sin(2iTF0t)+Y2sin(4TTF0t)+Y3sin(6TTF0t) +Y4sin(8irF0t)

[0009] Here, fundamental frequency F0 is the 1 st harmonic frequency, F2, F3, F4 are the 2nd, 3rd, 4th harmonic frequencies respectively; Y1 , Y2, Y3, Y4 are the amplitudes of the harmonics. Similarly, wind instruments produce resonant standing waveforms. In stringed instruments, the length, tension and material of the string affect the standing waveforms. In stringed instruments, the strings initiate the vibration, and the body of the instrument amplifies the vibrations on it to the sounds we can hear. The body of the musical instrument causes the normally small signal vibrations to be amplified and heard. The wavelength of a complete sine wave of the smallest frequency that can vibrate on a stringed instrument (A=1 / f) is equal to the length of the string (L). If the fundamental frequency is f, the frequencies of the harmonics will occur in the treble direction (2f, 3f, 4f ...). In this context, the frequencies of the waves on the wire coherent with a frequency f are (5f / 4, 4f / 3, 3f / 2, 5f / 3, ...). Figure-2 shows some harmonized note scale ratios on a string of length L.

[0010] Sinusoidal waves are waves that repeat with certain frequencies and alternate between certain amplitudes. By changing the amplitude and frequency values of a sine wave, different tones can be obtained. The international unit of frequency is Hertz (Hz) or (1 / second). When sinusoidal signals are subjected to signal processing, spectrum analysis is largely based on Fourier's theorem. According to Fourier's theorem, any signal with sinusoidal content can be expressed in terms of the sum of sine signals of different amplitudes and frequencies. Each instrument has its own harmonic spectrum. When an instrument is vibrated, for example, at a fundamental frequency of 200Hz, the resulting signal form can be described by Fourier's theorem as a sum of harmonic sine signals at different frequencies and noise levels such as 400Hz, 600Hz, ... in addition to the fundamental frequency 200Hz. The formant (resonant) frequencies emanating from an instrument represent the regions where the sound energy from the instrument is concentrated. These are concentrated in the region with the highest amplitude, called the fundamental frequency. Music signals contain many sinusoidal waves. For frequency analysis of the signal form, which is a combination of different tones in a musical signal, spectrum analysis is required.

[0011] For musical note frequencies, the ratio of any frequency to twice that frequency is defined as an 'octave' interval. Scales divide each octave into parts known as intervals, and the scale system determines how these intervals are divided. The combination of all these intervals forms musical notes. The scale system, a collection of tonal signals created by dividing two octaves into specific intervals according to its own scaling method, constitutes the musical system. The chromatic scale, also known as the 12-TET equal temperament system, is a musical system that is accepted in today's western music and is widely applied as a standard all over the world. The common tuning system used in Western music since the 18th century is the 12 equal temperament, also known as the 12-TET system (also known as the 12-pitch or 12-tone system), which has 12 intervals (12 pitches) in each octave at half-tone distances.

[0012] Western music 12-TET frequency ranges are defined in terms of the notes and corresponding frequencies in Table-1 in the range (16Hz-8kHz), as can be seen in Table-1 as used today. 12-TET equal temperament is a system that determines frequency calculations between two octaves based on logarithm-2. This system currently uses the 12th order root of 2 (2(1 / 12)1 .05946) as a multiplier to find the frequencies in each octave range, thus dividing each range into 12 parts on a logarithmic scale. The multiplier value here is the same for all intervals, but the distance between intervals is not the same and only the frequency ratios of any two adjacent notes are equal. As can be seen from Table-1 , in the 12-TET music system with equal temperament chromatic scale, the minimum frequency value in the Oth octave is 16.35Hz and the maximum frequency value in the 8th octave is 7902.13Hz. An octave layer is not defined for other frequency ranges, but can be generated by calculations in the scale system if desired.

[0013] The note frequencies in the chromatic scale 12-TET system were set to the pitch of 440Hz chosen for the note A4 (LA-4 note), with a standard document adopted in 1975 [2], The frequencies of all other notes in the chromatic scale are defined as semitone lower or higher multiples of 440Hz. In this context, all over the world, the instruments to be used for this music system, almost all western musical instruments such as pianos and guitars, are manufactured and tuned in accordance with the chromatic scale and its tuning frequency of 440Hz. On the other hand, as seen in Table-1 , even the note 'La', which has a tuning frequency of 440Hz, takes fractional values in the Oth octave and octaves below, where it is 55Hz. Another point is the fact that, especially in stringed instruments, when the relationship between the length of the string and the frequency of the resulting waves is reviewed, the string lengths and note locations of musical instruments must be adjusted using scale ratios within an octave range (1.0595, 1.1225, 1.1892, 1.2599, 1.3348, 1.4142, 1.4983, 1.5874, 1 .6818, 1 .7818, 1 .8877) in order to produce the 12-TET Chromatic scale notes in Table-1 .

[0014] When the frequency table based on the 12-TET chromatic scale with the frequency values presented in Table-1 is examined, there is no pure resonance (ringing) frequency except for the tuning frequency. In this case, using a note frequency table that does not contain any resonant frequencies and the scale ranges above, it is very difficult to claim that any piece of music is played with the correct note frequencies. Furthermore, by dividing the frequency ranges of the whole-tone notes between 2 octaves, which are more treble or more pest-like of a note, by the base logarithm-2, the ear's selectivity for treble frequencies within the octave is strengthened. In Table-1 , the frequency values in octave intervals contain fractional numbers when the A note is taken as the tuning frequency. In the 12-TET system, the ratio of whole 5ths between two notes is represented by (3 / 2 -> 2(7 / 12)= 1.4983) and the ratio of whole 4ths is represented by (4 / 3 -> (2(5 / 12)= 1.3348). On the chromatic scale, even the frequency ratios 3 / 2 and 4 / 3, which are considered the most harmonious in music, cannot be fully captured.

[0015] In some musical systems, the octave intervals are 19-TET, 24-TET, 31 -TET or 53-TET like the Turkish makam music of the Ottoman period. Since the 53-TET system contains 53 different tonal frequencies in the octave range, it is a system that can be more easily adapted to Pythagorean tuning, where the frequency ratios in the musical intervals are determined in a 3 / 2 ratio, than the 12-TET system.

[0016] In the known case of the technique, one of the methods is the 'Just intonation-Just intonation (JI)' scale method, in which musical scale tuning is determined in terms of rational numbers. This method uses a prime number as a limit and a range to generate harmonic ratios. For example, in the 5-limit JI method, intervals are determined in powers of 2, 3 and 5. Similarly, in 7-limit JI, interval scales in powers of 2, 3, 5, and 7 are determined. JI is a scale method in which musical scale tuning is specified in terms of rational numbers, and it is possible to find more than one JI scale range in open sources. Table-4 presents the scale ratios of the 7-limit JI scale to the notes in the 12-TET system. The JI method explains note tonal frequencies in terms of 12-tone and tries to create a tonal system from harmonic scales that the 12-TET chromatic scale system cannot fully capture. In this context, interval scaling is non-linear.

