Quantitative Integration of Traditional Music and Cultural Elements in Modern Informational Bel canto Teaching

Teachers are an indispensable key element in college education. Therefore, when integrating traditional folk music into Bel Canto teaching, it is very important to improve college teachers’ cognitive level of folk music. From the perspective of long-term development of folk music, China also needs a large number of high-quality teachers with professional level of folk music to promote its development, and to make corresponding teaching experience for the integration of traditional folk music in the teaching of Bel canto in colleges and universities, so as to prepare for the systematic teaching. Moreover, students are strongly influenced by teachers’ words and deeds, and the improvement of teachers’ ethnomusicological quality can indirectly influence their attitude towards ethnomusicology.

In addition to the influence of teachers’ professionalism on the integration of traditional folk music into the teaching of Bel canto, teachers’ teaching style and students’ interest in research are also key factors. At this stage, the focus of Chinese Bel canto education is still on the popularization of Western Bel canto culture and the practice of repertoire, and in the promotion of folk music, it still stays on the familiarity of concepts and the appreciation of music. If students do not major in folk music, most of them can only stay in the conceptual understanding and superficial appreciation, therefore, students’ interest in learning is not high and the focus of learning is not reflected.

Therefore, if college music teachers want to make traditional folk music culture elements can be more smoothly integrated into the Bel canto teaching, they should innovate in the teaching method, improve students’ learning interest, and make the two more efficiently integrated.

Teachers should effectively utilize classroom time to efficiently complete the basic knowledge of the course for students, so that students can have a basic direction in their spare time study and reasonably stimulate students’ interest in creating in their spare time. Secondly, teachers can provide students with basic learning materials, such as relevant historical materials about folk music culture and corresponding sheet music. These will enable students to find a basic direction for individual training in their spare time. Lastly, teachers can lead students in the daily teaching of relevant art appreciation, to help improve their appreciation abilities and develop basic research skills in their own research.

In addition to the teacher’s intention to expand the students’ display channels, as the main body of teaching and the disseminator of traditional culture, we should pay attention to the systematization of our own teaching in our daily teaching, so that we can go deeper and simplify the complexity of the actual teaching process, and let the students have their own insights into traditional folk music culture while mastering the knowledge of the Bel canto.

Spectrum analyzer is a tool to study the frequency distribution and intensity of a given signal, the horizontal axis of the display is the frequency the vertical axis is the amplitude, and the magnitude of the frequency and amplitude can be measured [24]. Spectrum analyzers are divided into Fourier spectrum analyzers and swept spectrum analyzers based on their operating principle. Fourier spectrum analyzer is the measured signal through the low-pass filter for filtering, and then through the analog-to-digital converter for sampling, after sampling the discrete signal is saved in the memory, and then discrete Fourier calculation, calculated the spectrum of the signal. The principle is shown in Figure 1.The working principle of FFT spectrum analyzer makes it unsuitable for the analysis of pulse signals, as well as the limitation of the speed of the AD converter, which can only measure low-frequency signals.

Figure 1.

Schematic diagram of the Fourier spectrum analyzer

Sweep spectrum analyzer is also known as ultra-external difference spectrum analyzer, its working principle is the measured signal after attenuation and filtering, and adjustable local oscillator signal into the mixer mixing converted into intermediate frequency signal, after the bandwidth filter for intermediate frequency filtering, through the logarithmic amplifier for intermediate frequency signal compression, and then envelope detection to get the video signal, in order to smooth the display can be video filtering, and finally on the display on the monitor [25]. Sweep signals have wide application, are easy to operate, and have a sweep function that can replace the frequency sweeper function. Therefore, high frequency experiments can be used in spectrum analysis with scanning function.

Based on the implementation method and spectrum test technology, spectrum analyzers can be generally divided into real-time spectrum analyzers and sweep spectrum analyzers. 1)

Real-time spectrum analyzer

Real-time spectrum analyzer refers to real-time display of the signal at a certain moment in the frequency components and the corresponding amplitude of the analyzer, there are two common forms: parallel filter-type analyzers (real-time type) and Fast Fourier Transform (FFT) type analyzer.

Before starting the spectrometer, make sure that the power supply voltage meets the technical requirements, the fuse is installed correctly, and the power cord is intact and unbroken. 1)

Power on and warm up

Press the power-on button (ON) to turn on the instrument, wait for the analyzer to complete a series of self-diagnostic and adjustment procedures to complete the power-on, and warm up for 30 minutes.

