# Analysis of Music Teaching in Basic Education Integrating Scientific Computing Visualization and Computer Music Technology

Authors: Yanyan Zhao
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In the current music education, the music teaching method is too simple, boring, relatively backward, unable to attract the attention of the students, and the students gradually lose their interest in music courses. In basic education, music, as a highly practical subject, must create a good classroom atmosphere, make the classroom active, and enable students to better experience music, enjoy music, and like music. Therefore, in order to change this situation, this paper, based on scientific computing visualization, studies the application of computer music technology in basic education music teaching, and proposes a related computing method based on scientific computing visualization-image segmentation method. This review compares the spectrum extraction accuracy between the improved algorithm and the two traditional algorithms and finds that the average accuracy of the improved algorithm is 90.88%. It can be seen that the method proposed in this review is more suitable for the study of computer music technology in basic education music teaching. Applied research and most students are more interested in music teaching combined with computer music technology, so learning music teaching combined with computer music technology is very necessary. The development of computer music technology is closely related to the development of modern information technology.


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## Body

## 1. Introduction

Scientific computing visualization, also known as visualization, is defined as follows: “Visualization is a computational method that converts symbols or data into intuitive geometric figures that allow researchers to observe their simulations and computational processes.” Visualization includes image synthesis. Today, Chinese science and technology has achieved unprecedented development, and the role of computers has become greater and greater, penetrating into various music fields including music education. Computer music education is a new education model based on computer software and hardware, which realizes the learning and creation of music. Now, China is paying more and more attention to the development of high-quality education, especially in the field of basic education. As a part of high-quality education, music education is receiving more and more attention. The correct and interesting way to understand music knowledge in the classroom is a problem that needs to be solved as soon as possible, and the introduction of computer music technology can help improve the efficiency of education. The visualization of scientific computing is a new research field proposed in the second half of the 1980s. In this article, we will study its application to music education in basic education.The teaching method of music subject should be different from other subjects, and the teaching method should be richer. The use of computer music technology can greatly improve the existing teaching mode, and students will also have a huge impact on the teaching concept of music. The use of computer music technology can explore new methods and approaches for improving the traditional music-teaching mode. The core of scientific computing visualization is the visualization of three-dimensional data fields, and it is believed that its use in music teaching can increase the visual impact, improve the interest of teaching, and make students’ classroom experience better. The combination of computer music technology and scientific computing visualization is believed to make the classroom more colorful.Since computer music technology was invented, it has been widely accepted by people and applied to various music fields. Since the introduction of computer music technology, many scholars have conducted research on it. In the middle of the twentieth century, the invention of software was a huge breakthrough for modern humans, and it is unique for computer musicians to predict the future through creation and coding. Scaletti combines the artist’s imagination and courage with the technology that can make fictional things become reality, which is innovative [1]. Mcpherson and Tahıroğlu studied the ways in which computer music language may also affect the aesthetic decision-making of digital music practitioners, with particular attention to the concept of habituation. Then, he communicated with developers of several major music-programming languages, and conducted surveys on creators of digital musical instruments, examining the relationship between idiomatic patterns of the language and the characteristics of the generated instruments and music, but the research lacks data support [2]. In this article, Hayes introduces the large-scale project of sound, electronics, and music. The themes of the project include collective electroacoustic synthesis, live recording, and improvisation. Particular emphasis is placed on providing a form of music education that should enable everyone to practice creatively, regardless of their musical ability and background. The findings and results of the project indicate that people should not limit the discussion of how to continue the practical education of computer music to the next generation at the university level [3]. El-Shimy and Cooperstock provide a set of key principles for the design and evaluation of new user-driven interactive music systems and investigate the evaluation techniques provided by the new directions of HCI, linguistics, interactive arts and social sciences. His goal is to lay the foundation for designers of new music interfaces to develop and customize their own methods, but there are few survey categories in this study [4]. Combining traditional art with advanced technology is a challenging task, and Park’s task is to instill tradition into technology, so as to protect and develop tradition at different levels. He believes that the future of Korean music education is to learn Korean music. As for the production materials and new works, it depends on how many materials and works are produced. The shortcoming of this research is that no specific countermeasures are proposed [5]. The purpose of Haning’s research is to investigate the type, quantity, and effect of technical teaching currently provided to undergraduates majoring in music education. The survey involved 46 undergraduates who received technical guidance during their undergraduate degree courses and their plans to implement technology in the classroom in the future. The results showed that 43% of the participants were not prepared for effective use of technology in future teaching positions, and it would be better if the study gave suggestions to enhance undergraduates’ use of technology for music education [6]. The term “music technology” defined by Chakraborty refers to electromagnetic and mechanical equipment, including musical instruments, electric sound generators, and related computer technology. Chakraborty started writing in the form of dialogue, introducing the ontology of music (where, why, and how) and the ontology of music (facts, processes, and gestures) [7].The innovation of this article is (1) combining scientific computing visualization and computer music technology and applying it to music teaching in basic education, and introduces its related methods, which is a methodological innovation. (2) A teaching experiment was designed based on scientific computing visualization and computer music technology, which proved the superiority of this new teaching method, which is an innovation in experiment.


## 2. Application Methods

### 2.1. Visualization of Scientific Computing

Scientific computing visualization refers to the use of computer graphics and image processing technology to convert data into graphics and images in the process of scientific computing [8]. The realization of scientific computing visualization can greatly speed up the data processing process so that the huge data generated every day can be effectively used; it can realize image communication between people and data, and between people, instead of text communication or communication. Digital communication allows scientists to understand what is happening in the computing process and can change parameters, observe their effects, and guide and control the computing process. In short, the tools and environment for scientific computing can be further modernized.


#### 2.1.1. Classification and Process of Visual Chemistry Subjects in Scientific Computing

There are many fields of scientific computing visualization design. Figure1 shows the subjects covered by the visualization of scientific computing.Figure 1
Visual classification of scientific computing.The basic process of scientific computing visualization is to first preprocess the data, then use the mapping algorithm to map the application data to obtain geometric data, then draw the geometric data to obtain image data, and finally output to the terminal device and display [9]. The details are shown in Figure 2.Figure 2
Visualization flow chart.


#### 2.1.2. Visualization Methods of Scientific Computing

(1) 3D Surface Editing Method Based on Sampling Points. Direct editing is parameter-free modeling, that is, you do not need to modify the parameters and features of the parts one by one, but directly modify the model and preview the modified model directly. First, the model needs to be embedded in the scalar field, and then the scalar value is calculated at each vertex of the embedded part. In the process of free deformation, each vertex is always restricted by the level set, and the level set is initialized with the vertex stream. When the user modifies the scalar field, the vertices will move according to the free deformation of the embedded object. After the scalar field is deformed in space, since there is no scalar deformation technology, the reconfigured vertices in the deformed object remain in the same level set [10] and get the derivative of f(X(t), t):(1)dfXt,tdX=∂fXt,t∂X·dXtdt+∂fXt,t∂t=0.In equation (1),dfXt,t/dX represents the gradient of X, and velocity dXt/dt is regarded as the velocity value along the three coordinate axes of x, y and Z in the three-dimensional space, adding smoothness constraints to the model to minimize the change of vertex velocity in a local area. Smoothness is an index for evaluating the degree of convexity and concavity on the surface of paper or cardboard, which is very important for printing paper. ∇f represents the gradient and replace fXt,t with f to obtain the following minimum objective function:(2)P=∫∂f∂t+v·∇f+θ·∇v2dX.In the formula,P represents the smoothing coefficient, θ represents the Lagrangian coefficient, and X represents the vertex. Discretizing this formula, let k represent a voxel mesh vertex, and Qk represents adjacent mesh vertices. The approximate error of the vulnerability constraint is(3)Ek=∂f∂t+∂f∂xvxk+∂f∂yvyk+∂f∂zvzk2.According to the speed difference between vertexk and its neighboring points, the smoothness of local area motion can be calculated [11]:(4)Pk=1Qk∑j∈Qkvxk−vxj2+vyk−vyj2+vzk−vzj2.S represents the smoothing coefficient,Qk represents the number of vertices of the voxel mesh in Qk, then(5)G=∑kEk+θPk.The previous level set algorithms have only a single velocity function, in the evolution process of the zero-level set, the minimization of the energy function is a very complicated process, and there are many problems with a single velocity function. Although the velocity field of the associated voxel, grid can be obtained according to the change of the scalar field, and their position cannot be changed. As an alternative, through the velocity function defined in the following level set method [12], use H to represent the velocity function of the curved surface scalar field, and use the velocity field v obtained above to update the curved surface scalar field:(6)H=−∇S·v∇S.(2) Surface Update and Resampling Method. Since the scalar free deformation technology requires that the relocation of the vertex X(t) should assume that the implicit function is a zero-level set, the reciprocal of f(X(t), t) can be expressed as follows:(7)dSXt,tdX=∂SXt,t∂X·dXtdt+∂SXt,t∂t.When the density of points on the surface becomes low, new sampling points need to be inserted so that the points on the surface remain uniform. The basic idea of the method is to calculate the Voronoi histogram of adjacent points on the tangent plane [13]. A histogram is a statistical chart that uses rectangular bars to compare numerical values of different categories. Use the length of vertical or horizontal columns to compare the magnitude of numerical values, where one axis represents the categorical dimension that needs to be compared, and the other axis represents the corresponding numerical value.(3) Level Set Method. Another advantage of the level set method is that it can easily track the topological changes of objects. For example, when the shape of the object is divided into two, creating a hole, or vice versa. The level set method is a numerical calculation method to solve the deformation evolution of implicit curves and curved surfaces [14], as shown in Figure 3. By moving the level set function, that is, through the rise, fall, and expansion of the level set function, the contours of the closed curve at different times can be obtained. The evolution result of the level set function surface must be related to the evolution result of the closed curve.Figure 3
Circle and its level function.