[0017] Another method in the known state of the technique is the octatonic 8-note scale. The octatonic scale can be obtained from a sequence of whole and semitones in the 12-TET chromatic scale. In other words, rather than a scale system such as rearranging the frequency table, it seems to be the process of obtaining an 8-part scale with the combination of 8 notes in the 12-TET note scale.

[0018] In their study [3], Schwartz et al. obtained the probability distribution function of the average frequency-amplitude behavior of speech signals using more than 600 recordings from the TIMIT acoustic phonetic audio database of English speech sentences. They also tested different spoken languages other than English, and the probability distribution functions in these graphs show that the resonance amplitudes of the different languages vary, but the scale ranges of the resonance frequencies are similar. It can be seen from the graphs here that the resonant frequency ranges within the two octave range of the probability distribution functions of speech signals and the harmonized note frequency ranges in musical signals are parallel to each other. Frequency resonance points in the statistical mean amplitudefrequency distribution of the human voice show that the human ear successfully perceives coherent tonal scales in music. These scales in the article are (1 , 1 .2, 1 .33, 1 .25, 1 .4, 1 .5, 1 .6, 1.67, 1.75, 1.8, 2). As seen in Table-3, these scales are included in the frequency ratios in the Invention.

[0019] Two different note frequency scale systems (12-TET and 53-TET systems) in the known state of the technique mentioned above were analyzed. In the known state of the technique, in the 12-TET western music chromatic scale, also known as the equal temperament chromatic scale, which is widely used in the world today, 440Hz is used as the tuning note frequency of the A-4 note in the 4th octave, and the frequency ranges of all other notes are calculated with reference to this tuning frequency value. In the 12-TET system, there are 12 notes (notes C, D, E, F, F, G, G, A, B), 7 main tones and 5 semitones in a two octave range. On the other hand, the number 12 is not a power of 2. In the 12-TET system, all frequencies except the 'La' note frequencies used as tuning notes are in fractional numbers. To find the 12-TET note frequencies, all other note frequencies are calculated by moving an 'i' index with a value of 0 at La-4 = 440Hz forward or backward from 440Hz with negative integers. Here, taking the index range between octaves [0-8] (i=-57-»50), the frequency values can be calculated with 440*2(i / 12). Here the ratio of all frequencies is equal and the ratio between two adjacent frequencies f2 / f1=2(1 / 12)=1 .059463 is the relative frequency value.

[0020] In the known case of the technique, the Turkish makam music scale, also called the 53-TET system, was also studied. Here, the frequencies in each octave range are divided into 53 segments (also called 'gam' in Turkish music), where each segment is called a 'coma'. The only note frequency where today's 53-TET Turkish makam music and 12-TET western music meet is 440Hz, which is the tuning frequency in western music. The tuning system in Turkish Music is usually determined according to the names of the 'Ney' instrument, and for example, according to the 'Mansur Ney' tuning, the 'Dugah' pitch corresponds to the A-4 pitch in western music, and the frequencies of both as used today are 440Hz. In this respect, all note frequencies can be calculated by moving an index 'i' with a value of 0 at La-4 = 440Hz forward or backward from 440Hz with negative integers. Here, taking the index interval between octaves [0-8] (i=-253->223), frequency values can be calculated with 440*2(i / 53). Here, for two 'scales' side by side, the ratio between frequencies f2 / f1 =2(1 / 53)= 1.013164 is the relative frequency value. Similar to Western music, the frequency ranges of other notes are calculated using this relative frequency. For 53-TET Turkish music note frequencies, all note frequencies are fractional numbers except for the tuning note La (La-4=440Hz). Table-1. The distribution table of note frequencies in the octave range [0-8] in the 12- TET chromatic note scale system of Western music according to octave intervals and the representation of LA-4 (440Hz) tuning frequency in the table

[0021] As a result of the researches in the literature, a Turkish patent application with the application number "2024 / 002499" and the invention title "MEASURING THE DISTANCE SENSOR WE DESIGNED AS MUSIC MATERIAL AND THE LENGTH OF DISTANCE DETECTED BY THE OBSTACLE PLACED IN FRONT OF THE DISTANCE SENSOR AND CONVERTING IT TO NOTAL" was found. The said application is about the distance sensor we designed as a music material, which measures the distance perceived by the obstacle placed in front of it and converts it into notes. However, in the mentioned application, there is no indication of a that brings the note frequency scale, which describes the tonal frequencies between two octaves in musical systems, to scale intervals that are more harmonious than the scale system intervals used today, and defines the note frequencies in the scaling as frequency values consisting of natural numbers.

[0022] As a result, the problems mentioned above, which could not be solved in the light of the existing technique, necessitated an innovation in the relevant technical field.

[0023] BRIEF DESCRIPTION OF INVENTION

[0024] It concerns a scale method in which the musical note frequencies are composed of natural numbers in order to eliminate the disadvantages mentioned in the current and known state of the art and to bring new advantages to the related technical field.

[0025] The main purpose of the invention is to bring the note frequency scale, which describes the tonal frequencies between two octaves in musical systems, into scale ranges more compatible with the scale system ranges used today, and to define the note frequencies in the scaling as frequency values consisting of natural numbers.

[0026] Another purpose of the invention is both to save fractional numbers by expressing musical note frequencies in terms of natural numbers and to bring the intervals in music to more harmonious sound ranges.

[0027] Another purpose of the invention is to provide a reference template model for obtaining resonant frequencies, natural harmonics and spectrum amplitudes in harmonics in spectrum analysis of signals in digital signal processing.

[0028] In order to accomplish all of the aforementioned objects and which will arise from the detailed description below, the present invention provides a value Kf to the power of 2 which is the number of octave layers, i which is the index value for determining Kf number of layers, j which is the interval value into which the octave intervals are divided or Sf to the power of 2 which is the number of notes / tones in each octave interval, j which is the index interval for determining Sf number of segments, m, comprising a FR matrix initialized as empty, m , a method of scaling musical note frequencies as natural numbers, which brings the note frequency scale describing tonal frequencies between two octaves in musical systems to scale intervals that are more compatible with the scale system intervals than the scale system intervals currently used, and defines the note frequencies in the scaling as frequency values consisting of natural numbers, characterized in that it comprises taking 1 Hz as the initial frequency value and for the calculation of the note frequency value in the jth segment of the ith layer in a chromatic scale system with Kf frequency octave layers with index (i) 1 for 1 Hz and Sf intervals between any two octave layers, performing the process steps of DIV=(Fi2-Fi1 ) / Sf, where Fi1=(2(M)) is the frequency value at the beginning of the (k=i-5)th octave layer and Fi2=(2(i)) is the frequency value at the beginning of the (k=i-4)th octave layer, and then the calculation process steps of the frequency value in the (i)th layer (j)th segment in the loop started for Sf segments using the equation FR(i,j)=Fi1 +(j-1 )*DIV.