1)

Pre-processing of audio signals

Before analyzing an audio signal, in order to improve the quality of the data it is first necessary to preprocess the signal so that it can be analyzed more efficiently. The signal can be flattened by increasing the high frequency part through pre-emphasis. Then, through frame splitting, the N sampling points are gathered into one observation unit, and a relatively stable short-time sequence is obtained from a long-time non-stationary sequence, and the length of one frame is usually taken as 10-30 ms. However, due to the discontinuity of the beginning and the end of the frame splitting, the error becomes bigger and bigger as the number of frames increases, and the problem of spectrum leakage occurs when truncating the non-periodic signals, therefore, it is usually necessary to Therefore, it is usually necessary to obtain the periodic signal by multiplying the windowing function with the original

Therefore, it is usually necessary to multiply the windowing function with the original signal to obtain the periodic signal, which will increase the continuity between frames. The commonly used windowing functions are rectangular window and Hamming window, of which the rectangular window is given by: (1)w(n)={1,0≤n≤(n−1)0,n=else$$w(n) = \left\{ {\begin{array}{l} {1,}&{0 \leq n \leq (n - 1)} \\ {0,}&{n = else} \end{array}} \right.$$

The formula for the Hamming window is: (2)W(ejw)=e−μN−12)wsin(wN2)sin(w2)$$W({e^{jw}}) = {e^{\left. { - \mu \frac{{N - 1}}{2}} \right)w}}\frac{{\sin \left( {\frac{{wN}}{2}} \right)}}{{\sin \left( {\frac{w}{2}} \right)}}$$ 2)

Time domain analysis

Musical signals vary over time, and so does their energy. The onset of a note is usually accompanied by a sharp increase in the energy of the music, and the energy of a piece of music is usually related to the arousal value. For the energy characteristics of the signal, it is necessary to calculate it after splitting frames and adding windows to obtain an audio sequence of length N, which is calculated by the formula: (3)En=∑m=nn+L−1x2(m)$${E_n} = \sum\limits_{m = n}^{n + L - 1} {{x^2}} (m)$$

Instead of short-time energy, short-time amplitude can also be calculated as Eq: (4)Mn=∑m=nn+L⋅1|x[m]|$${M_n} = \sum\limits_{m = n}^{n + L \cdot 1} {|x[m]|}$$ 3)

Frequency Domain Analysis

Through the time domain of the non-periodic signal f(t) is difficult to analyze the relevant characteristics of the information, so it is usually necessary to transform the original audio signal, the data compression and extraction of higher-level information. One of the most basic transforms is the Fourier Transform, by which the spectrum of a section of a Jinn frequency can be obtained.

Theoretically, the Fourier Transform is used to analyze continuous signals and cannot be used on a computer. In practice, the discrete time Fourier transform is used to analyze the sampled data. For a continuous audio signal x[n], and a DTFT of x[n], the calculation of the (5)Xf(θ)=∑n=−∞n=+∞x[n]⋅e−jθn$${X^f}(\theta ) = \sum\limits_{n = - \infty }^{n = + \infty } x [n] \cdot {e^{ - j\theta n}}$$

Where: n is the sequence number of the sampling point, θ is the unit in radians or the sampled result is discrete in the time domain but still continuous in the frequency domain, and the axis (0 ≤ k ≤ 2π) is sampled uniformly to obtain its discrete spectrum: (6)θ[k]=2kπN,0≤k≤N−1$$\theta [k] = \frac{{2k\pi }}{N},0 \leq k \leq N - 1$$

Where: N is the length of the time window, the sampled digital frequency θ can be tabulated and thus the formula for the discrete Fourier transform can be obtained: (7)Xd[k]=∑n=0n=N−1x[n]⋅e−2πknN,0≤k≤N−1$${X^d}[k] = \sum\limits_{n = 0}^{n = N - 1} x [n] \cdot {e^{ - \frac{{2\pi \:kn}}{N}}},0 \leq k \leq N - 1$$

where: X^d[k] is the result of a N-discrete-point DFT on x[n] in the time domain. 4)

Time-frequency analysis

Time-frequency analysis can simultaneously analyze and study the time direction and frequency direction of the audio signal, which can better present the transient characteristics of the signal frequency over time, and then improve the identification of the music on. (1)

Short-time Fourier Transform (DFT)

For DFT, it is a transformation of the global, which is the average frequency characteristics over a period of time. From Eq. (8), it is easy to see that if the frequency domain resolution is increased it will decrease the resolution on the time domain and vice versa. For this defect, the short-time Fourier transform can be introduced.

