Research on spatio-temporal feature extraction and algorithm optimization in music composition under traditional culture

The most basic way of music composition hand is to make changes in the original material of sound. This section summarizes the types of Chinese elements used in music composition through four aspects, as follows:

The term musical language is borrowed from the common language, which is a special language formed through a long period of excavation, exploration, and summarization. It has a fixed musical vocabulary and can transmit information. In modern linguistics, ordinary language is divided into three elements: phonetics, grammar, and vocabulary, and semioticians propose the use of “energy”and “reference” when expressing form and content. The scope of musical language includes the most fundamental elements, such as melody and rhythm, which are the foundation of traditional music, and these elements are still present in music creation and are manifested in the way they are used explicitly.

Psychological research has proposed the term “relational reflexes”. One is divided into natural instinctive reflexes, and the other is a habitual response that is gradually formed through the stimulation of multiple signal sources. This is also the case in music. For example, when we hear a melody in which most of the scales use the pentatonic seven-tone scale with partials, and the melody develops with the thematic motifs of 2, 6, and 5, it is a melody with the typical ethnic style of the Qiang folk songs in China. When the melody is lyrical, slow, and long, with a wide range, a lot of ornamental sounds, as well as a soothing rhythm in the upward movement of the melody, the tritone repetition is the basic means commonly used in the downward movement of the melody. The conditioned reflex will tell us that this is a piece of electronic music with the symbols of Chinese Mongolian music and culture.

The use of traditional Chinese cultural symbols in music creation is, in fact, to explore the hidden meaning of “reference” as an “energy reference”. It is extremely common for the philosophical ideas of traditional Chinese cultural symbols to be integrated into the layout of electronic music structure, which is a kind of implicit use that can not only enhance the height and depth of the electronic music works but also inherit and carry forward the Chinese philosophical ideas well.

Chinese calligraphy and painting pay attention to the charm and chi. They are a form of meaning that is both abstract and concrete, the beauty of the meaning revealed in the ink and brush, majestic, robust and simple, or hearty and dashing. In music, the same spirit of these temperaments exists and needs to be explored and expressed by our creators.

The artistic essence of the Chinese nation is embodied in Chinese aesthetics, and the expression of the aesthetic idea of the mood is a calm and indifferent state of mind. The Confucian doctrine of the middle way is one of the more common traditional cultural symbols, and its performance in music is mainly the overall conception. The internal structure is rigid and flexible, smooth in the middle of the structural hierarchy, the pursuit of gradual progress, a kind of writing of clouds, and a flowing water-like state of mind.

The period from the 21st century B.C. to the 3rd century A.D. includes the Xia, Shang, and Western Zhou periods to the Spring and Autumn, Warring States, Qin, and Han periods. During this period, traditional Chinese music underwent an evolution from primitive music and dance to court music and dance. In terms of melodic tones and scale forms, primitive music emphasized the intervals of small thirds and developed to the Spring and Autumn period and the Warring States period, which emphasized the upper and lower thirds of the gong, Shang, zheng, and yu, and the three-part loss and gain method, which gave rise to the pentatonic tones, the seven tones, and the twelve rhythms, and established the characteristics of the pentatonic nature of traditional Chinese music melody. The five tones of traditional Chinese music were initially established by the “three points of loss and gain” method.

The period from the 4th to the 10th centuries AD, from the Wei, Jin, and North and South Dynasties to the Sui and Tang dynasties. This period of political upheaval introduced new elements in musical instruments, rhythms, compositions, and music theory. A generation of new music styles was created in which music was nationalized. On the one hand, there was the Sinicization of world music, including the Sinicization of foreign compositions and the use of foreign instruments. On the other hand, Chinese music, with its brilliant achievements, had an important influence on many countries in the world.

During the Song, Yuan, Ming, and Qing dynasties, traditional music was characterized by secularism and sociality and had a broader social base in terms of performers and audiences. In terms of music theory, it showed the inheritance and cleanup of the previous period, and the characteristics of music forms were gradually solidified and stereotyped. The representative musical art form was opera and its music.

The inter-annual change intensity index reflects the average annual change trend of the visiting information flow of music non-heritage museums in Province A. Generally speaking, if the fluctuation of the visiting information flow of music non-heritage museums in Province A is bigger, the larger the T-value is, and conversely, if the fluctuation is smaller, the smaller the T-value is, with the formula as follows: (1) T=∑l−1n(yi−y¯)2ny¯ \[T=\frac{\sqrt{\sum\limits_{l-1}^{n}{\frac{{{\left( {{y}_{i}}-\bar{y} \right)}^{2}}}{n}}}}{{\bar{y}}}\] Where, T represents the intensity of inter-annual change in the information flow of visiting music non-heritage museums in province A, y_i represents the information flow of visiting music non-heritage museums in province A, n represents the total number of years, and y¯\[\bar{y}\] represents the annual average information flow of visiting music non-heritage museums in province A.