[0029] In addition, the invention comprises determining an interval (segment) value (Sf) and the number of octave layers (Kf) to the power of 2 and initializing the FR matrix as empty, starting a loop for the octave layers, finding the first frequency in the k=(i-5)th octave layer, Finding the first frequency in the (k+1 )th octave layer, calculating the distance of the frequencies in the octave range, starting a loop from j=1 to Sf for frequency calculations in the octave range and adding each calculated frequency value to the FR array, If j is smaller than Sf, the following steps are taken: starting the loop for frequency calculations in the octave range and returning to the process step of adding each calculated frequency value to the FR array; checking whether i is smaller than Kf if j is not smaller than Sf; returning to the process step of calculating the distance of frequencies in the octave range if i is smaller than Kf; and completing process steps the frequency if i is not smaller than Kf.

[0030] In addition, the invention FR(p,r) matrix with p octave layers and r segments containing the generated frequencies, an input signal spectrum vector (yf) sampled with a sampling rate of Fs to the power of 2 and with a sample number (N) to the power of 2, and a vector ff containing the frequencies of the signal in the range [0- Fs / 2], Initialization of the empty Hf (p,r) matrix representing the octave range and segments where the frequencies in the frequency vector ff match the harmonic frequencies in the FR(p,r) matrix and the empty Hy (p,r) matrix representing the harmonic amplitudes at these frequencies, Start a loop to compare the yf and ff vectors with the data in all octave bands and segments in the FR (p,r) matrix, start a loop for each octave from i = 1 to p, start a loop for each segment from j = 1 to r, start a loop for each octave and each segment, start a loop for each frequency from k = 1 to the length of the ff vector, starting a loop to check each frequency in the frequency vector ff with the value k in the loop, rechecking each frequency in the frequency vector ff with the value k in the loop if the frequency value in the corresponding octave and segment does not match the frequency value k in the ff vector, if it matches (Hf(i,j) = ff(k)); assigning the frequency value to the octave and segment matrix (Hf(i,j)=ff(k)), assigning the spectrum amplitude corresponding to the frequency of interest to the matrix of harmonic amplitudes (Hy(i,j)=yf(k)), continuing the loop k until it is completed on all elements of the vector ff, The process steps include repeating the process for each segment until the completion of cycle j, repeating the process for each octave of cycle i, ending the cycles and completing the process when the process for all octaves, segments and frequencies is completed.

[0031] In order to best understand the structure of the present invention and its advantages with additional elements, it should be evaluated together with the figures described below.

[0032] BRIEF DESCRIPTION OF FIGURES

[0033] Figure 1 is a representative representation of the fundamental harmonic and the 2nd, 3rd and 4th harmonic components of a sine signal.

[0034] Figure 2 is a representative representation of the location of some harmonized note scale ratios on a string of length L.

[0035] Figure 3a is a representative representation of the one-way FFT spectrum amplitudes of the one-way FFT spectrum amplitudes of the signals x(t) generated by the sum of sines containing the note frequencies of the 8-note invention frequencies (815Hz) in the frequency range 8-16Hz.

[0036] Figure 3b is a representative representation of the one-way FFT spectrum amplitudes of x(t) signals generated by the sum of sines containing 7 note frequencies between (8->15Hz) in 12-TET equal temperament

[0037] Figure 4a is a representative representation of the FFT spectrum amplitudes of the signal for the function x1 (t) = Sin(2*u*16*t) sampled at Fs = 64Khz

[0038] Figure 4b is a representative representation of the FFT spectrum amplitudes of the signal for the function x2(t) = Sin(2*u*16.35*t).

[0039] Figure 5 is a representative placement representation of the 7-note diatonic scale and the invented 8-note scale on the guitar string.

[0040] Figure 6 is a sketch of a sine signal with the first 8, 16, 32 components, and a representative representation of the note pitch locations in the invention respectively.

[0041] Figure 7 is a representative graph showing the Mel-frequency scale equivalents of the frequencies between [1 -8000Hz] with the 12-TET chromatic scale and the 16-TET scale achieved with the invention.

[0042] Figure 8 is a representative graph showing the Mel-frequency scale equivalents of the frequencies between [1 -500Hz] with the 12-TET chromatic scale and the 16-TET scale achieved by the invention.

[0043] Figure 9 is a representative representation of the frequency differences on the Mel scale of the 16-TET equal temperament scale system and the 16-note invention adjacent frequencies. Figure 10a is a representative representation of the workflow of the invention scale method where musical note frequencies are natural numbers.

[0044] Figure 10b is a representative representation of the workflow of the method, where the frequencies generated in Figure 10a are applied to determine the spectrum amplitudes and harmonics of the signals in accordance with the scale system, taking the natural sine harmonics of the signals as a reference scale system at the input.

[0045] The figures are not necessarily to scale and may omit details that are not necessary to understand the present invention. Furthermore, elements that are at least substantially identical or have at least substantially identical functions are indicated by the same number.

[0046] DETAILED DESCRIPTION OF INVENTION

[0047] In this detailed description, the inventive method of a scale in which musical note frequencies are composed of natural numbers is explained only by means of examples that do not have any limiting effect for a better understanding of the subject matter. An important factor in the formation of sound in string and wind instruments is the resonance zones formed on the instrument, which significantly determine the sound character of the instrument. With the vibration of the string in stringed and wind instruments or with the breath blown, the vibration characteristics of the air in the resonance zones of the instrument body are changed and strengthened, making the sound audible to the ear. The form of an instrument and the location of its resonance zones are directly related to the scaling system of the notes. In addition, the resonance regions are shaped by the material properties of the materials from which the instruments are made, such as elasticity, gravity, and properties such as body shape, thickness, and length. Stringed instruments are assembled to create note sequences and frequencies by the length and thickness of the string, the structure and scaling of the material on which it is mounted. A change in the note frequency scale on the instruments would require a complete change in the string and material sizes specified for production and would most likely have to be reproduced from scratch. The same is true for wind instruments. In musical instruments scaled according to all note frequencies, a change in the note frequency scale requires the material to be reproduced according to the new scale. In this context, the application of the invention system in musical instruments revitalizes industrial production in all stringed and wind instruments and brings vitality to the economy. The same is true for keyed instruments. For example, when the 8 major notes in an octave with the invention and the new frequency scale system need to be implemented on a piano, the piano keys and the strings to which they are connected need to be re-scaled and reproduced.