#### 2.1.3. Visualization Algorithms for Scientific Computing

In the early days of computer visualization, the visualization system only provided the functions of drawing and printing one-dimensional curves and two-dimensional contours and surface views. Three-dimensional visualization technology is the separation between the initial stage of computer visualization and the new era of scientific computing visualization [15]. Compared with the initial computer visualization system, the main feature of the scientific computing visualization technology is the three-dimensional visualization technology. The visualization algorithm is shown in Table 1.Table 1
Typical visualization techniques.
DimensionScalarTensorFitness vector1DLine drawing, histogram, bar chart——2DContour line, surface view, image display—2D arrow3DIsosurface, 3D point cloud surfaceTensor ellipse3D arrow, particle system, 3D streamline


### 2.2. Teaching Technology Based on Computer Music Technology

Music is divided into two parts: visual scores and auditory songs, and its teaching targets are usually young people. Therefore, the practical process often needs some methods that highlight the characteristics of music and art that can directly allow learners to see and hear than traditional theoretical teaching [16]. The spectrum recognition is to help music teachers to realize visual score recognition and auditory music recognition. Among them, “spectrum” refers to the recognition of graphic music scores using computer image processing, and “tone” refers to music recognition using computer signal processing, audio processing, and other knowledge. In general, it is necessary to realize both visual score recognition and auditory music recognition. Therefore, in order to explain the educational technology of computer music technology, this chapter is divided into two parts: score recognition and music recognition [17].


#### 2.2.1. Numbered Musical Notation Recognition

This section uses basic image processing techniques to study and identify the musical theory symbols in the numbered musical notation pictures, hoping to bring some convenience to the teaching of numbered musical notation. The numbered musical notation recognition is generally divided into image preprocessing, inclination correction, and bar line recognition.(1) Image Preprocessing. Preprocessing is basically the first step of all image recognition technologies, and the quality of preprocessing sometimes has a decisive impact on the recognition accuracy. The basic steps are as follows: the main purpose of image preprocessing is to eliminate irrelevant information in images, recover useful real information, enhance the detectability of relevant information, and simplify data to the greatest extent, thereby improving the reliability of feature extraction, image segmentation, matching, and recognition:Gray conversion:Before starting the score recognition, grayscale conversion can be performed. The RGB three-dimensional information of the image is converted into one-dimensional, which greatly reduces the amount of calculation and improves the efficiency of subsequent symbol recognition. The current gray conversion methods mainly include the maximum value method, the average value method, and the weighted average method. Through the image conversion of the image captured by the camera, the format of the image is converted to RGB565 first, then the grayscale conversion is performed, and finally the binarization process is performed. Different weights are assigned to RGB according to the sensitivity of human eyes to colors, and the grayscale calculation uses the weighting formula [18]:(8)y=0.299R+0.587G+0.114B.The weights of the red, green, and blue channels are measured according to the sensitivity of the human eye to color, and the above formula can be used to obtain a more ideal grayscale image.Denoising:This step is used to remove image noise and distortion. Methods to remove noise include Gaussian blur, bilateral filtering, median filtering, and so on. Under normal circumstances, the background of the music score is mainly bright colors, and the music score is mainly dark, because the noise in the form of isolated noise is the most, so if the Gaussian filter is used, the image itself can be restored most accurately. While maintaining the signal of the score itself, it reduces noise.Sharpen:Although Gaussian Blur can reduce noise, it blurs the key part of the image—the music score, so it needs to further sharpen the picture to highlight the characteristics of the music score. Laplace transform is an integral transform commonly used in engineering mathematics, also known as Laplace transform. The Laplace transform is a linear transform. Laplacian is the operation that can highlight the details of the image and enhance the region of the image with sudden grayscale changes. The Laplace transform of a two-dimensional image is defined as the formula:(9)Laplacef=∂2f∂x2+∂2f∂y2.Edge detection is a fundamental problem in image processing and computer vision. The purpose of edge detection is to identify points in digital images with obvious changes in brightness. Significant changes in image properties often reflect significant events and changes in properties. The Laplacian operator is very useful in edge detection, and its representation as a template is shown in Figure4:Binarization:Binarization is a simple form of thresholding. It selects the thresholdt and extreme values a, b for the entire image, and for any pixel f (x, y) at the coordinate (x, y) in the source image, if the pixel value at the target image coordinates (x, y) is g(x, y), then(10)gx,y=a,fx,y<t,gx,y=b,fx,y≥t.The local threshold segmentation rule is not the case. It divides the original image into multiple smaller subimages and selects the corresponding threshold for each subimage, and then performs local threshold segmentation [19] Due to the influence of illumination, the gray level of the image may be unevenly distributed, and the segmentation effect of the single threshold method is not good. Therefore, the local threshold segmentation method should be used.Figure 4
Laplacian operator template.(2) Inclination Correction. This step is to try to eliminate the influence of the inclination of the score caused by the angle error in the shooting process and make the spectrum line parallel to the axis of the image coordinate system [20].Angle extraction:To correct the angle of the sheet music, the most important thing is to extract the inclination of the sheet music. No matter how the notation is slanted, every line of the musical notation ends with a bar line at the end, and the bar lines between the lines are aligned. This means that as long as a straight line can be found from the image, and this straight line crosses the last bar of each line of the numbered musical notation, its inclination also represents the inclination of the musical score. It can be imagined that in the image coordinates, all the infinite straight lines passing through (i, j) correspond to infinite points in the (ρ,θ) coordinates, and these points constitute a characteristic curve.(11)ρ=xcosθ+ysinθ.Image rotation:After extracting the inclination of the score, you only need to perform a simple rotation operation on the binarized image to get the horizontal score image. An arbitrary affine transformation can be expressed in the form of multiplying by a matrix and adding a vector, which is defined as follows [21]:(12)A·X+B=X′·t=aooao1b0a1oa11b1.By changing the value oft, the mapping from any parallelogram to another parallelogram can be achieved. For a two-dimensional image with width w and height h, the 2 × 3 rotation matrix based on the counterclockwise rotation of the center in radians is as follows:(13)t=AB=cosθsinθ0.5w−sinθcosθ0.5h.


#### 2.2.2. Music Recognition

Music recognition refers to the digital recognition process of recorded human voice or musical instrument audio files. It involves physical acoustics, music art, computer science, and other interdisciplinary subjects and has very large application development prospects [22].(1) Basic Knowledge of Signal Processing. The human ear hears music directly in a perceptual way, but computers do not. The computer sound card converts the continuous waveform signal of the sampled sound wave into a digital signal, and then stores the music information in the form of a file after sampling according to the Nyquist sampling theorem. In practical applications, the human vocal frequency range is 85–1100 Hz, and the sampling rate of a general sound card can reach 44100 Hz, which is much higher than the human voice frequency, so its sound wave information can be completely preserved, laying the foundation for further fundamental frequency extraction.(2) Fundamental Frequency Extraction. There are many methods of fundamental frequency extraction, here are a few to introduce.Harmonic peak method:Harmonic peak method is a typical algorithm based on fast Fourier transform, which reflects the relationship between signal frequency and amplitude, so it is widely used to calculate the frequency spectrum of the signal.(14)Fx=Fft=∫−∞+∞fte−txtdt.The harmonic peak method considers that the peak with the highest amplitude in the spectrogram corresponds to the fundamental wave of the audio signal and takes its frequency value as the fundamental frequency value, that is, set the fundamental frequency value tom, then(15)m=F−1maxFx.The biggest advantage of this method is that it is simple enough, and the time complexity and space complexity are very low. Now, the fast Fourier transform is performed on the C1 key tone recorded in an environment without background noise, and the resulting spectrum is shown in Figure5 [23].The function of Fourier transform is mainly to convert the function into the form of multiple sine combinations. In essence, the signal after the transformation is still the original signal, just a different way of expression.Confidence method:In this method, a factor of 1 to 5 can be obtained for the maximum peak frequency as the candidate fundamental frequency, and then the amplitude of the nth harmonic of each candidate fundamental frequency is summed. The candidate fundamental frequency with the largest sum has the greatest confidence and the greater the likelihood of being the fundamental frequency. Its confidence is as follows:(16)LN=fN,1≤n≤5,RN=∑t=1npi.LN is the candidate fundamental frequency, f is the maximum peak frequency, RN is the confidence level, pi is the amplitude of a certain order of harmonics, and n is the number of harmonics.Figure 5
Spectrum of C1 button.(3) Semantic Understanding. So far, the time value and pitch of all the notes have been identified. To understand the semantics of the notes and restore them to notes, the reverse formula is needed as follows:(17)x=minr−r,1+r−r,r=12log2f440+49,1≤x≤88.In the formula,x represents the key number, and f is the pitch, which is the fundamental frequency value. Then it is further converted into the number num of numbered musical notation and the number of high and low points t, as shown in the following formula:(18)num=x−12t−k+22num=1,2,3,x−12t−k+32num=4,5,6,7,t=x−k12.As for the time value part, suppose the time signature is m/n, the speed is s, the duration of a note is t seconds, and the note is a z-quaver, and there is the following:(19)z=60nts.In this way, the frequency can be expressed as numbered musical notation and high and low points, and the duration can be converted into a time value.