The STFT slides on the time domain signal by setting the size and step of the window, performs the Fourier transform within each of the corresponding windows separately, and finally stitches them together, so that the frequency over time data is formed, constituting a two-dimensional representation of the joint distribution of time and frequency, and the STFT is given by Eq: (8)S(m,k)=∑n=0N−1x(n+mH)w(n)e−i2πknN$$S(m,k) = \sum\limits_{n = 0}^{N - 1} x (n + mH)w(n){e^{ - i2\pi \frac{{kn}}{N}}}$$

The main method of spectral analysis is spectral estimation, which aims to characterize the distribution of signal ratings on the basis of a finite dataset.Power spectral estimation is useful in many contexts, including the detection of signals in the annihilation of broadband noise.

Mathematically, the power spectrum of a smooth stochastic process x_n and the associated sequence form a link by means of a discrete-time Fourier transform. From the normalization point of view, there is the following equation: (10)Rxx(0)=∫−ππSxx(ω)2πdω=∫−fs/2f,/2Sxx(f)fsdf$${R_{xx}}(0) = \int_{ - \pi }^\pi {\frac{{{S_{xx}}(\omega )}}{{2\pi }}} d\omega = \int_{ - {f_s}/2}^{f,/2} {\frac{{{S_{xx}}(f)}}{{{f_s}}}} df$$

Pxx(ω)=Sxx(ω)2π$${P_{xx}}(\omega ) = \frac{{{S_{xx}}(\omega )}}{{2\pi }}$$ as well as Pxx(f)=Sxx(f)fs$${P_{xx}}(f) = \frac{{{S_{xx}}(f)}}{{{f_s}}}$$ in the above equation are defined as the power spectral density (PSD) of a smooth random signal x_n.

The average power of a signal over the frequency band [ω₁, ω₂], 0 ≤ ω₁ < ω₂ ≤ π can be found by integrating the power spectral density over the frequency band: (11)P¯[ω1,ω2]=∫ω1ω2P∞(ω)dω+∫−ω2−ω1P∞(ω)dω$${\bar P_{[{\omega _1},{\omega _2}]}} = \int_{{\omega _1}}^{{\omega _2}} {{P_\infty }} \left( \omega \right)d\omega + \int_{ - {\omega _2}}^{ - {\omega _1}} {{P_\infty }} \left( \omega \right)d\omega$$

From the above equation you can see that P_xx(ω) is the power concentration of a signal over an infinitesimal frequency band, which is why it is called the power spectral density.

For real signals, the power spectral density is a symmetric DC signal, so P_xx(ω) of 0 ≤ ω≤ π is sufficient for a complete description of the power spectral density. However, in order to obtain the average power over the entire Nyquist interval, the concept of unilateral power spectral density needs to be introduced: (12)Ponesided(ω),={0,−π≤ω≤02Pxx(ω),0≤ω≤π$${P_{onesided}}(\omega ), = \left\{ {\begin{array}{l} {\quad 0, - \pi \leq \omega \leq 0} \\ {2{P_{xx}}(\omega ),0 \leq \omega \leq \pi } \end{array}} \right.$$

The average power of the signal over band [ω₁, ω₂], 0 ≤ ω₁ < ω₂ ≤ π can be found ∀4 using the one-sided power spectral density: (13)P¯[ω1,ω2]=∫ω1ω2Poncsided(ω)dω$${\bar P_{[{\omega _1},{\omega _2}]}} = \int_{{\omega _1}}^{{\omega _2}} {{P_{oncsided}}} (\omega )d\omega$$

From the above analysis, it is clear that signal spectrum analysis is a method of converting a time domain signal into the frequency domain. The purpose of spectral analysis is to decompose a complex time-history waveform into several single harmonic components by means of the Fourier transform, so as to obtain the frequency structure and information of the harmonic ley phase.

In the experimental process, the use of spectrum meter real-time observation of a singing passage spectrum dynamics and fixed-point screenshot analysis of the combination of ways, that can be more clearly observed the overall vocal state of the singer, while making the collection of the spectrogram is more representative of the Fig. 3 to Fig. 6 for the students to sing the Bel canto of the vocal mapping. Analyzing Figures 3 to 6, the spectra of several students have striking similarities:

Figure 3.

