Composition of Variant Regional Music Based on Network Meilin Gu Electronic 15307130394 Abstract Regional music a carrier of local culture. As there are distinct cultural groups across different geographies, regional music can take different features. This paper tries to use network to model local music and bring forward a random walk algorithm with tendency to assist to create a variant regional music which is a combination of Chinese pop music and traditional regional music Key words. networks, music model, composition 1. Introduction. Regional music is an integral part of Chinese traditional culture. But now it is not as popular as past and even unfamiliar for young generation Combination of regional music and pop music can bring fresh vitality to make it shine out and receive eternal inheritance. Network science is a powerful tool and contributes a lot to music analysis and composition A small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other and most nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes grow proportionally to the logarithm of the number of nodes n in the network, that is L∝logN while the clustering coefficient is not small A motif is a short musical idea, a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition: The motive is the smallest structural unit possessing thematic identity!". Any motif may be used to construct complete melodies, themes and pieces. Musical development uses a distinct musical figure that is subsequently altered, repeated, or sequenced throughout a piece or section of a piece of music gt eeing its unity 2. Network Model of music 2.1 Coding mode. There are three key elements in the tune of music: tone range and rhythm For tone, 1, 2, 3, 4,5,6, 7 each represents C, D,E,F,G,A, B For rhythm, consider the duration of dotted crotchet is one, and some typical codes 1 Music and Discourse: Toward a Semiology of Music( Musicologie generale et semiologue, 1987). Translated by Carolyn Abbate. Princeton, NJ: Princeton University Press. ISBN 0691091366/ISBN 0691027145
Composition of Variant Regional Music Based on Network Meilin Gu Electronic Engineering 15307130394 Abstract. Regional music a carrier of local culture. As there are distinct cultural groups across different geographies, regional music can take different features. This paper tries to use network to model local music and bring forward a random walk algorithm with tendency to assist to create a variant regional music which is a combination of Chinese pop music and traditional regional music. Key words. networks, music model, composition 1. Introduction. Regional music is an integral part of Chinese traditional culture. But now it is not as popular as past and even unfamiliar for young generation. Combination of regional music and pop music can bring fresh vitality to make it shine out and receive eternal inheritance. Network science is a powerful tool and contributes a lot to music analysis and composition. A small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other and most nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes grow proportionally to the logarithm of the number of nodes N in the network, that is: L∝logN while the clustering coefficient is not small. A motif is a short musical idea, a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition: "The motive is the smallest structural unit possessing thematic identity".1Any motif may be used to construct complete melodies, themes and pieces. Musical development uses a distinct musical figure that is subsequently altered, repeated, or sequenced throughout a piece or section of a piece of music, guaranteeing its unity. 2. Network Model of Music. 2.1 Coding Mode. There are three key elements in the tune of music: tone, range and rhythm. For tone, 1,2,3,4,5,6,7 each represents C,D,E,F,G,A,B. For rhythm, consider the duration of dotted crotchet is one, and some typical codes 1 Music and Discourse: Toward a Semiology of Music (Musicologie générale et sémiologue, 1987). Translated by Carolyn Abbate. Princeton, NJ: Princeton University Press. ISBN 0691091366/ISBN 0691027145
are shown in the Table 1 Table 1 Coding mode of rhythm duration0.1250.250.5 4 glissandi 40 30 70 Other codes are follows the formula C=(tt)(t2-t1)+C C means the code of the rhythm in question. tI means duration of the rhythm in Table 1 that has the longest duration among the rhythm whose duration is shorter than the one of the rhythm in question. t] means the duration of the rhythm in Table I that has the shortest duration among the rhythm whose duration is longer than the one of the rhythm in question. ti means the duration of the rhythm in question. CI means the code of the rhythm whose duration is ti For range, I represents the lowest octave on an 88-key piano, and 7 represents the ighest octave. From 1 to 7, the octave it represents goes higher. The