## 2.1. Visualization of Scientific Computing

Scientific computing visualization refers to the use of computer graphics and image processing technology to convert data into graphics and images in the process of scientific computing [8]. The realization of scientific computing visualization can greatly speed up the data processing process so that the huge data generated every day can be effectively used; it can realize image communication between people and data, and between people, instead of text communication or communication. Digital communication allows scientists to understand what is happening in the computing process and can change parameters, observe their effects, and guide and control the computing process. In short, the tools and environment for scientific computing can be further modernized.


### 2.1.1. Classification and Process of Visual Chemistry Subjects in Scientific Computing

There are many fields of scientific computing visualization design. Figure1 shows the subjects covered by the visualization of scientific computing.Figure 1
Visual classification of scientific computing.The basic process of scientific computing visualization is to first preprocess the data, then use the mapping algorithm to map the application data to obtain geometric data, then draw the geometric data to obtain image data, and finally output to the terminal device and display [9]. The details are shown in Figure 2.Figure 2
Visualization flow chart.


### 2.1.2. Visualization Methods of Scientific Computing

(1) 3D Surface Editing Method Based on Sampling Points. Direct editing is parameter-free modeling, that is, you do not need to modify the parameters and features of the parts one by one, but directly modify the model and preview the modified model directly. First, the model needs to be embedded in the scalar field, and then the scalar value is calculated at each vertex of the embedded part. In the process of free deformation, each vertex is always restricted by the level set, and the level set is initialized with the vertex stream. When the user modifies the scalar field, the vertices will move according to the free deformation of the embedded object. After the scalar field is deformed in space, since there is no scalar deformation technology, the reconfigured vertices in the deformed object remain in the same level set [10] and get the derivative of f(X(t), t):(1)dfXt,tdX=∂fXt,t∂X·dXtdt+∂fXt,t∂t=0.In equation (1),dfXt,t/dX represents the gradient of X, and velocity dXt/dt is regarded as the velocity value along the three coordinate axes of x, y and Z in the three-dimensional space, adding smoothness constraints to the model to minimize the change of vertex velocity in a local area. Smoothness is an index for evaluating the degree of convexity and concavity on the surface of paper or cardboard, which is very important for printing paper. ∇f represents the gradient and replace fXt,t with f to obtain the following minimum objective function:(2)P=∫∂f∂t+v·∇f+θ·∇v2dX.In the formula,P represents the smoothing coefficient, θ represents the Lagrangian coefficient, and X represents the vertex. Discretizing this formula, let k represent a voxel mesh vertex, and Qk represents adjacent mesh vertices. The approximate error of the vulnerability constraint is(3)Ek=∂f∂t+∂f∂xvxk+∂f∂yvyk+∂f∂zvzk2.According to the speed difference between vertexk and its neighboring points, the smoothness of local area motion can be calculated [11]:(4)Pk=1Qk∑j∈Qkvxk−vxj2+vyk−vyj2+vzk−vzj2.S represents the smoothing coefficient,Qk represents the number of vertices of the voxel mesh in Qk, then(5)G=∑kEk+θPk.The previous level set algorithms have only a single velocity function, in the evolution process of the zero-level set, the minimization of the energy function is a very complicated process, and there are many problems with a single velocity function. Although the velocity field of the associated voxel, grid can be obtained according to the change of the scalar field, and their position cannot be changed. As an alternative, through the velocity function defined in the following level set method [12], use H to represent the velocity function of the curved surface scalar field, and use the velocity field v obtained above to update the curved surface scalar field:(6)H=−∇S·v∇S.(2) Surface Update and Resampling Method. Since the scalar free deformation technology requires that the relocation of the vertex X(t) should assume that the implicit function is a zero-level set, the reciprocal of f(X(t), t) can be expressed as follows:(7)dSXt,tdX=∂SXt,t∂X·dXtdt+∂SXt,t∂t.When the density of points on the surface becomes low, new sampling points need to be inserted so that the points on the surface remain uniform. The basic idea of the method is to calculate the Voronoi histogram of adjacent points on the tangent plane [13]. A histogram is a statistical chart that uses rectangular bars to compare numerical values of different categories. Use the length of vertical or horizontal columns to compare the magnitude of numerical values, where one axis represents the categorical dimension that needs to be compared, and the other axis represents the corresponding numerical value.(3) Level Set Method. Another advantage of the level set method is that it can easily track the topological changes of objects. For example, when the shape of the object is divided into two, creating a hole, or vice versa. The level set method is a numerical calculation method to solve the deformation evolution of implicit curves and curved surfaces [14], as shown in Figure 3. By moving the level set function, that is, through the rise, fall, and expansion of the level set function, the contours of the closed curve at different times can be obtained. The evolution result of the level set function surface must be related to the evolution result of the closed curve.Figure 3
Circle and its level function.


### 2.1.3. Visualization Algorithms for Scientific Computing

In the early days of computer visualization, the visualization system only provided the functions of drawing and printing one-dimensional curves and two-dimensional contours and surface views. Three-dimensional visualization technology is the separation between the initial stage of computer visualization and the new era of scientific computing visualization [15]. Compared with the initial computer visualization system, the main feature of the scientific computing visualization technology is the three-dimensional visualization technology. The visualization algorithm is shown in Table 1.Table 1
Typical visualization techniques.
DimensionScalarTensorFitness vector1DLine drawing, histogram, bar chart——2DContour line, surface view, image display—2D arrow3DIsosurface, 3D point cloud surfaceTensor ellipse3D arrow, particle system, 3D streamline


## 2.1.1. Classification and Process of Visual Chemistry Subjects in Scientific Computing

There are many fields of scientific computing visualization design. Figure1 shows the subjects covered by the visualization of scientific computing.Figure 1
Visual classification of scientific computing.The basic process of scientific computing visualization is to first preprocess the data, then use the mapping algorithm to map the application data to obtain geometric data, then draw the geometric data to obtain image data, and finally output to the terminal device and display [9]. The details are shown in Figure 2.Figure 2
Visualization flow chart.


## 2.1.2. Visualization Methods of Scientific Computing

(1) 3D Surface Editing Method Based on Sampling Points. Direct editing is parameter-free modeling, that is, you do not need to modify the parameters and features of the parts one by one, but directly modify the model and preview the modified model directly. First, the model needs to be embedded in the scalar field, and then the scalar value is calculated at each vertex of the embedded part. In the process of free deformation, each vertex is always restricted by the level set, and the level set is initialized with the vertex stream. When the user modifies the scalar field, the vertices will move according to the free deformation of the embedded object. After the scalar field is deformed in space, since there is no scalar deformation technology, the reconfigured vertices in the deformed object remain in the same level set [10] and get the derivative of f(X(t), t):(1)dfXt,tdX=∂fXt,t∂X·dXtdt+∂fXt,t∂t=0.In equation (1),dfXt,t/dX represents the gradient of X, and velocity dXt/dt is regarded as the velocity value along the three coordinate axes of x, y and Z in the three-dimensional space, adding smoothness constraints to the model to minimize the change of vertex velocity in a local area. Smoothness is an index for evaluating the degree of convexity and concavity on the surface of paper or cardboard, which is very important for printing paper. ∇f represents the gradient and replace fXt,t with f to obtain the following minimum objective function:(2)P=∫∂f∂t+v·∇f+θ·∇v2dX.In the formula,P represents the smoothing coefficient, θ represents the Lagrangian coefficient, and X represents the vertex. Discretizing this formula, let k represent a voxel mesh vertex, and Qk represents adjacent mesh vertices. The approximate error of the vulnerability constraint is(3)Ek=∂f∂t+∂f∂xvxk+∂f∂yvyk+∂f∂zvzk2.According to the speed difference between vertexk and its neighboring points, the smoothness of local area motion can be calculated [11]:(4)Pk=1Qk∑j∈Qkvxk−vxj2+vyk−vyj2+vzk−vzj2.S represents the smoothing coefficient,Qk represents the number of vertices of the voxel mesh in Qk, then(5)G=∑kEk+θPk.The previous level set algorithms have only a single velocity function, in the evolution process of the zero-level set, the minimization of the energy function is a very complicated process, and there are many problems with a single velocity function. Although the velocity field of the associated voxel, grid can be obtained according to the change of the scalar field, and their position cannot be changed. As an alternative, through the velocity function defined in the following level set method [12], use H to represent the velocity function of the curved surface scalar field, and use the velocity field v obtained above to update the curved surface scalar field:(6)H=−∇S·v∇S.(2) Surface Update and Resampling Method. Since the scalar free deformation technology requires that the relocation of the vertex X(t) should assume that the implicit function is a zero-level set, the reciprocal of f(X(t), t) can be expressed as follows:(7)dSXt,tdX=∂SXt,t∂X·dXtdt+∂SXt,t∂t.When the density of points on the surface becomes low, new sampling points need to be inserted so that the points on the surface remain uniform. The basic idea of the method is to calculate the Voronoi histogram of adjacent points on the tangent plane [13]. A histogram is a statistical chart that uses rectangular bars to compare numerical values of different categories. Use the length of vertical or horizontal columns to compare the magnitude of numerical values, where one axis represents the categorical dimension that needs to be compared, and the other axis represents the corresponding numerical value.(3) Level Set Method. Another advantage of the level set method is that it can easily track the topological changes of objects. For example, when the shape of the object is divided into two, creating a hole, or vice versa. The level set method is a numerical calculation method to solve the deformation evolution of implicit curves and curved surfaces [14], as shown in Figure 3. By moving the level set function, that is, through the rise, fall, and expansion of the level set function, the contours of the closed curve at different times can be obtained. The evolution result of the level set function surface must be related to the evolution result of the closed curve.Figure 3
Circle and its level function.