Student 1 sings “A” to use small words

Figure 4.

Student 1 sings two small-type d tones with “e”

Figure 5.

Student 2 sings two d tones with the “A”

Figure 6.

Student 3 sings small character d with the “A”

1. The fundamental and overtones are not spiky, but have a certain width (measured, up and down pitch amplitude within a small second, vibrato frequency is between 5 and 6 times per second), which indicates that they have a rich and reasonable vibrato (Bart’s frequency width is relatively narrower, which means that the amplitude of her vibrato fluctuations is smaller, which is reflected in the auditory, and the timbre of its relatively pure, which also provides a reference for the singer in the timbral 2.3000Hz near, have a significant resonance peak, its amplitude is even basically the same as the amplitude of the fundamental frequency, and from the auditory perception to the control, the sound is round and solid, with a strong penetrating power. 3. In addition to the resonance peak near 3000Hz, the first or second overtone is mostly more prominent.

A recording was made of a violin playing a small c-note without vibrato, and then a violin playing a small c-note with vibrato, and the spectra of the two recordings were compared. The spectrum obtained by playing the violin without vibrato is shown in Fig. 7, and the fundamental and overtones are in the shape of sharp peaks, while the spectrum obtained by playing the violin with vibrato (which is similar to the vibrato of the human voice) is shown in Fig. 8, and the pattern of the fundamental and overtones is obviously widened horizontally. From the listening experience, the tone is relatively dry and thin without vibrato, and relatively mellow and full when vibrating.

Figure 7.

Violin plays a group of c-tones without kneading strings

Figure 8.

The violin plays a group of c e in small strings

The vocal cords of tenor singers are stronger and thinner at the edges (about 16-18mm in length), and their voices are one octave lower than those of girls when they sing (in notation, a higher octave is generally used, but in the graphic description of this experiment, what is marked is the actual pitch). The timbre is beautiful and bright, with a high, prairie, firm, and powerful voice, but the voice tends to be hollow and weak when in the lower register. Three male students were selected to test the voice samples, and the sample spectra are shown in Figure 9-Figure 11.

Figure 9.

Student a is singing a little word a with avowel

Figure 10.

Student b sings the small group A with the “e”

Figure 11.

Student A sings a group of small words with the “e”

Its spectral characteristics are: 1. The fundamental and overtones are not in the form of spikes, but have a certain width (measured, the upper and lower pitch amplitude is also within a small second), with a rich and reasonable vibrato.2. Unlike the mezzo-soprano, its resonance peak is not in the 3000 HZ, but near 2500 Hz. Its amplitude is stronger, basically equal to that of the fundamental. From the auditory perception to contrast, the sound is full, solid, powerful, with strong penetrating power. 3. In addition to the resonance peak near 2500Hz, the first, second, third, and fourth overtones are mostly more prominent, which is the same as the mezzo-soprano. These overtones and the base just constitute a major triad sound, which can strengthen the sense of strength and fullness of the sound, so although the sound area is low, but the sound is not empty, false.

The vocal spectral analysis of the tenor soprano region is shown in Figure 12-Figure 16. The spectrograms of the tenor’s middle and bass regions are similar to that of the mezzo-soprano, but the characteristics of the spectrograms of the treble region are not the same as that of the mezzo-soprano, and they are also different from that of the soprano. Its characteristics are: 1. The shape of the fundamental and overtones is the same as that of the spectrograms of the middle and low registers, both of which are not in the form of spikes, but have a certain width (above the small character set #a, slightly narrower), with rich and reasonable vibrato.2. Unlike the mezzo-soprano, the tenor’s spectrograms of the treble region still have the resonant peaks near 2500Hz, which have a stronger amplitude (the spectrograms of the latter two bel cantones, whose The latter two spectrograms of Belgonqui, whose vibrato is controlled during the performance, so the resonance peak formation is less complete, and the tone is slightly thinner). From the auditory perception to contrast, the sound is bright, strong, round, full, powerful, with strong penetration and appeal. 3. In addition to the resonance peaks near 2500Hz, at the same time, the first, second, third, and fourth overtones are more prominent. These overtones, along with the resonance peak near 2500Hz, further strengthen the sense of strength and fullness of the sound, resulting in a brilliant and splendid treble.

Figure 12.

Student c sings “i”

Figure 13.

