Music teaching quality evaluation method based on artificial intelligence

Abstract

The invention discloses a music teaching quality evaluation method based on artificial intelligence, and particularly relates to the field of art education, comprising data acquisition, data analysis, comprehensive analysis and teaching quality evaluation. A triple coupling evaluation system is constructed through multi-source heterogeneous data fusion and an intelligent algorithm, objectivity and scientificity of music teaching quality evaluation are effectively improved, professional equipment is adopted to collect acoustic features, environmental parameters and playing technical data, subjective deviation is eliminated through standardized preprocessing, and the evaluation accuracy is improved. A particle swarm optimization algorithm is combined to optimize an acoustic compensation coefficient and an environment-technology regulation factor, collaborative analysis of multi-dimensional teaching elements is realized, the innovatively designed hierarchical coupling model breaks through the limitation of traditional one-dimensional detection, nonlinear interference of spatial reverberation on tone quality can be analyzed, a loss mechanism of equipment frequency response on playing details can be quantized, and the accuracy and the reliability of the system are improved. And the interactive influence of the environment and the technical defects is accurately revealed.

Description

Technical Field

[0001] The present invention relates to the technical field of art education. More specifically, the present invention relates to a method for evaluating the quality of music teaching based on artificial intelligence. Background Art

[0002] The evaluation of music teaching quality is an important part of the art education field. Traditional methods mainly rely on teachers' subjective experience combined with basic equipment detection. Existing technologies usually adopt a sub-item detection mode: First, judge the pitch and rhythm by artificial audition, use a decibel meter to detect environmental noise, and then analyze the teacher-student interaction by combining the playback of teaching videos; Subsequently, record the data of each dimension independently, and finally give an overall evaluation through weighted average or empirical judgment.

[0003] There are three defects in the existing technology: First, the evaluation process overly relies on expert experience and is significantly affected by individual auditory sensitivity and subjective preferences; Second, the detection dimensions are limited to single pitch or volume indicators, lacking systematic coupling analysis of acoustic characteristics, environmental interference, and performance techniques; Third, the data processing uses a linear superposition method, which cannot reflect the non-linear impact of environmental noise on sound quality attenuation, nor can it capture the dynamic propagation effect of performance technique defects. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the existing technology, the present invention provides a method for evaluating the quality of music teaching based on artificial intelligence, through the following solutions to solve the problems raised in the above background art.

[0005] To achieve the above object, the present invention provides the following technical solution: A method for evaluating the quality of music teaching based on artificial intelligence, including: S1: Data collection: Used to collect acoustic feature data, environment and equipment data, and performance technique data in the target vocal music teaching, and process the collected data; S2: Data analysis: Analyze the data processed in S1 by establishing a mathematical model, including an acoustic feature comprehensive index formula, an environmental quality attenuation factor formula, and a performance technique maturity formula; S3: Comprehensive analysis: Establish a comprehensive analysis model according to the data analysis structure of S2, and calculate the comprehensive optimization index of the target vocal music teaching according to the comprehensive analysis model; S4: Teaching quality evaluation: Evaluate the quality of the target vocal music teaching according to the comprehensive optimization index.

[0006] Preferably, the acoustic feature data includes pitch accuracy, rhythm error value, dynamic range, and harmonic distortion rate; the environment and device data includes environmental background noise decibel value, device frequency response flatness, recording signal-to-noise ratio, and spatial reverberation time; the performance technique data includes legato interval uniformity, dynamics control variance, interval frequency accuracy, and overtone energy distribution.

[0007] Preferably, the acoustic feature data collects audio signals in real time through a professional sound card connected to a high-precision microphone or instrument digital interface, and uses audio analysis software for analysis: pitch accuracy extracts the fundamental frequency through fast Fourier transform and calculates the percentage deviation of the frequency from the international standard pitch; the rhythm error value uses the beat tracking algorithm to compare the time stamp difference between the performance waveform and the target beat template; the dynamic range is calculated by detecting the peak and valley sound pressure levels of the audio waveform and calculating the difference; the harmonic distortion rate separates the harmonic components and non-harmonic noise energy in the audio spectrum and calculates their ratio.