## 2.1.3. Visualization Algorithms for Scientific Computing

In the early days of computer visualization, the visualization system only provided the functions of drawing and printing one-dimensional curves and two-dimensional contours and surface views. Three-dimensional visualization technology is the separation between the initial stage of computer visualization and the new era of scientific computing visualization [15]. Compared with the initial computer visualization system, the main feature of the scientific computing visualization technology is the three-dimensional visualization technology. The visualization algorithm is shown in Table 1.Table 1
Typical visualization techniques.
DimensionScalarTensorFitness vector1DLine drawing, histogram, bar chart——2DContour line, surface view, image display—2D arrow3DIsosurface, 3D point cloud surfaceTensor ellipse3D arrow, particle system, 3D streamline


## 2.2. Teaching Technology Based on Computer Music Technology

Music is divided into two parts: visual scores and auditory songs, and its teaching targets are usually young people. Therefore, the practical process often needs some methods that highlight the characteristics of music and art that can directly allow learners to see and hear than traditional theoretical teaching [16]. The spectrum recognition is to help music teachers to realize visual score recognition and auditory music recognition. Among them, “spectrum” refers to the recognition of graphic music scores using computer image processing, and “tone” refers to music recognition using computer signal processing, audio processing, and other knowledge. In general, it is necessary to realize both visual score recognition and auditory music recognition. Therefore, in order to explain the educational technology of computer music technology, this chapter is divided into two parts: score recognition and music recognition [17].


### 2.2.1. Numbered Musical Notation Recognition

This section uses basic image processing techniques to study and identify the musical theory symbols in the numbered musical notation pictures, hoping to bring some convenience to the teaching of numbered musical notation. The numbered musical notation recognition is generally divided into image preprocessing, inclination correction, and bar line recognition.(1) Image Preprocessing. Preprocessing is basically the first step of all image recognition technologies, and the quality of preprocessing sometimes has a decisive impact on the recognition accuracy. The basic steps are as follows: the main purpose of image preprocessing is to eliminate irrelevant information in images, recover useful real information, enhance the detectability of relevant information, and simplify data to the greatest extent, thereby improving the reliability of feature extraction, image segmentation, matching, and recognition:Gray conversion:Before starting the score recognition, grayscale conversion can be performed. The RGB three-dimensional information of the image is converted into one-dimensional, which greatly reduces the amount of calculation and improves the efficiency of subsequent symbol recognition. The current gray conversion methods mainly include the maximum value method, the average value method, and the weighted average method. Through the image conversion of the image captured by the camera, the format of the image is converted to RGB565 first, then the grayscale conversion is performed, and finally the binarization process is performed. Different weights are assigned to RGB according to the sensitivity of human eyes to colors, and the grayscale calculation uses the weighting formula [18]:(8)y=0.299R+0.587G+0.114B.The weights of the red, green, and blue channels are measured according to the sensitivity of the human eye to color, and the above formula can be used to obtain a more ideal grayscale image.Denoising:This step is used to remove image noise and distortion. Methods to remove noise include Gaussian blur, bilateral filtering, median filtering, and so on. Under normal circumstances, the background of the music score is mainly bright colors, and the music score is mainly dark, because the noise in the form of isolated noise is the most, so if the Gaussian filter is used, the image itself can be restored most accurately. While maintaining the signal of the score itself, it reduces noise.Sharpen:Although Gaussian Blur can reduce noise, it blurs the key part of the image—the music score, so it needs to further sharpen the picture to highlight the characteristics of the music score. Laplace transform is an integral transform commonly used in engineering mathematics, also known as Laplace transform. The Laplace transform is a linear transform. Laplacian is the operation that can highlight the details of the image and enhance the region of the image with sudden grayscale changes. The Laplace transform of a two-dimensional image is defined as the formula:(9)Laplacef=∂2f∂x2+∂2f∂y2.Edge detection is a fundamental problem in image processing and computer vision. The purpose of edge detection is to identify points in digital images with obvious changes in brightness. Significant changes in image properties often reflect significant events and changes in properties. The Laplacian operator is very useful in edge detection, and its representation as a template is shown in Figure4:Binarization:Binarization is a simple form of thresholding. It selects the thresholdt and extreme values a, b for the entire image, and for any pixel f (x, y) at the coordinate (x, y) in the source image, if the pixel value at the target image coordinates (x, y) is g(x, y), then(10)gx,y=a,fx,y<t,gx,y=b,fx,y≥t.The local threshold segmentation rule is not the case. It divides the original image into multiple smaller subimages and selects the corresponding threshold for each subimage, and then performs local threshold segmentation [19] Due to the influence of illumination, the gray level of the image may be unevenly distributed, and the segmentation effect of the single threshold method is not good. Therefore, the local threshold segmentation method should be used.Figure 4
Laplacian operator template.(2) Inclination Correction. This step is to try to eliminate the influence of the inclination of the score caused by the angle error in the shooting process and make the spectrum line parallel to the axis of the image coordinate system [20].Angle extraction:To correct the angle of the sheet music, the most important thing is to extract the inclination of the sheet music. No matter how the notation is slanted, every line of the musical notation ends with a bar line at the end, and the bar lines between the lines are aligned. This means that as long as a straight line can be found from the image, and this straight line crosses the last bar of each line of the numbered musical notation, its inclination also represents the inclination of the musical score. It can be imagined that in the image coordinates, all the infinite straight lines passing through (i, j) correspond to infinite points in the (ρ,θ) coordinates, and these points constitute a characteristic curve.(11)ρ=xcosθ+ysinθ.Image rotation:After extracting the inclination of the score, you only need to perform a simple rotation operation on the binarized image to get the horizontal score image. An arbitrary affine transformation can be expressed in the form of multiplying by a matrix and adding a vector, which is defined as follows [21]:(12)A·X+B=X′·t=aooao1b0a1oa11b1.By changing the value oft, the mapping from any parallelogram to another parallelogram can be achieved. For a two-dimensional image with width w and height h, the 2 × 3 rotation matrix based on the counterclockwise rotation of the center in radians is as follows:(13)t=AB=cosθsinθ0.5w−sinθcosθ0.5h.


### 2.2.2. Music Recognition

Music recognition refers to the digital recognition process of recorded human voice or musical instrument audio files. It involves physical acoustics, music art, computer science, and other interdisciplinary subjects and has very large application development prospects [22].(1) Basic Knowledge of Signal Processing. The human ear hears music directly in a perceptual way, but computers do not. The computer sound card converts the continuous waveform signal of the sampled sound wave into a digital signal, and then stores the music information in the form of a file after sampling according to the Nyquist sampling theorem. In practical applications, the human vocal frequency range is 85–1100 Hz, and the sampling rate of a general sound card can reach 44100 Hz, which is much higher than the human voice frequency, so its sound wave information can be completely preserved, laying the foundation for further fundamental frequency extraction.(2) Fundamental Frequency Extraction. There are many methods of fundamental frequency extraction, here are a few to introduce.Harmonic peak method:Harmonic peak method is a typical algorithm based on fast Fourier transform, which reflects the relationship between signal frequency and amplitude, so it is widely used to calculate the frequency spectrum of the signal.(14)Fx=Fft=∫−∞+∞fte−txtdt.The harmonic peak method considers that the peak with the highest amplitude in the spectrogram corresponds to the fundamental wave of the audio signal and takes its frequency value as the fundamental frequency value, that is, set the fundamental frequency value tom, then(15)m=F−1maxFx.The biggest advantage of this method is that it is simple enough, and the time complexity and space complexity are very low. Now, the fast Fourier transform is performed on the C1 key tone recorded in an environment without background noise, and the resulting spectrum is shown in Figure5 [23].The function of Fourier transform is mainly to convert the function into the form of multiple sine combinations. In essence, the signal after the transformation is still the original signal, just a different way of expression.Confidence method:In this method, a factor of 1 to 5 can be obtained for the maximum peak frequency as the candidate fundamental frequency, and then the amplitude of the nth harmonic of each candidate fundamental frequency is summed. The candidate fundamental frequency with the largest sum has the greatest confidence and the greater the likelihood of being the fundamental frequency. Its confidence is as follows:(16)LN=fN,1≤n≤5,RN=∑t=1npi.LN is the candidate fundamental frequency, f is the maximum peak frequency, RN is the confidence level, pi is the amplitude of a certain order of harmonics, and n is the number of harmonics.Figure 5
Spectrum of C1 button.(3) Semantic Understanding. So far, the time value and pitch of all the notes have been identified. To understand the semantics of the notes and restore them to notes, the reverse formula is needed as follows:(17)x=minr−r,1+r−r,r=12log2f440+49,1≤x≤88.In the formula,x represents the key number, and f is the pitch, which is the fundamental frequency value. Then it is further converted into the number num of numbered musical notation and the number of high and low points t, as shown in the following formula:(18)num=x−12t−k+22num=1,2,3,x−12t−k+32num=4,5,6,7,t=x−k12.As for the time value part, suppose the time signature is m/n, the speed is s, the duration of a note is t seconds, and the note is a z-quaver, and there is the following:(19)z=60nts.In this way, the frequency can be expressed as numbered musical notation and high and low points, and the duration can be converted into a time value.


