Research on Teaching Innovation Strategies in Music Theory Courses in Colleges and Universities under Digital Technology Support

Audio recognition technology is a technology that allows computers and other devices to parse and understand human speech through the use of various algorithms. The core of this technology lies in converting sound signals into digital signals that can be processed by machines, and then analyzing these digital signals through complex algorithms to convert them into text or execute the appropriate commands. The process of sound recognition involves sound acquisition, feature extraction, pattern matching, and final interpretation and execution, a sequence of operations that relies on digital signal processing.

The framework of the recognition system is shown in Fig. 2, and the technique consists of the following five main steps: Step 1: Audio Signal Acquisition This operation is the initial stage of pitch detection, which involves the use of a suitable hardware device, such as a microphone or an audio interface, to capture the sound signals and convert them into a numerical model for subsequent data processing. Step 2: Audio Preprocessing Before the audio signal enters the pitch detection algorithm, pre-processing, such as noise reduction, removing noise, adjusting the sampling rate, etc., is usually required to improve the accuracy of the pitch detection. Step 3: Feature Extraction This step involves extracting pitch-related features from the preprocessed audio signal. This usually involves the analysis of time and frequency domain features such as the Short Time Fourier Transform (STFT) or the Mel Frequency Cepstrum Coefficient (MFCC). Step 4: Pitch Estimation After extracting the relevant features, the pitch estimation algorithm estimates the pitch of the audio signal based on these features. This usually involves the application of pattern recognition or machine learning algorithms. Step 5: Result Output Finally, the pitch detection system outputs the result of the pitch estimation, which is usually presented in terms of notes, Hertz (Hz), or other pitch representations. Through these five steps, pitch detection technology is able to accurately identify and measure pitch from an audio signal.

Figure 2.

Voice recognition system framework

Cubase 12 can store and analyze large amounts of data, thus helping teachers better understand student progress and needs. For example, by comparing students’ rhythmic analysis results at different points in time, teachers can clearly see the trajectory of their students’ progress and provide them with more targeted instruction.

Each sound in the audio can be considered as a short-time energy pulse signal, so the endpoint of the musical signal can be determined by obtaining the moment of occurrence of the short-time pulse. The energy of the musical signal is continuous in the time dimension, and the original audio signal is divided into frames and windows and its short-time energy is calculated: (1) Ei=∑n=0L−1|x(n)|2

where x(n) denotes the amplitude of the n rd point in the i nd frame of the signal, and L denotes the window length, which takes the value of 2% of the sampling frequency value F_s. The short-time energy difference ΔE_i between the two frames before and after is calculated with the following equation: (2) ΔEi=Ei−Ei−1

Each note corresponding to the starting point of the band segmentation has a distinct pulse mutation. However, the results also show that there are several smaller peaks around the peak corresponding to the starting point of each note, and thus the range of the segment needs to be filtered so that only one peak is retained for each note. This was achieved by setting two thresholds, minimum peak height and minimum peak spacing, where the minimum peak height was used to identify the maximum energy mutation corresponding to the starting point of the note, and the minimum peak spacing was used to filter out the pseudo-starting point of the note, i.e., to filter out the influence of several smaller wave peaks around it. All peaks obtained from the short-time energy difference are filtered by these two threshold thresholds to initially obtain the starting point for notes.

Then, according to each starting point, its corresponding end point is searched. By setting two thresholds, short-time energy and short-time over-zero rate, when both parameters of the signal are below the thresholds, the point is determined to be the preliminary obtained note endpoint corresponding to the current starting point. In order to reduce the influence of the algorithm by artificial thresholds and to improve the generalization ability and accuracy of the algorithm, two determination means are used. Judgement one is directed towards the preliminary endpoint obtained. If the endpoint corresponding to the current start point is located after the start point of its next note, the endpoint is judged to be found incorrectly, and the first n frame of the start point of the next note is taken as the endpoint corresponding to that start point. Judgment and for the difference of each pair of starting and ending points, set the shortest note length for the shortest duration of each note, calculate the difference of each pair of starting and ending points, if the difference is less than the shortest duration of the note, then the pair of starting and ending points is judged as noise and removed from the set.

After the audio signal is segmented, the pitch recognition task is carried out for each note obtained from the segmentation. From the frequency point of view, a musical signal is composed of fundamental and overtones. The fundamental is the lowest frequency in the sound wave formed by the vibration of an object. The overtones, which are integer multiples of the fundamental frequency, are distributed differently, resulting in different timbres.

Correlation functions, including the correlation function and the autocorrelation function, describe the degree of similarity between two signals. The correlation function describes the correlation between two signals, while the autocorrelation function describes the synchronization and periodicity of the signals themselves. Consider a discrete periodic signal x(n), whose autocorrelation function is expressed as follows: (3) R(k)=limN→∞12N+1∑n=−NNx(n)x(n+k) where N is the frame length and k is the number of delay sample points.