[0008] Preferably, for the environment and device data, in a standard teaching scenario, the environmental background noise decibel value is measured using an integrating sound level meter, and the average value is taken after continuously sampling for 1 minute with all sound sources turned off; the device frequency response flatness is calculated by playing a sweep signal to the teaching device, collecting it through a measuring microphone, and then calculating the sound pressure level fluctuation value of each octave band using a spectrum analyzer; the recording signal-to-noise ratio is calculated by simultaneously recording a standard test signal and environmental noise, and using audio analysis software to calculate the energy ratio of the signal segment to the silent segment; the spatial reverberation time is measured by triggering a sound source using the balloon burst method or sine sweep method, recording the sound pressure decay curve through a multi-channel acoustic analysis system, and calculating the time required for a 60 dB attenuation.

[0009] Preferably, the performance technique data synchronously collects the original instrument signals through a multi-track recording device or captures physical vibration signals using contact sensors: legato interval uniformity extracts the sequence of start time points of consecutive notes and calculates the standard deviation of the adjacent time differences; dynamics control variance analyzes the MIDI velocity values or the amplitude sequence of the audio waveform and statistics its dispersion; interval frequency accuracy uses a real-time spectrum analyzer to capture the pitch frequencies of each note in a chord and calculates the percentage deviation of the actual interval ratio from the theoretical value; overtone energy distribution generates a spectrogram through short-time Fourier transform, and after determining the fundamental frequency, accumulates the proportion of the energy of the first 6 overtones in the total spectrum energy.

[0010] Preferably, in S1, the original physical quantities are made dimensionally consistent, and the Z-score normalization is used to eliminate the differences in magnitudes of different sensors; the time series data is smoothed by moving window mean filtering; the logarithmic transformation is performed on the spectral data to improve the distribution symmetry; linear interpolation is used to fill the time series gaps caused by differences in device sampling rates; the Box-Cox transformation is used for discrete parameters to reduce skewness.

[0011] Preferably, the formula of the comprehensive acoustic feature index is specifically expressed as: , S a represents the comprehensive acoustic feature index, ΔP is the pitch deviation rate, R is the rhythm error, D is the dynamic range, H is the harmonic distortion rate, k p = 0.4, k r = 0.3, λ = 0.02, k h = 0.2 are empirical constants, P0 = 5% is the pitch tolerance threshold, D ref = 50 dB is the reference dynamic range.

[0012] Preferably, the formula of the environmental quality attenuation factor is specifically expressed as: , Q e represents the environmental quality attenuation factor, N is the environmental background noise, ΔF is the frequency response fluctuation, T 60 is the reverberation time, C = 100 is the reference constant, α = 0.15, β = 0.25, γ = 0.4 are penalty coefficients.

[0013] Preferably, the formula of the playing technique maturity is specifically expressed as: , M t represents the playing technique maturity, σ L is the standard deviation of the legato interval, σ V is the variance of the dynamics control, ΔI is the interval deviation rate, E is the proportion of the overtone energy, ∈ = 20 ms, V0 = 15, I0 = 8%, E0 = 35% are reference constants.

[0014] Preferably, the comprehensive analysis model is specifically expressed as: , T represents the comprehensive anomaly index, η = 1.2 is the acoustic compensation coefficient, Q ref = 85 is the environmental reference value, μ = 0.6, ν = 0.4 are the environmental and technical adjustment factors, κ = 1.5 is the non-linear strengthening parameter, C = 100, M0 = 8 are normalization constants.

[0015] Preferably, in S4, when T > 75, it is determined that the target vocal music teaching is high-quality teaching; when 50 < T ≤ 75, it is determined that the target vocal music teaching is qualified; when T ≤ 50, it is determined that the target vocal music teaching is unqualified.