[0048] The invention can be used in signal processing to find natural harmonics in the spectrum of signals. For example, spectrum analyzer devices used for monitoring and measurement in systems such as television broadcasting, radar systems, defense industry, mobile networks, spectrum analyzers widely used in industry to measure the spectrum power density of signals, detect possible noise signals on the signal, and determine whether the signal is operating at the correct band frequency, the detection of resonant frequency regions in the signal by revealing their relationship with the natural harmonics of the signals themselves, and the re-expression of the natural form of the signal in terms of dominant harmonic sine components can also be used to separate the signal from noise. It can also be used in music signal processing and audio signal processing programs to detect frequency regions and amplitudes representing natural sine harmonics in the signal spectrum. In other applications of digital signal processing, it can be used to detect natural sine harmonics in the spectrum of a signal. For the JI scale with a scale method in which musical note frequencies are natural numbers, note frequency ranges are different from each other in a 12-note scale. The scale method of the invention, in which musical note frequencies are natural numbers, not only provides some of the harmonized scale intervals of the JI method, but also has a systematic for determining note frequency intervals. Scale intervals in accordance with the invention are obtained by linearly dividing the octave interval by intervals in numbers to the power of 2. The invention provides an equation for derivation within the segment range determined by the invention, and in JI, as stated in the known state of the art, more than one JI scaling can be generated over the prime number limit component it considers. For example, even though 21 is not a prime number, since it is a power of the prime number 7, a JI scaling can be created over 21 / 20.

[0049] In music, the product of scale intervals should give the interval of 2 octaves. The product of scales in the octave range of the invention gives exactly 2 (e.g. (9 / 8)x (10 / 9)x (11 / 10)x (12 / 11)x (13 / 12)x (14 / 13)x (15 / 14)x 16 / 15). The most important feature of the invention that distinguishes it from the 12-TET equal scale is that the note frequencies in an octave range are equidistant from each other, thus providing all harmonized scale ratios in an octave range. On the other hand, the 12-TET system performs a logarithmic interval operation according to the logarithm-2 scale at frequencies within the octave. This type of scaling, however, fails to capture any scales that are considered to be harmonious intervals in the octave range.

[0050] In the 16-tone note frequency ranges scaled by the invention scale method, where musical note frequencies are natural numbers, all tone note frequencies starting from the Octave-O layer are natural numbers. On the other hand, if a detailed scaling of our invention to the quarter-tone and lower micro-tone ranges is desired, it is normal for some tonal note frequencies at the quarter-tone and micro-tone levels to be fractional numbers.

[0051] Although a scale method in which musical note frequencies are natural numbers was developed as a scale system for musical signals, since it is a note scale system in which all note frequencies are natural numbers, it can also be used as a reference scale system in digital signal processing for modeling the spectrum amplitudes of signals in relation to their harmonics.

[0052] In a scale method in which musical note frequencies are natural numbers, starting with a 1 Hz sine signal with the smallest integer frequency value,, we move on to generate the other tone frequency ranges in integers. 1 octave above a 1 Hz sine signal is 2Hz. In octaves of 2Hz and higher, frequency values in multiples of 2 are reached. In a scale method where musical note frequencies are natural numbers, the division value of the interval between two octaves is important so that all note frequencies are integer values. For example, if the frequencies between two octaves are to be divided by 8 with the invention, the note frequencies in all intervals of 8Hz and above are obtained in whole numbers. By proceeding in this way and using the equality in the invention, the octave intervals were arranged. A 16-segment note frequency table was created in, a scale method in which musical note frequencies are natural numbers. Here, as can be seen in Table-2, when the Oth octave is divided into 16 intervals, all note frequencies are natural numbers. Similarly, when the 1st octave is divided into 32 intervals, all note frequencies from the 1st octave onwards are natural numbers.

[0053] In order to compare the octave layers index values and the range of note frequencies with the 12-TET system, a scale method where the musical note frequencies are composed of natural numbers was created and chromatic note scaling was performed in the range [16Hz- 8kHz] and presented in Table-2. In this context, in order to calculate note frequencies of 16Hz and above in the system of the invention, i=5 is taken to calculate the frequency values in the Oth octave layer in accordance with the definition of k=i-5 octave layers as shown in Figure 10a. When we define note frequency ranges in music in terms of powers of 2 and proceed without specifying any tuning frequency and starting the calculation of note frequencies from the frequency of 1 Hz, in the Invention, instead of increasing the note frequencies in each octave range by a multiplier value, the note frequencies in each octave range are increased by equalizing the distance differences between two adjacent note frequencies and thus the frequencies in the same octave band are separated by equal distances and represented in the scale system. As a result, it was observed that the frequencies progressed as integer values and the harmonics followed each other regularly in the upper octave layer. The scaling between intervals in the invention is equal intervals, where the number of intervals in two octaves is equal to the number of intervals in two octaves divided by a number that is the nth power of 2 (e.g. 8, 16, 32, 64, ...), where n is an integer. There is also an advantage of equalizing the distances between frequencies: Even if the chromatic scale in the invention is divided into quarter-tone or micro-tone intervals, since the mathematical operation in the scaling between intervals is performed by dividing the previous interval scaling by 2, the resulting proportional figures are expressed in simpler ratios than the diatonic scale or the 12-TET scale, and there is no rapid departure from harmonic scale intervals.

[0054] Figure 5 shows the placement of the diatonic scale and some inventive scales on a guitar string for comparison. With the invention, if we scale the number of note frequency intervals in an octave range of musical signals to include the 7 notes used today and by choosing a value in multiples of 2 (for example 8,16,32,64,128,256...), tonal systems with different resolution frequency note scales can be obtained with these values. In the 16-note scale system created with the invention and shown in Table-2, the frequency values in the intervals in each octave are twice the value of the previous octave. As can be seen from Table-2 and Table-3, the frequencies and frequency ratios of the notes in the frequency table in Table-2, which was created according to the invention, changed significantly according to the 12-TET system. The invention includes some of the scales of the diatonic scale, but is also different from the diatonic scale. The diatonic scale has 7 consecutive notes (C-D-E-F-G-A-B) designated as five whole tones and two semitones in each octave, and is a scale system in which the two semitones are separated by two or three whole steps. In the diatonic scale, there are intervals called 'devil intervals' where highly dissonant sounds occur. The diatonic scale was used in church music in the Medieval Ages.

[0055] One of the purposes of the invention is both to free musical note frequencies from fractional numbers by expressing them in terms of natural numbers and to bring the intervals in music to more harmonious sound ranges. The musical note frequencies are the frequencies that represent the resonant frequencies in the signal, and all other frequencies in the musical signal are harmonics of the resonant frequencies (notes). The fact that the fundamental tone frequencies are fractional numbers causes some technical problems, especially in digital signal analysis of music signals. The originality of the invention stems from the originality of the calculation of the frequencies of the notes, the linear scaling of the octave intervals instead of the logarithmic scaling of the octave intervals in the known state of the art, and the fact that all note frequencies are natural numbers, in addition to being expressed with an 8- note scale instead of a 7-note scale between two octaves. The invention is different from the techniques in the literature for calculating note scales. The invention provides both an octave-based scaling of note frequencies and a linear scaling of octave intervals.

[0056] Since the note frequencies in the invention increase as integers and as multiples of 2 at the beginning of octaves, it is much easier to produce and tune a musical instrument with these frequencies than with fractional frequencies. In addition, the ringing sounds produced by natural sine signals are much purer and stronger than ringing sounds produced by fractional frequencies, as shown in the example in Figure 3.