structure of the code is rhythm-tone-range. For example, the code of 3 is 4033 When music is converted into code serial, only the theme is taken into consideration and information about chord and accompaniment is abandoned to extrude the most crucial features and simplify the coding process 2.2 Network model Consider every note as a node and edges stand for chronological sequence. a note is connected directedly with the node next to it, and if they show up in the music repeatedly, the weight of the edge will increase 3. Features of music Distinguishing regional music and pop music by listening is easy. In the music model, they also show different features. To be more specific, Jiangnan music and Menggu music are chosen to represent regional music. Figure I is the modeling results of Jiangnan music. Figure 2 is the modeling results of Menggu music. Figure 3 is the modeling results of pop music
are shown in the Table 1. Table 1 Coding Mode of Rhythm duration 0.125 0.25 0.5 1 2 4 glissandi code 60 50 40 30 20 10 70 Other codes are follows the formula: C= (ti-t1)/(t2-t1) +C1. C means the code of the rhythm in question. t1 means duration of the rhythm in Table 1 that has the longest duration among the rhythm whose duration is shorter than the one of the rhythm in question. t2 means the duration of the rhythm in Table 1 that has the shortest duration among the rhythm whose duration is longer than the one of the rhythm in question. ti means the duration of the rhythm in question. C1 means the code of the rhythm whose duration is t1. For range, 1 represents the lowest octave on an 88-key piano, and 7 represents the highest octave. From 1 to 7, the octave it represents goes higher. The structure of the code is rhythm-tone-range. For example, the code of 3 is 4033. When music is converted into code serial, only the theme is taken into consideration and information about chord and accompaniment is abandoned to extrude the most crucial features and simplify the coding process. 2.2 Network Model. Consider every note as a node and edges stand for chronological sequence. A note is connected directedly with the node next to it, and if they show up in the music repeatedly, the weight of the edge will increase. 3. Features of Music. Distinguishing regional music and pop music by listening is easy. In the music model, they also show different features. To be more specific, Jiangnan music and Menggu music are chosen to represent regional music. Figure 1 is the modeling results of Jiangnan music. Figure 2 is the modeling results of Menggu music. Figure 3 is the modeling results of pop music
,. Figure 1 model of Jiangnan music Figure 2 model of menggu music
Figure 1 model of Jiangnan music Figure 2 model of menggu music
Figure 3 model of pop music Average degree, average clustering coefficient and average shortest path (use Floyd Warshall algorithm to calculate)are listed in Table 2. Table 2 characteristics of models verage degree Average clustering coefficient Average shortest path Jiangnan music model 4.11 62.6 Menggu music model 0.019 Pop music model 9.63 0.339 3.03 Compared with Jiangnan music model and Menggu music model, pop music model has large average clustering coefficient and small average shortest path, so pop music model fits Small World From chart 1 to chart 6, indegree distribution and out degree distribution of pop music, Jiangnan music and Menggu music all follow power law, so they all fit scale free network
Figure 3 model of pop music Average degree, average clustering coefficient and average shortest path (use Floyd_Warshall algorithm to calculate) are listed in Table 2. Table 2 characteristics of models Average degree Average clustering coefficient Average shortest path Jiangnan music model 4.11 0.09 62.6 Menggu music model 2.69 0.019 40.1 Pop music model 9.63 0.339 3.03 Compared with Jiangnan music model and Menggu music model, pop music model has large average clustering coefficient and small average shortest path, so pop music model fits Small World Model. From chart 1 to chart 6, indegree distribution and out degree distribution of pop music, Jiangnan music and Menggu music all follow power law, so they all fit scale-free network
Chart 1 indegree distribution of pop music model -2.5 1509 amount of nodes Chart 2 outdegree distribution of pop music odel 0 -1.5 amount of nodes Chart 3 indegree distribution of Jiangnan music mode 0.15 0.1 y=-0.0705x+0.2893 amount of nodes
y = -0.0607x - 1.5095 -3 -2.5 -2 -1.5 -1 -0.5 0 0 5 10 15 20 log di/N amount of nodes Chart 1 indegree distribution of pop music model y = -0.1267x - 1.2016 -3 -2.5 -2 -1.5 -1 -0.5 0 0 2 4 6 8 10 12 logdo/N amount of nodes Chart 2 outdegree distribution of pop music model y = -0.0705x + 0.2893 0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 25 30 logdi/N amount of nodes Chart 3 indegree distribution of Jiangnan music model