[0016] The technical effects and advantages of the present invention: Through the multi-source heterogeneous data fusion technology, the present invention constructs a triple-coupling analysis model of acoustic features, environmental quality and playing techniques, effectively eliminates the subjective deviation in the evaluation process, collects the original data of the teaching site by using professional acoustic equipment, eliminates the individual perception differences through standardized preprocessing, and combines the particle swarm algorithm to optimize the parameter weights, ensuring that the evaluation results objectively reflect the actual quality level of the teaching; The environment-technology dual-channel synthesizer designed in the present invention breaks through the limitations of traditional single-dimensional detection, synchronously analyzes the impact of spatial reverberation on sound quality and the loss of equipment frequency response on performance details, reveals the interaction between environmental interference and technical defects through a hierarchical coupling model, introduces an acoustic compensation coefficient and a non-linear strengthening parameter, accurately quantifies the progressive impact of noise attenuation on teaching effects, and realizes the collaborative evaluation of multi-dimensional teaching elements; The dynamic evaluation system established in the present invention has the characteristics of self-optimization. It automatically matches the three-level evaluation criteria through a comprehensive optimization index, uses a logarithmic function to compress the magnitude of environmental interference, uses a power function to amplify high-quality performance features, and continuously optimizes the model parameters in combination with an expert scoring database to form an evaluation system with the ability of learning and evolution, significantly improving the timeliness and guiding value of teaching quality diagnosis. Brief Description of the Drawings

[0017] Figure 1 It is a schematic diagram of the overall structure of the present invention. Detailed Embodiment

[0018] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0019] Refer to Figure 1 A method for evaluating the quality of music teaching based on artificial intelligence shown, including: S1: Data collection: used to collect acoustic feature data, environment and equipment data, and performance technology data in target vocal music teaching, and process the collected data.

[0020] The acoustic feature data includes pitch accuracy, rhythm error value, dynamic range, and harmonic distortion rate; the environment and equipment data includes environmental background noise decibel value, equipment frequency response flatness, recording signal-to-noise ratio, and spatial reverberation time; the performance technology data includes legato interval uniformity, dynamics control variance, interval frequency accuracy, and overtone energy distribution.

[0021] The acoustic feature data collects audio signals in real time through a professional sound card connected to a high-precision microphone or a musical instrument digital interface, and uses audio analysis software for analysis: pitch accuracy extracts the fundamental frequency through fast Fourier transform and calculates the frequency deviation percentage from the international standard pitch; the rhythm error value uses the beat tracking algorithm to compare the time stamp difference between the performance waveform and the target beat template; the dynamic range calculates the difference by detecting the peak and valley sound pressure levels of the audio waveform; the harmonic distortion rate separates the harmonic components and non-harmonic noise energy in the audio spectrum and calculates their ratio.

[0022] In the standard teaching scenario for environmental and equipment data, when measuring the environmental background noise decibel value using an integrating sound level meter, all sound sources need to be turned off and continuous sampling for 1 minute is taken to obtain the average value; for the flatness of the equipment frequency response, a sweep signal is played to the teaching equipment, and after being collected by the measuring microphone, the sound pressure level fluctuation value of each octave is calculated using a spectrum analyzer; for the recording signal-to-noise ratio, a standard test signal and environmental noise are recorded simultaneously, and the energy ratio of the signal segment and the silent segment is calculated respectively using audio analysis software; for the spatial reverberation time, a sound source is triggered by the balloon burst method or the sine sweep method, and the sound pressure decay curve is recorded through a multi-channel acoustic analysis system, and the duration required for the decay of 60 dB is calculated.

[0023] The performance technique data is synchronously collected through a multi-track recording device to capture the original instrument signal or a contact sensor is used to capture the physical vibration signal: for the evenness of legato intervals, the starting time point sequence of consecutive notes is extracted, and the standard deviation of the adjacent time differences is calculated; for the variance of dynamics control, the MIDI velocity value or the amplitude sequence of the audio waveform is analyzed, and its dispersion degree is statistically analyzed; for the accuracy of interval frequency, a real-time spectrum analyzer is used to capture the pitch frequencies of each note in the chord, and the percentage deviation of the actual interval ratio from the theoretical value is calculated; for the overtone energy distribution, a spectrogram is generated through short-time Fourier transform, and after the fundamental frequency is determined, the proportion of the sum of the first 6 overtone energies in the total spectrum energy is accumulated.

[0024] S1 unifies the dimensions of the original physical quantities, uses Z-score standardization to eliminate the magnitude differences of different sensors; smooths the time series data through moving window mean filtering; performs logarithmic transformation on the spectrum data to improve the distribution symmetry; uses linear interpolation to fill the time series gap caused by the difference in equipment sampling rates; uses Box-Cox transformation for discrete parameters to reduce skewness.