[0057] Another purpose of the invention is to be used as a reference template model for obtaining resonant frequencies and natural harmonics in spectrum analysis of signals in digital signal processing. In the known state of the art, the Fourier transform method describes all signals in nature in terms of a combination of natural sine harmonics, and the analysis of signals in the frequency domain is mostly done by the Fourier transform method. Since the note frequencies of the invention contain natural sine harmonics, a relationship can be established between the note frequency spectrum produced by the inventive method and the spectrum of any signal in nature. In this way, it can be used as a reference scale system for the conversion of signals to notes and notes to signals. The use of the invention for this purpose transforms the system from being just a music signal scale system into a common scale system for analysis between different signals.

[0058] In the known state of the art, the purest signal that can represent a tone frequency in signal processing is a sine signal. Moreover, according to Fourier's theorem, all other signals in nature can be expressed as a combination of sine signals of different frequencies and amplitudes. Therefore, all signals other than the sine signal are harmonic signals and are far from being resonant signals. Sine signals with fractional frequency values, on the other hand, generate harmonic distortion and the spectrum amplitudes are scattered in sidebands, as can be seen in the examples in Figure-3. This weakens the resonant frequency characteristic. A note frequency table created with fractional numbers not only fails to create a strong ringing sound but also creates harmonic distortion due to the energy of the tones dissipating to other frequencies through spectral leakage. In music signals composed with a scale system whose entire note frequency table is composed of fractional-numbered tones, there is a high probability of fractal noise (fractal noise (1 / f)), called pink noise, which is located in the low frequency band. In Table-1 of the frequency table based on the 12-TET chromatic scale, there is no pure resonant frequency, except for the tuning frequency 440Hz and multiples thereof.

[0059] Another point is that in the 12-TET chromatic scale, no ratios that are called harmonious in music can be fully achieved. This includes the ratio of perfect fifths between two notes (3 / 2 -> 2(7 / 12)=1.4983) and perfect fourths which are considered the most harmonious ratios in music after the octave interval. The 12-TET system is not able to fully capture even the frequency ratios that are considered the most harmonious in music (3 / 2 and 4 / 3).

[0060] Furthermore, in the 12-TET system, as a result of dividing the frequency ranges of the wholetone notes between 2 octaves by the base logarithm-2, the frequency ranges within the octave band are continuously increasing and the ear selectivity of the treble frequencies within the octave is more pronounced than in the invention. This can be seen in Figures 7-9 and in the test results in Table 6. This is where the side effects of prolonged hearing of high- frequency sounds in musical signals come into play.

[0061] Although the 53-TET Turkish music scale system, with its precise scaling by dividing the interval between two octaves by the ratio 2(1 / 53), achieves values close to most of the harmonized ratios needed for the 53 intervals in the octave, it is not practical to represent a musical instrument with 53 note keys in each octave. Also in the 53-TET system, the calculation of the tone frequency ranges is determined by a ratio of (2(1 / 53)) and the ranges have fractional frequency values.

[0062] The note tone frequencies generated by the invention are natural numbers and it is possible to represent each tone as a pure sine signal. In signal processing, the spectrum amplitude of any sine signal with a natural number frequency is represented by the 'Delta Function' and is seen as a strong peak signal with no harmonic distortion on the spectrum axis.

[0063] Furthermore, the invention provides a model for deriving tonal frequencies in each octave range, and due to the linear scaling of tonal ranges, there is no rapid departure from harmonized note ranges even in microtones. Another feature of the invention, thanks to its use of linear scaling, is that, in contrast to the 12-TET chromatic scale, the note frequency ratios in each octave range are scaled on the MEL spectrum scale in favor of the pest notes, making the treble notes less selective to the ear (Figure 7-9). For very high frequency sounds, this is considered to be important for ear health.

[0064] The ability to establish a one-to-one correlation between tonal frequencies and spectrum amplitudes of signals allows all signals to be correlated and analyzed in terms of their resonant frequencies, and different signals to be correlated with each other based on signal resonant (formant) frequencies, freeing the signal spectrum from the complex signal frequency distribution. In addition, in this way, relationships can be established between the sounds emitted by all living and non-living objects in nature through note frequencies, for example, the pattern of different sounds emitted by a living creature in different situations in nature can be made sense of through note frequencies. As a result of detailed analysis of the signals to be collected for this purpose, the sounds emitted by any living thing can be transformed into sentences by associating their resonance frequencies with note frequencies consisting of natural harmonics and redefining them. Similarly, by structuring the sound patterns of other living / inanimate objects in nature through note frequencies, it will be much easier to establish and classify the relationships between different sound patterns. In addition, when the signal spectrum of an object is to be evaluated, various evaluations of the signal can be made by associating the invention with note frequencies.

[0065] The invention can also be used as a reference signal model in spectrum analyzers. In this way, spectrum analyzers, which are used in many fields from sound analysis, noise and vibration analysis to structural dynamics analysis, contribute to the evaluation of various types of complex signal forms through resonant frequencies and harmonics. What makes the note frequencies of the invention superior to the scales of the state of the art in this sense is both the possibility of evaluating the spectrum analysis of different signals scaled with the invention on a common reference scale, since they contain natural sine harmonics, and the ease of scaling the sine signal down to microtone note frequencies to include all harmonics. In summary, the note frequency model including natural sine harmonics will be an important step for both music signal processing and digital signal processing.

[0066] To find the frequencies in the new note scale system, the system in Figure-10a is used and a 16-tone scale system created by the invention is shown in Table-2. In Figure 10a, Kf represents the number of octave layers. Sf is the interval value into which octave intervals are divided. As can be seen in Table-2, the method, which is generated using the workflow in Figure-10a and calculates the note frequencies starting from the Oth octave and the note frequencies in each octave interval (Sf), can generate note frequencies starting from 16Hz and progressing with natural numbers between octaves [0-8].

[0067] In this context, a scale that considers the number of notes containing the nearest multiple of 2, including the 7 whole-tone notes used today, as a sequence of notes and includes 8 whole-tone note frequencies in an octave range using the invention system (C, D, E, F, G, A, H, B) is presented here in detail. In the scale method of the invention, when the number of notes (tones) between two octaves is chosen as 16 so that the intervals between any two octaves cover all the tones in the current 12-TET system, 16 note frequencies are created between two octaves, 8 of which are master-tone notes, as seen in Table-2. Here, the note that is missing in current notation systems is called the 'H' note in letter and the 'Ve' note in name. Similarly, when the number of notes between two octaves is 32, note frequencies including quarter tone intervals can be calculated by the invention method. In this context, the number of notes between two octaves can be increased to higher integer values in order to create microtonal musical intervals. Thus, the proposed invention can be taken to the depth of including microtonal frequencies by dividing the intervals in an octave into more intervals in multiples of 2. If the invention is intended to generate 32-tone musical note frequencies including, for example, quarter tones between two octaves, all frequencies 32Hz and above in the Octave-1 layer in Table-2 will be natural numbers. It is also recommended that the note C (C), whose note frequencies are at the beginning of the octave interval, be chosen as the tuning frequency (256Hz), since its numerical value is in multiples of 2. For note frequencies in the invention system, 256Hz is the first frequency of the 4th octave layer.