## 2.2.1. Numbered Musical Notation Recognition

This section uses basic image processing techniques to study and identify the musical theory symbols in the numbered musical notation pictures, hoping to bring some convenience to the teaching of numbered musical notation. The numbered musical notation recognition is generally divided into image preprocessing, inclination correction, and bar line recognition.(1) Image Preprocessing. Preprocessing is basically the first step of all image recognition technologies, and the quality of preprocessing sometimes has a decisive impact on the recognition accuracy. The basic steps are as follows: the main purpose of image preprocessing is to eliminate irrelevant information in images, recover useful real information, enhance the detectability of relevant information, and simplify data to the greatest extent, thereby improving the reliability of feature extraction, image segmentation, matching, and recognition:Gray conversion:Before starting the score recognition, grayscale conversion can be performed. The RGB three-dimensional information of the image is converted into one-dimensional, which greatly reduces the amount of calculation and improves the efficiency of subsequent symbol recognition. The current gray conversion methods mainly include the maximum value method, the average value method, and the weighted average method. Through the image conversion of the image captured by the camera, the format of the image is converted to RGB565 first, then the grayscale conversion is performed, and finally the binarization process is performed. Different weights are assigned to RGB according to the sensitivity of human eyes to colors, and the grayscale calculation uses the weighting formula [18]:(8)y=0.299R+0.587G+0.114B.The weights of the red, green, and blue channels are measured according to the sensitivity of the human eye to color, and the above formula can be used to obtain a more ideal grayscale image.Denoising:This step is used to remove image noise and distortion. Methods to remove noise include Gaussian blur, bilateral filtering, median filtering, and so on. Under normal circumstances, the background of the music score is mainly bright colors, and the music score is mainly dark, because the noise in the form of isolated noise is the most, so if the Gaussian filter is used, the image itself can be restored most accurately. While maintaining the signal of the score itself, it reduces noise.Sharpen:Although Gaussian Blur can reduce noise, it blurs the key part of the image—the music score, so it needs to further sharpen the picture to highlight the characteristics of the music score. Laplace transform is an integral transform commonly used in engineering mathematics, also known as Laplace transform. The Laplace transform is a linear transform. Laplacian is the operation that can highlight the details of the image and enhance the region of the image with sudden grayscale changes. The Laplace transform of a two-dimensional image is defined as the formula:(9)Laplacef=∂2f∂x2+∂2f∂y2.Edge detection is a fundamental problem in image processing and computer vision. The purpose of edge detection is to identify points in digital images with obvious changes in brightness. Significant changes in image properties often reflect significant events and changes in properties. The Laplacian operator is very useful in edge detection, and its representation as a template is shown in Figure4:Binarization:Binarization is a simple form of thresholding. It selects the thresholdt and extreme values a, b for the entire image, and for any pixel f (x, y) at the coordinate (x, y) in the source image, if the pixel value at the target image coordinates (x, y) is g(x, y), then(10)gx,y=a,fx,y<t,gx,y=b,fx,y≥t.The local threshold segmentation rule is not the case. It divides the original image into multiple smaller subimages and selects the corresponding threshold for each subimage, and then performs local threshold segmentation [19] Due to the influence of illumination, the gray level of the image may be unevenly distributed, and the segmentation effect of the single threshold method is not good. Therefore, the local threshold segmentation method should be used.Figure 4
Laplacian operator template.(2) Inclination Correction. This step is to try to eliminate the influence of the inclination of the score caused by the angle error in the shooting process and make the spectrum line parallel to the axis of the image coordinate system [20].Angle extraction:To correct the angle of the sheet music, the most important thing is to extract the inclination of the sheet music. No matter how the notation is slanted, every line of the musical notation ends with a bar line at the end, and the bar lines between the lines are aligned. This means that as long as a straight line can be found from the image, and this straight line crosses the last bar of each line of the numbered musical notation, its inclination also represents the inclination of the musical score. It can be imagined that in the image coordinates, all the infinite straight lines passing through (i, j) correspond to infinite points in the (ρ,θ) coordinates, and these points constitute a characteristic curve.(11)ρ=xcosθ+ysinθ.Image rotation:After extracting the inclination of the score, you only need to perform a simple rotation operation on the binarized image to get the horizontal score image. An arbitrary affine transformation can be expressed in the form of multiplying by a matrix and adding a vector, which is defined as follows [21]:(12)A·X+B=X′·t=aooao1b0a1oa11b1.By changing the value oft, the mapping from any parallelogram to another parallelogram can be achieved. For a two-dimensional image with width w and height h, the 2 × 3 rotation matrix based on the counterclockwise rotation of the center in radians is as follows:(13)t=AB=cosθsinθ0.5w−sinθcosθ0.5h.


## 2.2.2. Music Recognition

Music recognition refers to the digital recognition process of recorded human voice or musical instrument audio files. It involves physical acoustics, music art, computer science, and other interdisciplinary subjects and has very large application development prospects [22].(1) Basic Knowledge of Signal Processing. The human ear hears music directly in a perceptual way, but computers do not. The computer sound card converts the continuous waveform signal of the sampled sound wave into a digital signal, and then stores the music information in the form of a file after sampling according to the Nyquist sampling theorem. In practical applications, the human vocal frequency range is 85–1100 Hz, and the sampling rate of a general sound card can reach 44100 Hz, which is much higher than the human voice frequency, so its sound wave information can be completely preserved, laying the foundation for further fundamental frequency extraction.(2) Fundamental Frequency Extraction. There are many methods of fundamental frequency extraction, here are a few to introduce.Harmonic peak method:Harmonic peak method is a typical algorithm based on fast Fourier transform, which reflects the relationship between signal frequency and amplitude, so it is widely used to calculate the frequency spectrum of the signal.(14)Fx=Fft=∫−∞+∞fte−txtdt.The harmonic peak method considers that the peak with the highest amplitude in the spectrogram corresponds to the fundamental wave of the audio signal and takes its frequency value as the fundamental frequency value, that is, set the fundamental frequency value tom, then(15)m=F−1maxFx.The biggest advantage of this method is that it is simple enough, and the time complexity and space complexity are very low. Now, the fast Fourier transform is performed on the C1 key tone recorded in an environment without background noise, and the resulting spectrum is shown in Figure5 [23].The function of Fourier transform is mainly to convert the function into the form of multiple sine combinations. In essence, the signal after the transformation is still the original signal, just a different way of expression.Confidence method:In this method, a factor of 1 to 5 can be obtained for the maximum peak frequency as the candidate fundamental frequency, and then the amplitude of the nth harmonic of each candidate fundamental frequency is summed. The candidate fundamental frequency with the largest sum has the greatest confidence and the greater the likelihood of being the fundamental frequency. Its confidence is as follows:(16)LN=fN,1≤n≤5,RN=∑t=1npi.LN is the candidate fundamental frequency, f is the maximum peak frequency, RN is the confidence level, pi is the amplitude of a certain order of harmonics, and n is the number of harmonics.Figure 5
Spectrum of C1 button.(3) Semantic Understanding. So far, the time value and pitch of all the notes have been identified. To understand the semantics of the notes and restore them to notes, the reverse formula is needed as follows:(17)x=minr−r,1+r−r,r=12log2f440+49,1≤x≤88.In the formula,x represents the key number, and f is the pitch, which is the fundamental frequency value. Then it is further converted into the number num of numbered musical notation and the number of high and low points t, as shown in the following formula:(18)num=x−12t−k+22num=1,2,3,x−12t−k+32num=4,5,6,7,t=x−k12.As for the time value part, suppose the time signature is m/n, the speed is s, the duration of a note is t seconds, and the note is a z-quaver, and there is the following:(19)z=60nts.In this way, the frequency can be expressed as numbered musical notation and high and low points, and the duration can be converted into a time value.


## 3. The Teaching Application Method of Computer Music Technology

In today’s music classrooms, most of them are still teacher-oriented. Teachers teach music theory, teach singing, and let students enjoy music. The modern education theory believes that students are the main body of the classroom and should be based on students. At this time, the application of computer music technology can bring new development to music teaching [24].


### 3.1. The Application of Computer Music Technology in the Teaching of Music Theory

The guiding method of music theory is relatively traditional, and it is no longer suitable for this fast-developing society. Teachers can use computer music technology to play the songs they want to teach at any time. In addition, teachers can also input music scores on the computer when preparing lessons. This can greatly save the time of copying the blackboard, and students can have a new perspective on music. Music theory is no longer an intangible thing, but a subject that can be understood face to face. Many schools have limited musical instruments, so all the musical instruments cannot be displayed in the classroom. According to computer technology, it is possible to combine the image of the musical instrument and the sound of the musical instrument to achieve the effect of unifying the eyes and ears of students. Through the combination of vision and hearing, the difficulty of music theory knowledge can be reduced, and the learning efficiency of students can be improved.