Student A sings a set of g tones with the “e”

Figure 14.

Student c sings a group of A in small words with the “i”

Figure 15.

Student b sings a group of A sounds in small words with the A “o” mother tone

Figure 16.

Students sing a group of A notes in small words with the first voice of “e”

The research object of this paper is the timbre of American singing under the teaching of Bel canto that integrates traditional music and cultural elements, and mainly adopts the spectrometer measurement method mentioned before. From the point of view of music acoustics, it is mainly the harmonic columns and the onset state of the tone that have an impact on the timbre, usually, the number of harmonics is large, it will feel the sound is more full and round; if the number of high-frequency harmonics is large, the resulting timbre will bring people a bright auditory sensation, and on the contrary, it will bring the feeling of darkness.

In the analysis and experiment of this paper, the main use of the “Universal Chime Measurement System” software, which can be used for the dynamic measurement of voice and different types of musical instrument sound, and provides an interface suitable for people in the music industry, with the tone score to indicate the pitch, and f, p to indicate the intensity of the sound, which enhances the applicability of the system.

The sound sources used in this experiment were sampled from standard studio recordings, with a reverberation time of 0.35-0.61 seconds, background noise of less than 24 dB, and ambient temperature and humidity of room temperature. Other recording equipment and methods are also strictly required for music acoustic measurements, effectively guaranteeing the normality of the sound source samples.

In order to ensure the reliability and accuracy of the experimental data, the experiments in this paper strictly follow the principle of comparability of sound source samples. Comparability refers to the comparison of sound source samples at the same pitch, vocal range, source, volume, and vowel. Respectively, female ethnic singing (narrow sense) (the same as below), American singing, and Peking Opera Qingyi vocalized the a vowel in the high vocal range in the small character two group a (short form 6), and the resultant spectrograms are shown in Figures 17-Figure 19.

Figure 17.

Sound spectrum of vowel of a national group e

Figure 18.

Sound spectrum of a vowels in the high voice area of a Bel canto soprano

Figure 19.

Sound spectrum of flower ts in a loud area of Qingyi e

In Figure 17, the frequency range of the ethnic singing girl’s voice is 2000-3000Hz and 3500-3800Hz, forming two very clear resonance peaks, with the peaks remaining at about 2800Hz-3400Hz. The peak is maintained at about 2800Hz-3400Hz. In addition, when the frequency domain value in the 3300 - 3800 Hz is also formed by a high frequency resonance peak.

The vocalizations of the female singer of the traditional Bel canto teaching of American singing in Figure 18 showed two singer resonance peaks in the ranges of 1400-2220 Hz and 2850-2970 Hz, respectively. High-frequency harmonics appear in the subsequent 4400Hz frequency domain, but although these resonance peaks have a certain width, the peak height values are generally low like dwarf bushes, indicating that the female vocalist’s vocalization is drier and less rounded.

The American vocalizations in Figure 19 that incorporate traditional music and cultural elements of American vocal teaching appear two singer resonance peaks in the ranges of 1900-2200Hz and 3643-3721Hz, respectively, both of which have certain peak widths and peak heights, and interestingly enough, five resonance peaks appear in the subsequent high-frequency bands, which indicates that the female vocalist’s singing has more overtones, the voice is brighter and rounder.

Through the use of spectrum measuring instrument to derive the integration of traditional music and cultural elements of Bel canto teaching vocalization and ordinary Bel canto teaching singing vocalization spectrum shown in Figure 20 and Figure 21. From the figure, it can be found that the difference between the traditional music and culture elements of Bel canto teaching and ordinary Bel canto teaching is not very big in the spectrum, and there are resonance peaks in the same position, but there are still some differences, and the low-frequency part of the ordinary Bel canto teaching is louder than the low-frequency part of the traditional music and culture elements of Bel canto teaching, which explains that the chest resonance in the ordinary Bel canto teaching will be higher than the chest resonance in the traditional music and culture elements of the Bel canto teaching. The chest resonance in the common Bel canto teaching singing method is more than the chest resonance in the vocal singing method which integrates the traditional music and cultural elements of Bel canto teaching, and the high frequency part in the ethnic singing method is louder than the high frequency part in the Bel canto singing method, which indicates that there are more falsetto voices in the ethnic singing method, and the frequency is higher.

Figure 20.

Singing of ordinary sound teaching

Figure 21.

Integrated into the sound of traditional music culture elements