[0025] S2: Data analysis: The data processed in S1 is analyzed through establishing a mathematical model, including the acoustic feature comprehensive index formula, the environmental quality attenuation factor formula, and the performance technique maturity formula.

[0026] The specific expression of the acoustic feature comprehensive index formula is: , S a represents the acoustic feature comprehensive index, ΔP is the pitch deviation rate, R is the rhythm error, D is the dynamic range, H is the harmonic distortion rate, k p = 0.4, k r = 0.3, λ = 0.02, k h = 0.2 are empirical constants, P0 = 5% is the pitch tolerance threshold, D ref = 50 dB is the reference dynamic range.

[0027] The formula for the comprehensive acoustic feature index first establishes the normalized expressions for each parameter: for the pitch term, it uses threshold ratio attenuation; for the rhythm error, it simulates the perceptual sensitivity with an exponential decay function; for the dynamic range, it performs linear normalization; for harmonic distortion, it applies linear penalty; the constant is determined by fitting the data of instrument teachers' scores. It uses multiple linear regression to solve for the coefficient weights, and finally adjusts the dimension coefficient so that the total score range is [0, 1].

[0028] The formula for the environmental quality attenuation factor is specifically expressed as: , Q e represents the environmental quality attenuation factor, N is the environmental background noise, ΔF is the frequency response fluctuation, T 60 is the reverberation time, C = 100 is the reference constant, and α = 0.15, β = 0.25, γ = 0.4 are the penalty coefficients.

[0029] The formula for the environmental quality attenuation factor is based on the acoustic quality attenuation model: the square term processes non - linear interference, the frequency response fluctuation is linearly superposed, and the constant is determined in three steps: first, measure the data of a professional recording studio to obtain the reference value C; second, quantify the influence degree of each parameter on the subjective score through controlled variable experiments; finally, use the least - squares method to optimize the coefficient combination to minimize the mean square error between the formula output and the expert scoring result.

[0030] The formula for the maturity of playing techniques is specifically expressed as: , M t represents the maturity of playing techniques, σ L is the standard deviation of legato intervals, σ V is the variance of dynamics control, ΔI is the interval deviation rate, E is the proportion of overtone energy, and ∈ = 20ms, V0 = 15, I0 = 8%, E0 = 35% are the reference constants.

[0031] The formula for the maturity of playing techniques uses reciprocal quantization for stability (legato), logarithmic function to describe the sensitivity of dynamics control, linear attenuation for interval deviation, and linear gain for overtone distribution. The reference constants are obtained from the statistical analysis of data of 100 professional players: ϵ takes the median of the legato standard deviation of excellent players, V0 is the 75th percentile of the dynamics control variance, I0 is the upper limit of acceptable interval deviation, E0 is the average value of the proportion of overtones in high - quality timbre, and the formula output is adjusted to a 10 - point scale through a dimension - unifying coefficient.

[0032] S3: Comprehensive analysis: Establish a comprehensive analysis model based on the data analysis structure in S2, and calculate the comprehensive optimization index of the target vocal music teaching according to the comprehensive analysis model.

[0033] The comprehensive analysis model is specifically expressed as: , T represents the comprehensive anomaly index, η = 1.2 is the acoustic compensation coefficient, Q ref=85 is the environmental benchmark value, μ = 0.6, ν = 0.4 are the environmental and technological adjustment factors, κ = 1.5 is the non-linear strengthening parameter, and C = 100, M0 = 8 are the normalization constants.

[0034] The comprehensive analysis model adopts a hierarchical coupling model: First, convert the acoustic index into an environmental quality correction coefficient, and then construct an environment-technology dual-channel synthesizer, where the environmental factor uses a logarithmic function to compress the magnitude to avoid the influence of negative values, the technological maturity uses a power function to amplify the discrimination of high-quality performances, and the constants are determined through orthogonal experimental design: Use 50 sets of teaching recording data, fix C as the original benchmark value of the environmental formula, use the teacher's score as the target value, and use the particle swarm algorithm to optimize η, μ, ν, κ to minimize the prediction error. Finally, constrain μ + ν = 1 to maintain dimensional balance.