### 3.2. The Application of Computer Music Technology in the Teaching of Music Appreciation

Music appreciation covers a wide range of fields and requires a wide range of knowledge. If only traditional teaching methods and CDs or tapes are used, such courses will lose vitality. The application of computer music technology in appreciation courses can expand students’ knowledge fields and improve educational efficiency. Through the application of computer music technology, knowledge can be clearly conveyed to students. Just like appreciating an opera, if you use computer technology, the whole course will become more beautiful and get better results. Through the use of computer technology, the theoretical knowledge of music appreciation can be made more intuitive, and the score and the lyrics of the music can be completely combined, which greatly improves the enthusiasm and initiative of students in learning. In the music appreciation classroom, teachers can use computer music technology to set various performance methods according to the guidance needs so that students can start playing at any time, so as to concentrate on learning.


### 3.3. The Application of Computer Music Technology in the Teaching of Music Composition

The curriculum standards of primary and secondary schools require students to cultivate and cultivate creativity. The students are young and their music knowledge is relatively weak, unable to reach the level that can create works [25], so it is enough to cultivate students’ creative spirit. Using computer technology, text, audio, video, etc., can be integrated to arouse the enthusiasm of students from a visual and auditory perspective. In this way, the efficiency of teaching will also be improved. In addition, through the use of computer technology, students can also hear the sounds of musical instruments other than the piano, and then try to create on musical instruments.To sum up, as an interdisciplinary subject, computer music education must be combined with actual conditions to find a practical and feasible path for the development of computer music education. From the perspective of building a computer music curriculum system and practice system, a set of teaching system construction plans suitable for the actual situation of the college are formulated, as shown in Figure6. Establish a more systematic and scientific education and teaching quality assurance system that reflects the concept of total quality management, highlights process control, and achieves the satisfaction of the government and society.Figure 6
Teaching system construction.


## 3.1. The Application of Computer Music Technology in the Teaching of Music Theory

The guiding method of music theory is relatively traditional, and it is no longer suitable for this fast-developing society. Teachers can use computer music technology to play the songs they want to teach at any time. In addition, teachers can also input music scores on the computer when preparing lessons. This can greatly save the time of copying the blackboard, and students can have a new perspective on music. Music theory is no longer an intangible thing, but a subject that can be understood face to face. Many schools have limited musical instruments, so all the musical instruments cannot be displayed in the classroom. According to computer technology, it is possible to combine the image of the musical instrument and the sound of the musical instrument to achieve the effect of unifying the eyes and ears of students. Through the combination of vision and hearing, the difficulty of music theory knowledge can be reduced, and the learning efficiency of students can be improved.


## 3.2. The Application of Computer Music Technology in the Teaching of Music Appreciation

Music appreciation covers a wide range of fields and requires a wide range of knowledge. If only traditional teaching methods and CDs or tapes are used, such courses will lose vitality. The application of computer music technology in appreciation courses can expand students’ knowledge fields and improve educational efficiency. Through the application of computer music technology, knowledge can be clearly conveyed to students. Just like appreciating an opera, if you use computer technology, the whole course will become more beautiful and get better results. Through the use of computer technology, the theoretical knowledge of music appreciation can be made more intuitive, and the score and the lyrics of the music can be completely combined, which greatly improves the enthusiasm and initiative of students in learning. In the music appreciation classroom, teachers can use computer music technology to set various performance methods according to the guidance needs so that students can start playing at any time, so as to concentrate on learning.


## 3.3. The Application of Computer Music Technology in the Teaching of Music Composition

The curriculum standards of primary and secondary schools require students to cultivate and cultivate creativity. The students are young and their music knowledge is relatively weak, unable to reach the level that can create works [25], so it is enough to cultivate students’ creative spirit. Using computer technology, text, audio, video, etc., can be integrated to arouse the enthusiasm of students from a visual and auditory perspective. In this way, the efficiency of teaching will also be improved. In addition, through the use of computer technology, students can also hear the sounds of musical instruments other than the piano, and then try to create on musical instruments.To sum up, as an interdisciplinary subject, computer music education must be combined with actual conditions to find a practical and feasible path for the development of computer music education. From the perspective of building a computer music curriculum system and practice system, a set of teaching system construction plans suitable for the actual situation of the college are formulated, as shown in Figure6. Establish a more systematic and scientific education and teaching quality assurance system that reflects the concept of total quality management, highlights process control, and achieves the satisfaction of the government and society.Figure 6
Teaching system construction.


## 4. Experimental Analysis and Results

### 4.1. Music Teaching Experiment Based on Computer Music Technology

#### 4.1.1. Numbered Musical Notation Recognition Experiment

(1) Experimental Design. The platform of this experiment is Visual Studio, and the test of numbered musical notation recognition is carried out on this platform. This experiment studies music teaching in basic education, so the numbered musical notation of several songs in the textbooks of elementary and middle schools is selected for experiment. The selected songs include the song of selling newspapers, two tigers, the song of the seven sons, and the song of the fishing boat. The resolution of the numbered musical notation of these songs is increased in turn, and the accuracy of the numbered musical notation recognition algorithm for each numbered musical notation element is tested to explore the relationship between the resolution and the recognition accuracy of the numbered musical notation. It needs to number the numbered musical notation of several songs first, as shown in Table 2.Table 2
Numbering table.
ABCDNameSelling newspaper songsTwo tigersSong of seven sonsFishing boat singing nightResolving power857 × 784991 × 6191586 × 22422481 × 3508Time-consuming (ms)5691127325710294(2) Experimental Results and Analysis. Statistics on the identification results of each element are obtained, and Table 3 is obtained.Table 3
Numbered musical notation recognition results.
ABCDTrue valueIdentification valueTrue valueIdentification valueTrue valueIdentification valueTrue valueIdentification valueContinuous note1010669833Digital note757624244848179168Underline2729454567652323Short horizontal line1212333156553737Attachment point331917661212Gross value127129197193186183254243Accuracy98.4%98.0%98.4%95.7%Time-consuming (ms)5691127325710294It can be seen from the table that the experiment counts the number of tuplets, digital notes, underscores, dashes, and dots in each numbered musical notation, and the true and recognized values of these numbers in the numbered musical notation. We calculated the total amount of these values to solve the accuracy of numbered musical notation recognition, and the results obtained were 98.4, 98.0, 98.4, and 95.7%. It proves that there is no significant difference between the recognition accuracy and the resolution of the numbered musical notation. Looking at the recognition time again, it can be seen from the table that the higher the resolution of the picture, the longer the recognition time.


#### 4.1.2. Music Recognition Experiment

(1) Algorithm Design. There are many ways to extract the fundamental frequency mentioned above. This experiment proposes an improved fundamental frequency extraction method, and this algorithm is designed based on the harmonic peak method and the confidence method introduced above.The steps of the algorithm are as follows: the frequency range needs to be found first, and then the spectrum function is obtained. The expression of the spectrum function is(20)fx=FFTy,where x is in the frequency range; then the first n extreme points of f(x) need to be calculated, and these extreme points are set as candidate frequency bases; each candidate frequency base is calculated using a confidence function; finally, it is calculated according to the following formula:(21)x=maxihxi.The following compares the performance of the improved method with the traditional harmonic peak method and confidence method.(2) Experimental Design. The music recognition experiment platform is also Visual Studio, and the object of this experiment is a 5 s piano recording in a noise-free environment. The applied algorithm of this experiment is the harmonic peak method and the confidence method mentioned above, as well as the improved algorithm involved in this experiment. In order to test the accuracy of different algorithms in different situations, this study designed several sets of different signal-to-noise ratio environments, and designed the signal-to-noise ratio from 30 dB to 100 dB to test the accuracy of the algorithm for fundamental frequency extraction.(3) Experimental Results and Analysis. Figure 7 shows the fundamental frequency extraction accuracy results of the three algorithms at different signal-to-noise ratios.Figure 7
Fundamental frequency extraction accuracy.It can be seen from the figure that, regardless of the signal-to-noise ratio, the accuracy of the fundamental frequency extraction of the improved algorithm is always the highest. The accuracy curve is hovering around 90%, and after calculation, the average accuracy of the improved algorithm is 90.88% during the period when the signal-to-noise ratio is 30–100 dB. This value is relatively high, and even if the signal-to-noise ratio increases, the accuracy of the improved algorithm does not decrease significantly, indicating that the algorithm is not interfered by noise. The accuracy of the harmonic peak method is stable at about 62% during the period when the signal-to-noise ratio is 30–100 dB, and it is not interfered by noise. In the confidence method, when the signal-to-noise ratio is 30–60 dB, the accuracy rate increases with the increase of the signal-to-noise ratio. After 60 dB, it stabilizes at about 70%, and its accuracy is greater than that of the harmonic peak method. In addition to accuracy, the execution time of the fundamental frequency extraction is also an important evidence to measure the algorithm. Figure8 shows the average time of processing all samples and the average time of processing 1s samples for the three algorithms.Figure 8
Sample processing time.It can be seen from the figure that among all the algorithms, the harmonic peak method has the shortest average processing time for all samples or 1s samples. The improved algorithm has the longest processing time, and the improved algorithm has 18.6% longer average time for processing all samples than the harmonic peak method, and 11.2% longer average time for processing 1s samples.In summary, although the traditional harmonic peak method has low accuracy, it has strong noise immunity and takes less time; the accuracy rate of the confidence method is slightly higher than that of the harmonic peak method, but it also takes slightly more time than the harmonic peak method. The accuracy of the improved algorithm proposed in this paper is much higher than the other two algorithms. Although it takes more time, it is only more than 10% more than the harmonic peak method, which is within the acceptable range.