[0068] In Table-2, the value of the frequencies in the upper octaves progresses as twice the frequencies in the previous octave (congeners). In the invention method, although the ratio of adjacent frequencies is not equal, the difference between them is equal (Table-2 and Table- 3). In the invention, the note frequencies in two octave intervals are equidistant from each other. It is evaluated that the chromatic note frequency table presented in the invention will provide a significant benefit both in the music industry and in the signal processing industry, as it contains strong sinusoidal signal samples representing resonant frequencies consisting of natural numbers.

[0069] Table-2: The note frequency table created by selecting the number of notes in the two octave range according to the invention as 16.

[0070] Table-3: is the representation as rational numbers and fractional values of the ratios of the frequencies of the 16-tone notes in the two octave range of the invention. As seen in Table-3, full-4 intervals and full-5 intervals in music are formed by the invention. Another important advantage of the invention is the formation of full-5 intervals between two different notes in the same octave range (frequency ratios f9 / f 1 and f15 / f5).

[0071] Tests

[0072] In FFT signal analysis of a signal, frequency resolution and frequency distributions are formed in terms of natural numbers after Fourier transforms of signals sampled with sampling frequency (Fs) in multiples of 2 are taken with FFT sample length (N) determined in multiples of 2. In this respect, for example, it is important that the spectrum distribution of musical signals composed and recorded with frequencies in accordance with the tonal scale system of the invention in Figure 10a is again in integer values, and that the FFT sample length (N) and the number of signal samples (Fs) are multiples of 2 for accurate detection and analysis of the location of resonant frequencies (formants). In general, in order to generate and record an input signal with the invention scale system using Figure 10a and then perform spectrum analysis and detect natural sine harmonics using Figure 10b, it is important to choose both the sampling rate (Fs) of the signal and the sample length (N) of the signal FFT (Fast Fourier Transform) in multiples of 2. This must be taken into account in order to obtain the input signal spectrum resolution value (Af=Fs / N) as an integer value and to reconstruct the spectrum amplitudes of the signal in natural numbers at the harmonic frequencies. In spectrum analysis or note frequency table production, if fractional frequencies are to be taken into account for the frequency values produced with the inventive system, the starting point of the frequencies produced in Figure 10a should be from 0Hz.

[0073] The following tests were performed to see the distribution of the spectrum amplitudes of note frequencies in the invention and the 12-TET chromatic scale system:

[0074] First, for the tests, the FFT sample length was taken as N=32 and the sampling rate as Fs=32, and a sine signal X(t) containing 8 note frequencies (f1 -» f8) in the two octave range was generated as follows.

[0075] Equation 1 :

[0076] X(t) as frequency values in the sine signal; i) In the invented 8-note system, the frequencies of 8 notes (Do, Re, Mi, Fa, Sol, La, Ve, Si) between 8Hz and 16Hz (f1=8Hz; f2=9Hz; f3=10Hz; f4=11 Hz; f5=12Hz; f6=13Hz; f7=14Hz; f8=15Hz) were applied to the X(t) signal in equation-1 and the FFT of the X(t) signal was taken. ii) The frequencies of 7 notes (Do, Re, Mi, Fa, Sol, La, Si) between 8Hz and 16Hz in the 12-

[0077] TET chromatic system were applied to the X(t) signal in Equation-1 as follows; The note frequencies f1 =8,176Hz, f2=9,177Hz, f3=10,301 Hz, f4=10,913Hz, f5=12,250Hz, f6=13,750Hz, f7=15,434Hz (since there is no 8th note in the 12-TET system, f8=0 was taken) found for the 12-TET (-1 ) th octave interval were applied to the X(t) signal in Equation-1 and its FFT was taken. When the signal X(f)=FFT(X(t),N) is plotted as a linear spectrum of the unidirectional FFT signal in the frequency range [0-16Hz] with the FFT transform applied to the signal for the time t=1sec, the shapes shown in Figure-3a are obtained. As seen in Figure 3a, in the first graph, which includes integer frequencies up to 8Hz->15Hz representing the invention frequencies, the frequency linear spectrum of each sine signal shows that the amplitude of each line spectrum value retains its strength and no spectral leakage to the sidebands is observed, Since the sinusoidal signal consisting of the frequency samples of the 12-TET system has spectral leakage at different signal frequencies, both the linear spectrum amplitudes change and spectral leakage to the sidebands is observed (Figure 3b). In this respect, the note frequency values in the 12-TET system seem to be far from being accepted as resonant frequencies.

[0078] Figure 4a shows the FFT amplitudes and frequency distribution after Fourier transform of 2 sine signals with frequencies f1 =16Hz and f2=16.35Hz in Figure 4b. As can be seen, the FFT behavior of the sine signal with a frequency of f1=16Hz shows a spectrum very close to the 'Delta' (8) function behavior expected from Fourier transforms of sine functions, while the sine signal with a frequency of f2=16.35Hz has both a decrease in harmonic amplitude and its energy is distributed to the side frequency bands. This shows that sine signals with fractional number frequency values lose their characteristic of being signals with resonant frequency.

[0079] The intervals for the 7 notes (C, D, E, F, G, A, B) in the diatonic scale based on the Pythagorean theorem are (1 , 9 / 8, 81 / 64, 4 / 3, 3 / 2, 27 / 16, 243 / 128) respectively. For the 8 notes in the invention (C, D, E, F, G, H, A, B), the note intervals starting from the first note frequency are (1 , 9 / 8, 5 / 4, 1 1 / 8, 3 / 2, 13 / 8, 7 / 4, 15 / 8) respectively. Since the note intervals in the invention are found by dividing the octave by the number of intervals, rather than multiplying by a ratio, the very high numbered ratios that occur as the number of intervals increases in logarithmic scale systems are not included in the invention and simpler numbers are used in interval calculations.