[0035] S4: Teaching quality evaluation: Evaluate the quality of the target vocal music teaching according to the comprehensive optimization index.

[0036] In S4, when T > 75, it is determined that the target vocal music teaching is high-quality teaching; when 50 < T ≤ 75, it is determined that the target vocal music teaching is qualified; when T ≤ 50, it is determined that the target vocal music teaching is unqualified.

[0037] The present invention first synchronously collects acoustic feature data, environmental and equipment data, and performance technology data in the teaching scene through a professional sound card, a high-precision microphone, an integrating sound level meter, and a multi-track recording device, and performs data preprocessing using Z-score standardization, sliding window mean filtering, and logarithmic transformation; then establishes a mathematical model to perform multi-dimensional analysis on the data, where the comprehensive acoustic feature index quantifies the pitch and rhythm errors through threshold ratio attenuation and exponential decay functions, the environmental quality attenuation factor uses a quadratic term to process non-linear interference and combines expert scoring to optimize the coefficient, and the performance technology maturity formula uses a reciprocal function and logarithmic transformation to evaluate the performance stability; then constructs a comprehensive analysis model, optimizes the acoustic compensation coefficient and the environment-technology adjustment factor through the particle swarm algorithm, and performs hierarchical coupling calculation on the acoustic index, environmental factor, and technology maturity to obtain the comprehensive optimization index T; finally, conducts a three-level evaluation based on the T value to realize the intelligent quantitative evaluation of teaching quality.

[0038] Through the multi-source heterogeneous data fusion technology, the present invention constructs a triple-coupling analysis model of acoustic features, environmental quality and performance techniques, effectively eliminating the subjective deviation in the evaluation process. Professional acoustic equipment is used to collect the original data on the teaching site, and individual perception differences are eliminated through standardized preprocessing. The particle swarm algorithm is combined to optimize the parameter weights to ensure that the evaluation results objectively reflect the actual teaching quality level. The environment-technology dual-channel synthesizer designed by the present invention breaks through the limitations of traditional single-dimensional detection, synchronously analyzes the influence of spatial reverberation on sound quality and the loss of equipment frequency response on performance details, reveals the interaction between environmental interference and technical defects through a hierarchical coupling model, introduces an acoustic compensation coefficient and a non-linear strengthening parameter, accurately quantifies the progressive influence of noise attenuation on teaching effects, and realizes the collaborative evaluation of multi-dimensional teaching elements. The dynamic evaluation system established by the present invention has the characteristics of self-optimization. By automatically matching the three-level evaluation criteria through the comprehensive optimization index, the logarithmic function is used to compress the environmental interference level, the power function is used to amplify the high-quality performance features, and the model parameters are continuously optimized in combination with the expert scoring database to form an evaluation system with the ability of learning and evolution, significantly improving the timeliness and guiding value of teaching quality diagnosis.

[0039] Secondly, in the attached drawings of the disclosed embodiments of the present invention, only the structures related to the disclosed embodiments are involved, and other structures can refer to the general design. Without conflict, the same embodiment and different embodiments of the present invention can be combined with each other. Finally, the above are only the preferred embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for evaluating the quality of music teaching based on artificial intelligence, characterized in that, Including: S1: Data acquisition: Used to collect acoustic feature data, environment and equipment data, and performance technique data in target vocal music teaching, and process the collected data. S2: Data analysis: Analyze the data processed in S1 by establishing mathematical models, including the comprehensive acoustic feature index formula, the environmental quality attenuation factor formula, and the performance technique maturity formula. S3: Comprehensive analysis: Establish a comprehensive analysis model based on the data analysis results in S2, and calculate the comprehensive optimization index of the target vocal music teaching according to the comprehensive analysis model. S4: Teaching quality assessment: Assess the quality of the target vocal music teaching according to the comprehensive optimization index.

2. The method for evaluating the quality of music teaching based on artificial intelligence according to claim 1, wherein: The acoustic feature data includes pitch accuracy, rhythm error value, dynamic range, and harmonic distortion rate; the environment and equipment data includes environmental background noise decibel value, equipment frequency response flatness, recording signal-to-noise ratio, and spatial reverberation time; the performance technique data includes legato interval uniformity, dynamics control variance, interval frequency accuracy, and overtone energy distribution.