### 4.2. Student Satisfaction Survey Experiment

#### 4.2.1. Experimental Design

In order to have a thorough and accurate understanding of the effects of scientific computing visualization and computer music technology on music teaching in basic education, we will conduct a questionnaire survey for elementary and middle school students and divide these students into two groups. One group is an experimental group, accepting the computer technology-based music teaching described in Section 2.3, which we call the new type of teaching. The other group is the control group, still receiving traditional music teaching. The number of students in both groups is 80, and both are middle-school students and elementary-school students each with 40 students. After a month of teaching, a questionnaire survey was conducted among these students.


#### 4.2.2. Experimental Results and Analysis

This experiment conducted a satisfaction survey on students and asked them to score music lessons. Figure9 shows the scoring results of the two groups.Figure 9
Satisfaction score results.It can be seen from the figure that whether it is the experimental group or the control group, the number of people with a score between 91 and 100 is the largest, and as the score interval increases, the number of people selected is increasing. It can be seen that students have a natural interest in music classes and generally prefer music classes. Comparing the two groups, it was found that 49 people in the experimental group scored between 91 and 100, while 35 people in the control group had a 40% increase in the number of people in the experimental group compared to the control group, proving that new music teaching methods can greatly improve students' interest. In order to explore the difference between the influence of new music teaching methods on junior high school students and elementary school students, this experiment separated the junior high school students from the elementary school students and made a statistics. The result is shown in Figure10.Figure 10
Satisfaction results for different age groups.It can be seen from the figure that for the control group, the number of pupils in the 91–100 interval is higher than that of junior high school students. It can be seen that primary school students are more interested in music lessons than junior high school students, which is related to the characteristics of primary school students. Among elementary school students, for the 91–100 scoring area, the number of people in the experimental group is 26 and the number in the control group is 21, an increase of 23.8%. Among junior high school students, for the 91–100 scoring area, the number of people in the experimental group was 23 and the number in the control group was 14, which increased by 50%. It can be seen that the new teaching method has a greater impact on junior high school students and is more popular with junior high school students.


## 4.1. Music Teaching Experiment Based on Computer Music Technology

### 4.1.1. Numbered Musical Notation Recognition Experiment

(1) Experimental Design. The platform of this experiment is Visual Studio, and the test of numbered musical notation recognition is carried out on this platform. This experiment studies music teaching in basic education, so the numbered musical notation of several songs in the textbooks of elementary and middle schools is selected for experiment. The selected songs include the song of selling newspapers, two tigers, the song of the seven sons, and the song of the fishing boat. The resolution of the numbered musical notation of these songs is increased in turn, and the accuracy of the numbered musical notation recognition algorithm for each numbered musical notation element is tested to explore the relationship between the resolution and the recognition accuracy of the numbered musical notation. It needs to number the numbered musical notation of several songs first, as shown in Table 2.Table 2
Numbering table.
ABCDNameSelling newspaper songsTwo tigersSong of seven sonsFishing boat singing nightResolving power857 × 784991 × 6191586 × 22422481 × 3508Time-consuming (ms)5691127325710294(2) Experimental Results and Analysis. Statistics on the identification results of each element are obtained, and Table 3 is obtained.Table 3
Numbered musical notation recognition results.
ABCDTrue valueIdentification valueTrue valueIdentification valueTrue valueIdentification valueTrue valueIdentification valueContinuous note1010669833Digital note757624244848179168Underline2729454567652323Short horizontal line1212333156553737Attachment point331917661212Gross value127129197193186183254243Accuracy98.4%98.0%98.4%95.7%Time-consuming (ms)5691127325710294It can be seen from the table that the experiment counts the number of tuplets, digital notes, underscores, dashes, and dots in each numbered musical notation, and the true and recognized values of these numbers in the numbered musical notation. We calculated the total amount of these values to solve the accuracy of numbered musical notation recognition, and the results obtained were 98.4, 98.0, 98.4, and 95.7%. It proves that there is no significant difference between the recognition accuracy and the resolution of the numbered musical notation. Looking at the recognition time again, it can be seen from the table that the higher the resolution of the picture, the longer the recognition time.


### 4.1.2. Music Recognition Experiment

(1) Algorithm Design. There are many ways to extract the fundamental frequency mentioned above. This experiment proposes an improved fundamental frequency extraction method, and this algorithm is designed based on the harmonic peak method and the confidence method introduced above.The steps of the algorithm are as follows: the frequency range needs to be found first, and then the spectrum function is obtained. The expression of the spectrum function is(20)fx=FFTy,where x is in the frequency range; then the first n extreme points of f(x) need to be calculated, and these extreme points are set as candidate frequency bases; each candidate frequency base is calculated using a confidence function; finally, it is calculated according to the following formula:(21)x=maxihxi.The following compares the performance of the improved method with the traditional harmonic peak method and confidence method.(2) Experimental Design. The music recognition experiment platform is also Visual Studio, and the object of this experiment is a 5 s piano recording in a noise-free environment. The applied algorithm of this experiment is the harmonic peak method and the confidence method mentioned above, as well as the improved algorithm involved in this experiment. In order to test the accuracy of different algorithms in different situations, this study designed several sets of different signal-to-noise ratio environments, and designed the signal-to-noise ratio from 30 dB to 100 dB to test the accuracy of the algorithm for fundamental frequency extraction.(3) Experimental Results and Analysis. Figure 7 shows the fundamental frequency extraction accuracy results of the three algorithms at different signal-to-noise ratios.Figure 7
Fundamental frequency extraction accuracy.It can be seen from the figure that, regardless of the signal-to-noise ratio, the accuracy of the fundamental frequency extraction of the improved algorithm is always the highest. The accuracy curve is hovering around 90%, and after calculation, the average accuracy of the improved algorithm is 90.88% during the period when the signal-to-noise ratio is 30–100 dB. This value is relatively high, and even if the signal-to-noise ratio increases, the accuracy of the improved algorithm does not decrease significantly, indicating that the algorithm is not interfered by noise. The accuracy of the harmonic peak method is stable at about 62% during the period when the signal-to-noise ratio is 30–100 dB, and it is not interfered by noise. In the confidence method, when the signal-to-noise ratio is 30–60 dB, the accuracy rate increases with the increase of the signal-to-noise ratio. After 60 dB, it stabilizes at about 70%, and its accuracy is greater than that of the harmonic peak method. In addition to accuracy, the execution time of the fundamental frequency extraction is also an important evidence to measure the algorithm. Figure8 shows the average time of processing all samples and the average time of processing 1s samples for the three algorithms.Figure 8
Sample processing time.It can be seen from the figure that among all the algorithms, the harmonic peak method has the shortest average processing time for all samples or 1s samples. The improved algorithm has the longest processing time, and the improved algorithm has 18.6% longer average time for processing all samples than the harmonic peak method, and 11.2% longer average time for processing 1s samples.In summary, although the traditional harmonic peak method has low accuracy, it has strong noise immunity and takes less time; the accuracy rate of the confidence method is slightly higher than that of the harmonic peak method, but it also takes slightly more time than the harmonic peak method. The accuracy of the improved algorithm proposed in this paper is much higher than the other two algorithms. Although it takes more time, it is only more than 10% more than the harmonic peak method, which is within the acceptable range.


## 4.1.1. Numbered Musical Notation Recognition Experiment

(1) Experimental Design. The platform of this experiment is Visual Studio, and the test of numbered musical notation recognition is carried out on this platform. This experiment studies music teaching in basic education, so the numbered musical notation of several songs in the textbooks of elementary and middle schools is selected for experiment. The selected songs include the song of selling newspapers, two tigers, the song of the seven sons, and the song of the fishing boat. The resolution of the numbered musical notation of these songs is increased in turn, and the accuracy of the numbered musical notation recognition algorithm for each numbered musical notation element is tested to explore the relationship between the resolution and the recognition accuracy of the numbered musical notation. It needs to number the numbered musical notation of several songs first, as shown in Table 2.Table 2
Numbering table.
ABCDNameSelling newspaper songsTwo tigersSong of seven sonsFishing boat singing nightResolving power857 × 784991 × 6191586 × 22422481 × 3508Time-consuming (ms)5691127325710294(2) Experimental Results and Analysis. Statistics on the identification results of each element are obtained, and Table 3 is obtained.Table 3
Numbered musical notation recognition results.
ABCDTrue valueIdentification valueTrue valueIdentification valueTrue valueIdentification valueTrue valueIdentification valueContinuous note1010669833Digital note757624244848179168Underline2729454567652323Short horizontal line1212333156553737Attachment point331917661212Gross value127129197193186183254243Accuracy98.4%98.0%98.4%95.7%Time-consuming (ms)5691127325710294It can be seen from the table that the experiment counts the number of tuplets, digital notes, underscores, dashes, and dots in each numbered musical notation, and the true and recognized values of these numbers in the numbered musical notation. We calculated the total amount of these values to solve the accuracy of numbered musical notation recognition, and the results obtained were 98.4, 98.0, 98.4, and 95.7%. It proves that there is no significant difference between the recognition accuracy and the resolution of the numbered musical notation. Looking at the recognition time again, it can be seen from the table that the higher the resolution of the picture, the longer the recognition time.