Generally speaking, the short-time autocorrelation function has the following properties: 1)

The short-time autocorrelation function of a periodic signal has the same period as it.

The above properties show that the signal period is T, and the maximum value of its short-time autocorrelation function must be at an integer multiple of the period, then the fundamental frequency can be found by the distance between the peaks of the short-time autocorrelation function. If a frame of the signal, its short-time autocorrelation function between the neighboring peaks of the number of sampling points for k, then the fundamental frequency of f=Fsk $f = {\raise0.5ex\hbox{$\scriptstyle {{F_s}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle k$}}$, of which F_s is the sampling frequency, this paper takes F_s = 44.1kHz.

Take the actual piano playing note A5 as an example, seek its short-time autocorrelation function, the curve is as follows, according to the nature of the autocorrelation function, obtain the position between the two wave peaks, can be calculated as the fundamental frequency of 888.89Hz, the fundamental frequency frequency of A5 in the piano pitch frequency control table is 880Hz, with an error of 1%, to verify the effectiveness of the method.

The short-time amplitude difference function adopts the difference operation, retaining the short-time autocorrelation function of similar nature, which can reduce the amount of calculation. Consider the discrete periodic signal x(n), whose amplitude difference function is expressed as follows: (4) γn(k)=∑m=nn+N−k−1|xω(m+k)−xω(m)|

Where N is the frame length and k is the number of delayed sample points.

Similarly, the fundamental frequency of the current frame is calculated to be 888,89 Hz, which is an effective method and faster calculation.

The fundamental component is not always the highest intensity component, and the harmonic components can have a significant impact on the actual waveform, which can have a significant impact on the fundamental frequency solution. It should be noted that when using the above two methods to extract the fundamental frequency, the calculation result may be half or twice the actual fundamental frequency, because most of the peaks or valleys are generated by the resonance characteristics, resulting in a large number of redundant calculations, affecting the efficiency and accuracy.

Fundamental frequency extraction based on cepstrum is one of the frequency domain methods. Cepstrum analysis is a homomorphic signal analysis method, and its calculation process is as follows: 1)

Find the Fourier transform of the signal.

For continuous signal x(n), its complex inverse spectrum is: (5) x^(n)=12π∫−ππln|X^(ejω)|ejωn dω

X^(ejω) is generally complex, and if an inverse transformation is performed on its real part, then the real inverse spectrum c(n) can be obtained, calculated as follows: (6) c(n)=12π∫−ππln|X(ejω)|ejωn dω

The calculated fundamental frequency is 872.73 Hz with an error of 1%. It should be noted that the cepstrum method has the disadvantages of large computational volume, high complexity, and poor immunity to noise.

A total of 60 test papers were recovered, and after analyzing the data as a whole, the distribution of grades was as shown in Figure 5, with an average score of 76.35 for Group A and 68.84 for Group B. We can see that the grades of the two classes were mostly distributed at the level of 70-90, with fewer scores below 50.

Figure 5.

Test data

The whole paper includes four types of questions: fill in the blanks (1~4), multiple choice questions (5~8), connecting questions (9~12) and listening and distinguishing questions (13~15), and from the data collected, the data situation of different types of questions is as shown in Fig. 6: This is a graphical representation of the distribution of the correct rate of the four major types of questions, and according to the above, it can be seen that for the listening and distinguishing questions, the students of the two groups are relatively weak, and in general, students from the class of group A are In general, the students of Group A class were relatively outstanding in some aspects, and the two groups were almost in the same proportion in terms of grasping the basic music theory. However, the listening questions in Group A were mainly played through the Cubase 12 music software, and in Group B, the traditional MP3 playback or video playback was chosen, and the questions were exactly the same. We found that the similarity between Group B and Group A is mainly for listening to the song title and writing the instrumentation, but in Group A the transformation of the score to the pentatonic score is very good. From the final results, in the 2nd, 4th and 9th questions, Group A did not have much obvious advantage, but in the 13th question about “the descending sign is located in the (direction) of the note” Group A, who had used Cubase12 music software, had a correct rate of 83%, which shows that for music teaching, sound and image should be synchronized, or mainly based on perceptual understanding.

Figure 6.

Different questions

Overall both classes had the highest error rate for the final multiple choice questions in terms of the distribution of error rates. From the correct rate, the highest percentage of questions were connecting, listening, and recognizing. However, from the perspective of Group A and Group B, the Cubase 12 music software class had a higher percentage of correct listening questions than Group B. There was also a higher percentage of fill-in-the-blanks questions on note writing than Group B. There was no significant difference between multiple choice and linking questions. In terms of the overall distribution of errors, the highest error rate was in the multiple-choice questions, and most of the errors were due to details, such as choosing the wrong instrument or getting the wrong time value for rhythmic notes. In the listening questions, the lowest error rate was found when listening to popular songs, which shows that popular music genres other than books are very popular among students when selecting music courses.