3. The method for evaluating the quality of music teaching based on artificial intelligence according to claim 2, wherein: The acoustic feature data collects audio signals in real time through a professional sound card connected to a high-precision microphone or instrument digital interface, and uses audio analysis software for analysis: pitch accuracy extracts the fundamental frequency through fast Fourier transform and calculates the frequency deviation percentage from the international standard pitch; the rhythm error value uses the beat tracking algorithm to compare the time stamp difference between the performance waveform and the target beat template; the dynamic range detects the peak and valley sound pressure levels of the audio waveform and calculates the difference; the harmonic distortion rate separates the harmonic components and non-harmonic noise energy in the audio spectrum and calculates their ratio.

4. The method for evaluating the quality of music teaching based on artificial intelligence according to claim 2, characterized in that: For the environment and equipment data in the standard teaching scenario, use an integrating sound level meter to measure the environmental background noise decibel value, and continuously sample for 1 minute with all sound sources turned off and take the average value; the equipment frequency response flatness plays a sweep signal to the teaching equipment, and after being recorded by a measuring microphone, uses a spectrum analyzer to calculate the sound pressure level fluctuation value of each octave; the recording signal-to-noise ratio simultaneously records a standard test signal and environmental noise, and uses audio analysis software to calculate the energy ratio of the signal segment and the silent segment respectively; the spatial reverberation time triggers the sound source using the balloon burst method or the sine sweep method, and records the sound pressure decay curve through a multi-channel acoustic analysis system to calculate the time required to decay 60 dB.

5. The method for evaluating the quality of music teaching based on artificial intelligence according to claim 2, wherein: The performance technique data synchronously collects the original instrument signals through a multi-track recording device or captures physical vibration signals using contact sensors: legato interval uniformity extracts the starting time point sequence of consecutive notes and calculates the standard deviation of the adjacent time differences; dynamics control variance analyzes the MIDI velocity value or the amplitude sequence of the audio waveform and statistics its dispersion degree; interval frequency accuracy uses a real-time spectrum analyzer to capture the pitch frequencies of each note in the chord and calculates the percentage deviation of the actual interval ratio from the theoretical value; overtone energy distribution generates a spectrogram through short-time Fourier transform, and after determining the fundamental frequency, accumulates the proportion of the first 6 overtone energies in the total spectrum energy.

6. The method for evaluating the quality of music teaching based on artificial intelligence according to claim 1, wherein: The specific expression of the comprehensive acoustic feature index formula is as follows: , S a denotes the comprehensive acoustic feature index, ΔP is the pitch deviation rate, R is the rhythm error, D is the dynamic range, H is the harmonic distortion rate, k p = 0.4, k r = 0.3, λ = 0.02, k h = 0.2 are empirical constants, P0 = 5% is the pitch tolerance threshold, D ref = 50dB is the reference dynamic range.

7. A method for evaluating the quality of music teaching based on artificial intelligence according to claim 1, characterized in that: The formula for the environmental quality attenuation factor is specifically expressed as: , Q e represents the environmental quality attenuation factor, N is the environmental background noise, ΔF is the frequency response fluctuation, and T 60 is the reverberation time, C = 100 is the reference constant, and α = 0.15, β = 0.25, γ = 0.4 are the penalty coefficients.

8. The method for evaluating the quality of music teaching based on artificial intelligence according to claim 1, wherein: The performance technology maturity formula is specifically expressed as: , M t represents the performance technology maturity, σ L is the legato interval standard deviation, and σ V is the dynamics control variance, ΔI is the interval deviation rate, E is the overtone energy ratio, and ∈ = 20 ms, V0 = 15, I0 = 8%, E0 = 35% are reference constants.

9. The method for evaluating the quality of music teaching based on artificial intelligence according to claim 1, wherein: The specific expression of the comprehensive analysis model is as follows: , where T represents the comprehensive anomaly index, η = 1.2 is the acoustic compensation coefficient, Q ref = 85 is the environmental benchmark value, μ = 0.6, ν = 0.4 are the environmental and technical adjustment factors, κ = 1.5 is the non-linear strengthening parameter, and C = 100, M0 = 8 are the normalization constants.

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