## 4.1.2. Music Recognition Experiment

(1) Algorithm Design. There are many ways to extract the fundamental frequency mentioned above. This experiment proposes an improved fundamental frequency extraction method, and this algorithm is designed based on the harmonic peak method and the confidence method introduced above.The steps of the algorithm are as follows: the frequency range needs to be found first, and then the spectrum function is obtained. The expression of the spectrum function is(20)fx=FFTy,where x is in the frequency range; then the first n extreme points of f(x) need to be calculated, and these extreme points are set as candidate frequency bases; each candidate frequency base is calculated using a confidence function; finally, it is calculated according to the following formula:(21)x=maxihxi.The following compares the performance of the improved method with the traditional harmonic peak method and confidence method.(2) Experimental Design. The music recognition experiment platform is also Visual Studio, and the object of this experiment is a 5 s piano recording in a noise-free environment. The applied algorithm of this experiment is the harmonic peak method and the confidence method mentioned above, as well as the improved algorithm involved in this experiment. In order to test the accuracy of different algorithms in different situations, this study designed several sets of different signal-to-noise ratio environments, and designed the signal-to-noise ratio from 30 dB to 100 dB to test the accuracy of the algorithm for fundamental frequency extraction.(3) Experimental Results and Analysis. Figure 7 shows the fundamental frequency extraction accuracy results of the three algorithms at different signal-to-noise ratios.Figure 7
Fundamental frequency extraction accuracy.It can be seen from the figure that, regardless of the signal-to-noise ratio, the accuracy of the fundamental frequency extraction of the improved algorithm is always the highest. The accuracy curve is hovering around 90%, and after calculation, the average accuracy of the improved algorithm is 90.88% during the period when the signal-to-noise ratio is 30–100 dB. This value is relatively high, and even if the signal-to-noise ratio increases, the accuracy of the improved algorithm does not decrease significantly, indicating that the algorithm is not interfered by noise. The accuracy of the harmonic peak method is stable at about 62% during the period when the signal-to-noise ratio is 30–100 dB, and it is not interfered by noise. In the confidence method, when the signal-to-noise ratio is 30–60 dB, the accuracy rate increases with the increase of the signal-to-noise ratio. After 60 dB, it stabilizes at about 70%, and its accuracy is greater than that of the harmonic peak method. In addition to accuracy, the execution time of the fundamental frequency extraction is also an important evidence to measure the algorithm. Figure8 shows the average time of processing all samples and the average time of processing 1s samples for the three algorithms.Figure 8
Sample processing time.It can be seen from the figure that among all the algorithms, the harmonic peak method has the shortest average processing time for all samples or 1s samples. The improved algorithm has the longest processing time, and the improved algorithm has 18.6% longer average time for processing all samples than the harmonic peak method, and 11.2% longer average time for processing 1s samples.In summary, although the traditional harmonic peak method has low accuracy, it has strong noise immunity and takes less time; the accuracy rate of the confidence method is slightly higher than that of the harmonic peak method, but it also takes slightly more time than the harmonic peak method. The accuracy of the improved algorithm proposed in this paper is much higher than the other two algorithms. Although it takes more time, it is only more than 10% more than the harmonic peak method, which is within the acceptable range.


## 4.2. Student Satisfaction Survey Experiment

### 4.2.1. Experimental Design

In order to have a thorough and accurate understanding of the effects of scientific computing visualization and computer music technology on music teaching in basic education, we will conduct a questionnaire survey for elementary and middle school students and divide these students into two groups. One group is an experimental group, accepting the computer technology-based music teaching described in Section 2.3, which we call the new type of teaching. The other group is the control group, still receiving traditional music teaching. The number of students in both groups is 80, and both are middle-school students and elementary-school students each with 40 students. After a month of teaching, a questionnaire survey was conducted among these students.


### 4.2.2. Experimental Results and Analysis

This experiment conducted a satisfaction survey on students and asked them to score music lessons. Figure9 shows the scoring results of the two groups.Figure 9
Satisfaction score results.It can be seen from the figure that whether it is the experimental group or the control group, the number of people with a score between 91 and 100 is the largest, and as the score interval increases, the number of people selected is increasing. It can be seen that students have a natural interest in music classes and generally prefer music classes. Comparing the two groups, it was found that 49 people in the experimental group scored between 91 and 100, while 35 people in the control group had a 40% increase in the number of people in the experimental group compared to the control group, proving that new music teaching methods can greatly improve students' interest. In order to explore the difference between the influence of new music teaching methods on junior high school students and elementary school students, this experiment separated the junior high school students from the elementary school students and made a statistics. The result is shown in Figure10.Figure 10
Satisfaction results for different age groups.It can be seen from the figure that for the control group, the number of pupils in the 91–100 interval is higher than that of junior high school students. It can be seen that primary school students are more interested in music lessons than junior high school students, which is related to the characteristics of primary school students. Among elementary school students, for the 91–100 scoring area, the number of people in the experimental group is 26 and the number in the control group is 21, an increase of 23.8%. Among junior high school students, for the 91–100 scoring area, the number of people in the experimental group was 23 and the number in the control group was 14, which increased by 50%. It can be seen that the new teaching method has a greater impact on junior high school students and is more popular with junior high school students.


## 4.2.1. Experimental Design

In order to have a thorough and accurate understanding of the effects of scientific computing visualization and computer music technology on music teaching in basic education, we will conduct a questionnaire survey for elementary and middle school students and divide these students into two groups. One group is an experimental group, accepting the computer technology-based music teaching described in Section 2.3, which we call the new type of teaching. The other group is the control group, still receiving traditional music teaching. The number of students in both groups is 80, and both are middle-school students and elementary-school students each with 40 students. After a month of teaching, a questionnaire survey was conducted among these students.


## 4.2.2. Experimental Results and Analysis

This experiment conducted a satisfaction survey on students and asked them to score music lessons. Figure9 shows the scoring results of the two groups.Figure 9
Satisfaction score results.It can be seen from the figure that whether it is the experimental group or the control group, the number of people with a score between 91 and 100 is the largest, and as the score interval increases, the number of people selected is increasing. It can be seen that students have a natural interest in music classes and generally prefer music classes. Comparing the two groups, it was found that 49 people in the experimental group scored between 91 and 100, while 35 people in the control group had a 40% increase in the number of people in the experimental group compared to the control group, proving that new music teaching methods can greatly improve students' interest. In order to explore the difference between the influence of new music teaching methods on junior high school students and elementary school students, this experiment separated the junior high school students from the elementary school students and made a statistics. The result is shown in Figure10.Figure 10
Satisfaction results for different age groups.It can be seen from the figure that for the control group, the number of pupils in the 91–100 interval is higher than that of junior high school students. It can be seen that primary school students are more interested in music lessons than junior high school students, which is related to the characteristics of primary school students. Among elementary school students, for the 91–100 scoring area, the number of people in the experimental group is 26 and the number in the control group is 21, an increase of 23.8%. Among junior high school students, for the 91–100 scoring area, the number of people in the experimental group was 23 and the number in the control group was 14, which increased by 50%. It can be seen that the new teaching method has a greater impact on junior high school students and is more popular with junior high school students.


## 5. Discussion

This article believes that computer music technology and scientific computing visualization technology entering the basic education music classroom will have very good results and powerful implementation possibilities. With the application of computer music technology, demonstrations under the guidance of teachers will become more intuitive, reducing the difficulty of learning for students and improving the plasticity of work. Computer music technology has many advantages in music education. Computer music technology is becoming more and more perfect, and its functions are not only suitable for music production but also for music education. Visualization of scientific computing can visually present students with more beautiful and intuitive music content. With the reform of the music education system and the pursuit of music teaching methods by all parties, the combination of computer music technology, scientific computing visualization, and music education will become a trend, and its advantages such as intuitive teaching demonstration and easy learning process will gradually appear.


## 6. Conclusion

This article introduces the related methods of scientific computing visualization and computer music technology, and introduces their application methods in music teaching. It also designed experiments based on scientific computing visualization and computer music technology. The first experiment is to test the accuracy of numbered musical notation recognition and the accuracy of music recognition, and the results are as follows: (1) The average recognition rate of numbered musical notation is higher than 95%, and there is no obvious change with the increase of the resolution of numbered musical notation pictures. (2) Comparing the accuracy of music recognition between the improved algorithm in this paper and the two traditional algorithms, it is found that the average accuracy of the improved algorithm is 90.88%, which is the highest. However, the identification time is the longest, but it is within an acceptable range. The second experiment divided students into a control group who studied in traditional music classes and an experimental group who learned in new teaching based on scientific computing visualization and computer music technology. Comparing students’ satisfaction with music lessons, the experiment found that (1) in the 91–100 interval, the number of people in the experimental group increased by 40% compared to the control group, proving that the new music teaching method can greatly increase the interest of students. (2) The analysis of elementary school students and junior high school students separately proves that the new teaching method has a greater impact on junior high school students and is more popular with junior high school students.



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*Source: 3928889-2022-05-19.xml*