[0080] In the known state of the art, the frequencies 44100Hz and 48000Hz were adopted as the standard for music signals, taking CD-quality digital audio coding and television broadcasting standards as a framework. For example, there is information in the literature that the 44100Hz frequency was determined as the result of a calculation (3*490*30 = 44100Hz) for recording and storing a 30 frames / sec video image with 490 lines in each frame and 3 sound samples in each line. On the other hand, the frequencies 44100Hz or Fs=48000Hz do not appear to be suitable sampling frequencies for generating the frequencies in natural numbers in the invention, as they are not multiples of 2. The closest sampling frequency (Fs) value in multiples of 2 to cover 22kHz, the maximum frequency perceived by the human ear, and to be determined in accordance with the Nyquist criterion, appears to be 65536Hz (64kHz). In digital signal analysis of an audio signal sampled at Fs=64kHz and filtered for frequencies outside the hearing range, when both the Fs value and the number of samples (N) included in the analysis window are chosen as multiples of 2, the frequency resolution value (Af=(Fs / N)), which indicates the minimum inter-frequency interval, will be integer, so the frequency values in the FFT analysis result will be integer values. In this way, in the spectrum analysis of music signals whose note frequencies are determined by the invention, it is possible to display the musical note frequencies as natural numbers again in the spectrum distribution. When we plot a sine signal at fundamental frequency F0 together with its 8 spawns, as shown in Figure 6, the nodal points found on the axis by considering only standing wave intervals equidistant from each other correspond to 8 note frequencies (the circled points in the first figure in Figure 6). In this context, when we divide the interval [0-> 1 ] into 8 equal intervals considering a 1 unit wire, the nodes [0, 0.125, 0.375, 0.375, 0.5, 0.625, 0.75, 0.875, 1] are formed at equal distances on the axis with the invention. The inventive process is to divide an octave interval into equal distances in multiples of 2 and to take the frequencies corresponding to these interval points as note frequencies. In order to take into account more standing wave points and still capture frequency values in natural numbers, it is necessary to divide an octave into intervals defined as multiples of 2 in the form (8, 16, 32 ...). In this context, in Figure-5, the first 8 harmonics, 16 harmonics and 32 harmonics of a fundamental sine signal are plotted together with the fundamental signal and only the nodes where the intervals are equidistant from each other, i.e. the frequency of 8 notes for the first 8 harmonics, 16 notes for the first 16 harmonics and 32 notes for the first 32 harmonics, respectively, are defined in an octave range in the invention. This is one of the things that distinguishes the invention from other scales. Since in other scales the chosen interval scale is usually a multiplier, the invention is constructed by adding tones that are not included in the sensitivity scale of the number of intervals in linear scaling to the scale system. For example, the interval scales (1.20, 1.33, 1.40, 1.60, 1.67) in the ratios (fi / f1 , i=1 :12) in 12-Ton JI in Table-4 are approached in the invention when the number of intervals is 32 and reached when 64 is chosen, as seen in Table 5. Table 4. is the notation of tonal scale ratios in the 2-octave range for the Pythagorean scale, 12-TET equal temperament scale, 53-TET Turkish music, JI and invention 16- Nota scale.

[0081] In Table 4, the tone ratios in the 2-octave range for the Pythagorean scale, the 12-TET equal-temperament scale and the 16-note scale in the invention are presented comparatively. As can be seen here, since both the 12-TET and Pythagorean scales have intervals with a multiplier value, the interval values are close. In the 12-TET scale, the intervals between tones are scaled according to the logarithm-2 base, and in this way the differences between note intervals increase continuously as one moves in the treble direction, as can be seen in Figure-7 and Figure-8. In the invention, the distances between frequencies in the same octave are equal, but the frequency ratios narrow towards the end of the band.

[0082] In the known state of the art, the most common method for finding the relative frequency effect of sound emitted from a source on the ear is the Mel-Frequency calculation method. According to this method, the Mel-frequency equivalent of a sound at a frequency f is found by the formula in Equation 2 below: Equation 2: Mf=2595*log(1 +f / 700).

[0083] In the invention, as can be seen from Table-4, since the adjacent frequency ratios towards the end of the octave band are constantly narrowing, the frequency values of the sounds close to the octave band in the Mel scale are more prominent and therefore better distinguishable by the ear. Towards the end of the octave band, the frequency ranges in the Mel scale narrow. This can be seen in Figure-7 and Figure-8. In the invention, the scales marked in Table-4 overlap with other scales, and the unmarked frequency intonations are either present at different frequency ratios in the octave band as seen in Table-3, or more precise scaling ranges can be found when divided into 32-note scale or 64-note scale ranges with the invention. This can be seen from the 16, 32 and 64-note frequency rates in Table-5. Comparing Table-3 and Table-4, most of the harmonized ratios in JI in Table-4 are present in different frequency ratios in Table-3. (In Table 4, the 'coma' intervals of the 53-TET system and the 2 scale values in the 53-TET system are written for the intervals that do not correspond exactly to the other scales.)

[0084] Table-5, is the notation of note interval scales formed by creating intervals with 16, 32, 64 notes in the invention. Figure-7 and Figure-8 show the frequencies in the 12-TET scale system using the Mel- frequency calculation formula and the Mel-scale frequency equivalents of the invention frequencies. In the invention, the frequencies are equally distributed in each octave band. Scaling the octave band linearly suppresses the effect of treble frequencies towards the end of the band.

[0085] Since the 12-TET equal temperament scale creates wider frequency distances towards the end of each octave band due to the effect of logarithmic scaling, the differences of the frequency equivalent of adjacent frequencies in the Mel scale increase at the end of the octave band, and the frequency difference of the notes towards the end of the band in the Mel scale and thus the selectivity of the frequencies at the end of the band in the ear seems to be more prominent than the invention. When the regions (octave layers) where the frequencies on the horizontal axis increase in multiples of 2 (octave intervals) are examined in Figure-7, the Mel-scale frequency differences of the adjacent frequencies in the octave band intervals in the invention, in terms of the synthetic frequency equivalent of the tone frequencies in the octave interval in the ear, seem to favor the notes at the beginning of the octave band, while in the 12-TET scale system, the Mel frequency difference of the adjacent notes at the end of the octave band increases in favor of the treble notes.

[0086] In Figure 8, the frequency differences are examined in more detail, focusing on the [0-500Hz] range on the axis, where the differences of the two scale systems are clearly visible. In the invention, the balanced distribution of the frequencies of the current octave band brings the ratios of the treble frequencies towards the end of the octave band closer to each other in exchange for the Mel frequency, reducing the selectivity of the treble frequencies in the ear and reducing the dominant effect of these frequencies. In Table 6, the Mel frequency equivalents of the 12-TET equal-temperament system and the 12-note model of the invention are presented, extended to cover the range [128Hz-8kHz],

[0087] Figure 9 shows the frequency difference values of adjacent frequencies in the Mel frequency equivalent of adjacent frequencies in the 16-note scale in the invention formed by choosing 16-TET equal temperament and octave segment number Sf=16, which was formed by taking the multiplier value (2(1 / 16)) in 12-TET scale. As seen in Figure 9, in the 16-TET scale, the selectivity of the high notes in the octave band gradually increases as the Mel frequency ranges get larger and larger. In the invention, MEL-frequency differences at octave band transitions are higher than in 16-TET, but the Mel frequency difference range of treble notes decreases throughout the octave band. This increases the clarity of the octave band transitions in the invention, while the frequency selectivity within the band decreases as you move towards the high notes. This feature is considered to be beneficial for hearing health, especially for high-frequency music signals. Figure 9 shows that the ratio of adjacent frequencies in the 16-TET equal-temperament scale remains constant across all frequencies, while the frequency differences in the Mel scale increase continuously across octave bands. This means that as the equal temperament moves towards higher frequencies in the chromatic system, the higher notes in the band are more highly selective to the ear than the pest notes, especially for tones at higher frequencies. For example, in a musical signal composed on an equal temperament scale and sampled at 48kHz, high-frequency treble tones in each octave band stimulate the ear more prominently than more pest tones, compared to the invention scale system. From the data in Figure-9 and Table-6, it can be concluded that the equal-temperament scale system is a system that strengthens the selectivity of the higher pitched sounds in an octave band over the lower pitched sounds. The same seems to be true for all music scale methods that use interval scaling using a multiplier value based on frequency ratios within the octave band. In the invention, the selectivity of the pest notes within the same octave band is strengthened, while the Mel frequency difference decreases towards the treble voices. Since the Mel frequency scale represents the ear's synthetic perception of frequencies, the reflection of the music signals composed with the invention on the ear is that it will strengthen the selectivity of the pest frequencies in the octave band, especially at high frequencies, and suppress the selectivity of the treble frequencies.