The seasonal intensity index reflects the concentration degree of visiting information flow of music non-heritage museums in province A in seasonal dimension, and the expression formula is as follows: (2) R=(Xi−100/12)2/12 \[R=\sqrt{{{{\left( {{X}_{i}}-{100}/{12}\; \right)}^{2}}}/{12}\;}\] Where: R is the seasonal intensity index of visiting information flow of music non-heritage museum in province A. The proportion of visiting information flow of province A music non-heritage museum in month i to the whole year is expressed as X_i. 100/12 represents the average value of the proportion of each month. If the R-value tends to 0, it indicates that the average distribution of visiting information flows in each month of the year in the music non-heritage museum of province A. On the contrary, the larger the R-value is, the larger the seasonal difference is, then it indicates that there is a more significant off-peak season.

Intra-week distribution skewness index reflects the skewness index of the virtual passenger flow distribution of the music non-heritage museum in province A within a week, which can effectively calculate the set distribution characteristics of the information flow of the music non-heritage museum in province A within a short period, and the formula is as follows: (3) G=100×27{ ∑i=17iXi−(7+1)2 } \[G=100\times \frac{2}{7}\left\{ \sum\limits_{i=1}^{7}{i}{{X}_{i}}-\frac{\left( 7+1 \right)}{2} \right\}\]

In the formula, the ratio of the i st day of the visit information flow of the Music Non-heritage museum in province A to all the visit information flow in a week is X_i, and the values of the visit information flow of the Music Non-heritage museum in province A are arranged according to descending order, and the number of the order is i. Theoretically, the value of the G index ranges from [-600/7, 600/7] if G < 0, reflecting that the flow of information about the visit to the Museum of Musical Nonheritage in Province A is mostly focused on the first half of the week. G > 0, it is reflected that the information flow of visiting the music non-heritage museum in province A is mostly focused on the second half of the week. G = 0, then it is reflected that the information flow of visiting music non-heritage museums in province A shows symmetrical distribution in a week.

In the natural discontinuity method, the study subjects are divided into groups with similar properties by calculating the natural discontinuities in the sequence [21-22]. The method iteratively compares the sum of the squared differences between the mean and the observed values of the elements in each group, i.e., the variance of the fit, to determine the best alignment. The best classification threshold calculated is the breakpoint in the ordered distribution of the sequence, and the variance fit goodness-of-fit is defined in the following equation: (4) VGFj=SDAM−SCDMjSDAM \[VG{{F}_{j}}=\frac{SDAM-SCD{{M}_{j}}}{SDAM}\] (5) SDAM=∑i=1n(xi−∑i=1nxin)2 \[SDAM=\sum\limits_{i=1}^{n}{{{\left( {{x}_{i}}-\frac{\sum\limits_{i=1}^{n}{{{x}_{i}}}}{n} \right)}^{2}}}\] (6) SCDMj=∑i=1k(xi−x¯j,k)2 \[SCD{{M}_{j}}=\sum\limits_{i=1}^{k}{{{\left( {{x}_{i}}-{{{\bar{x}}}_{j,k}} \right)}^{2}}}\] where VGF_j denotes the variance fit goodness of fit for j iterations, SDAM denotes the sum of squared variances of the sequence, SCDM_j denotes the sum of squared variances of the category means for the jth iteration, n denotes the sum of the sequences, x_i denotes the ith value in the sequence, and x¯j,k\[{{\bar{x}}_{j,k}}\] denotes the average of all values in the kth combination of the jth iteration.

Square grid-based methods and Tyson polygon methods commonly involve the division of Province A into grid areas for analysis. A square grid of 1000 × 1000 m was used in this study. The calculation formula is as follows:

1) Calculate the latitude and longitude increase for each grid: (7) ΔLon=x⋅3602π⋅Re⋅cos((lat1−l1t2)⋅π360) \[\Delta Lon=\frac{x\cdot 360}{2\pi \cdot {{R}_{e}}\cdot \cos \left( \frac{\left( la{{t}_{1}}-{{l}_{1}}{{t}_{2}} \right)\cdot \pi }{360} \right)}\] (8) ΔLat=x⋅3602π⋅Re \[\Delta Lat=\frac{x\cdot 360}{2\pi \cdot {{R}_{e}}}\]

Kernel density estimation, the basic idea of which is derived from the histogram method, considers that the magnitude of the density value at a point is related to the sample points contained within a certain range of the point [23-24]. Taking the coordinate point (x,y) as the kernel center S and the wide window h as the search radius, the kernel density value of each sample point for the center coordinate (x,y) is calculated by the kernel function k within the radius h. The kernel density value of each sample point for the center coordinate (x,y) is then calculated by the kernel function k.