[0088] Table 6 is a representation of the frequencies of the 12-TET equal temperament and invention 12-note between octaves [3-8], Mel frequency equivalents and differences. REFERENCES

[0089]

[0001] Barry Parker, “Strong vibrations: The physics of music”, 2009, John Hopkins University press, Maryland, ISBN: 978-975-403-986-3. [2] International standard, ISO 16, “Acoustics-Standard Tuning Frequency (Standard musical pitch)”, International Organization for Standardization, 1975, first edition, ref.no: ISO-16- 1975(E), UDC 534.321.7.08:681.831.3. Retrieved 2023-01-09

[0090] [3] David A.Schwartz, Catherine Q. Howe, andDalePurves, “The Statistical Structure of Human Speech Sounds Predicts Musical Universals”, The Journal of Neuroscience, August 6, 2003, 23(18):7160-7168.

Claims

CLAIMS1. A method of scaling musical note frequencies as natural numbers, comprising m, which brings the note frequency scale describing tonal frequencies between two octaves in musical systems to scale intervals that are more harmonious than the scale system intervals currently used, and defines note frequencies in the scaling as frequency values consisting of natural numbers, and comprises the following• a Kf value to the power of 2, the number of octave layers,• Index value i to determine kf layers,• the interval value into which the octave intervals are divided, or an Sf value to the power of 2, which is the number of notes / tones in each octave interval,• The index range for sf segments is j,• An FR matrix initialized as empty characterized in that for the calculation of the note frequency value in the jth segment of the ith layer in a chromatic scale system with Kf octave frequency layers with index (i) 1 for 1 Hz and Sf intervals between any two octave layers, taking 1 Hz as the initial frequency value, it comprises performing the DI V=(Fi2-Fi1 ) / Sf process steps with the frequency value Fi1 =(2(i-1)) at the beginning of the (k=i-5)th octave layer and Fi2=(2(i)) at the beginning of the (k=i-4)th octave layer and then in the loop started to calculate the note frequencies in Sf number of segments, the calculation process steps of the frequency value in the (i)th layer (j)th segment using the equation FR(i,j)=Fi1 +(j- 1 )*DIV.

2. The scale method in which musical note frequencies are composed of natural numbers according to claim 1 , characterized by comprising following process steps;• Specifying an interval / segment value (Sf) and the number of octave layers (Kf) to the power of 2 and initializing of the FR matrix as empty,• Initiating a cycle from i=1 to Kf for octave layers,• Finding the first frequency in the k=(i-5)th octave layer,• Finding the first frequency in the (k+1 )th octave layer,• Calculating the distance of frequencies in the octave range,• Starting a loop from j=1 to Sf for frequency calculations in the octave range and adding each calculated frequency value to the FR array,• returning to cycle j for frequency calculations in the octave range and returning to the process step of adding each calculated frequency value to the FR array if j is less than Sf,• Checking whether i is smaller than Kf if j is not smaller than Sf,• returning to the beginning of cycle i and returning to the step of calculating the distance of frequencies in the octave range if i is less than Kf,• completion of the frequency generation process if i is not smaller than Kf.

3. The scale method in which musical note frequencies are composed of natural numbers according to claim 1 and / or claim 2, characterized by comprising following process steps;• Taking as input data a p octave layer containing the generated frequencies and FR(p,r) matrix containing r segment,• Receiving as input data an input signal spectrum vector (yf) sampled at a sampling rate Fs to the power of 2 and with spectrum amplitudes and frequencies calculated with a sample number (N) to the power of 2, and a vector ff containing the frequencies of the signal in the range [0- Fs / 2],• Initiating of the empty Hf (p,r) matrix representing the octave range and segments where the frequencies in the frequency vector ff match the harmonic frequencies in the FR(p,r) matrix and the empty Hy (p,r) matrix representing the harmonic amplitudes at these frequencies,• Initiating a loop to compare the yf and ff vectors with the data in all octave bands and segments in the FR (p,r) matrix, o Starting a loop for each octave from i = 1 to p, o Starting a loop for each segment from j = 1 to r, o Starting a loop for each frequency from k = 1 to the length of the vector ff for each octave and each segment, o Starting a loop to control each frequency in the frequency vector ff with the value k in the loop, o If the frequency value in the relevant octave and segment does not match the frequency k in the ff vector, checking again the k value in the loop and each frequency in the ff frequency vector, if they match (Hf(i,j) = ff(k));■ assignment of the frequency value to the octave and segment matrix (Hf(i,j)=ff(k)),■ assignment of the spectrum amplitude corresponding to the frequency of interest to the matrix of harmonic amplitudes (Hy(i,j)=yf(k)), o Continuation the cycle k until it is completed on all elements of the vector ff, o Repeating the process for each segment until the completion of cycle j, o Repeating the process for each octave of cycle i,• when processing is complete for all octaves, segments and frequencies, ending the cycles and completing the processing.

4. The scale method in which musical note frequencies are composed of natural numbers according to claim 1 , characterized in that when it is desired to generate a distribution table of note frequencies divided by any integer interval Sf in multiples of 2 and composed of natural numbers, it comprises the step of finding the note frequencies by dividing the two octave intervals by the value Sf and generating all note frequencies in terms of natural numbers from the octave frequency layer to which the frequency value equivalent to the interval (Sf) value belongs.

5. The scale method in which musical note frequencies are composed of natural numbers according to claim 1 , characterized by comprising the process step of dividing the distance between intervals by half when the number of notes in a two octave interval is increased to reach half-tone intervals or microtone intervals.

6. The scale method in which musical note frequencies are composed of natural numbers according to claim 1 , characterized by comprising the process step of placing the interval value (Sf) between two octaves as a multiple of 2.

7. The scale method in which musical note frequencies are composed of natural numbers according to claim 1 , characterized by in the spectrum analysis of a composed music signal, comprising the processing step of determining the sampling rate of the signal (Fs) and the FFT sample length (N) of the signal as numerical values in multiples of 2, so that the spectrum resolution value (Af=Fs / N) is an integer and the frequencies are displayed as natural numbers.

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