(x_i,y_i) is the n sample points that are independently and identically distributed, (x,y) is the spatial location of the center point, the probability density function is set to f^(x,y)\[\hat{f}\left( x,y \right)\], and the kernel density is estimated as the following equation: (11) f^(x,y)=1nh2∑i=1nK(x−xih,y−yih) \[\hat{f}\left( x,y \right)=\frac{1}{n{{h}^{2}}}\sum\limits_{i=1}^{n}{K}\left( \frac{x-{{x}_{i}}}{h},\frac{y-{{y}_{i}}}{h} \right)\] Where K is the kernel function and h is called the window width.

In this paper, kernel density estimation is realized based on Arc GIS, and the kernel function in Arc GIS 10.2 adopts the most widely used Epanechnikov function.

The global spatial autocorrelation analysis can determine whether the music creation NRLs in province A have spatial aggregation characteristics and discover the relationship between the spatial objects themselves. The pattern of spatial distribution of geographic objects can be divided into three modes: uniform distribution, random distribution and aggregated distribution.The statistics of Moran I are expressed as: (12) I=n∑i=1n∑j=1nWijzizj∑i=1n∑j=1nWij∑i=1nzi2 \[I=\frac{n\sum\limits_{i=1}^{n}{\sum\limits_{j=1}^{n}{{{W}_{ij}}}}{{z}_{i}}{{z}_{j}}}{\sum\limits_{i=1}^{n}{\sum\limits_{j=1}^{n}{{{W}_{ij}}}}\sum\limits_{i=1}^{n}{z_{i}^{2}}}\] Where z_i denotes the deviation of the attribute of element i from its mean value, W_ij denotes the spatial weight between element i and element j, and n is the sum of the elements.

The original hypothesis H0 is that the values of the analyzed attributes are randomly distributed within the study area.The statistical significance of MoranI is indicated by the Z_I test, where a positive value of Z_I indicates clustering of the values of the study variables within the study area, and a negative value of Z_I indicates that the high values are distributed at intervals with the low values within the study area. The statistical Z_I scores were calculated as follows: (13) ZI=I−E[ I ]V[ I ] \[{{Z}_{I}}=\frac{I-E\left[ I \right]}{\sqrt{V\left[ I \right]}}\] (14) E[ Ii ]=−∑j=1,j≠inwijn−1 \[E\left[ {{I}_{i}} \right]=-\frac{\sum\limits_{j=1,j\ne i}^{n}{{{w}_{ij}}}}{n-1}\] (15) V[I]=E[ I2 ]−E[I]2 \[V[I]=E\left[ {{I}^{2}} \right]-E{{[I]}^{2}}\] where E[I_i] is the weighted average of total emissions and V[I] is the standard deviation.

Bringing in equation (15) yields equation (17): (17) f^(x,y)=3nπh2∑i=1n(1−(x−xi)2+(y−yi)2r2)2 \[\hat{f}\left( x,y \right)=\frac{3}{n\pi {{h}^{2}}}\sum\limits_{i=1}^{n}{{{\left( 1-\frac{{{\left( x-{{x}_{i}} \right)}^{2}}+{{\left( y-{{y}_{i}} \right)}^{2}}}{{{r}^{2}}} \right)}^{2}}}\] Where: f^(x,y)\[\hat{f}\left( x,y \right)\] is the estimated density value of event point S(x,y), h is the bandwidth, n is the total number of time points in the bandwidth range; (x_i,y_i) is the coordinates of time point i; (x – x_i)² + (y – y_i)² is the square of the Euclidean distance between the estimated event point (x,y) and the event point (x_i,y_i) in the bandwidth range.

The default bandwidth calculation method used in Arc GIS10.2: first determine the mean center of the n event points, then take the median D_m of the distance from the mean center to each event point, and calculate the standard distance S_D of the event points and its default bandwidth calculation method is: (18) r=0.9×min(SD,1ln2×Dm)×n−0.2 \[r=0.9\times \min \left( {{S}_{D}},\sqrt{\frac{1}{\ln 2}}\times {{D}_{m}} \right)\times {{n}^{-0.2}}\]

The p-test is often used to estimate the significance of the Moran I index, and the expression for the p-test is given below: (19) p=M+1S+1 \[p=\frac{M+1}{S+1}\] Where M is the number of examples where the Moran I index is equal to or greater than the observed data, and S is the total number of alignments.