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
Chart 4 oudegree distribution of Jiangnan music model -1.5 y=-0.2388x-0.4807 2.5 amount of nodes Chart 5 indegree distribution of Menggu music model 0 -1.5 0.6451x+0.3136 amount of nodes Chart 6 outdegree distribution of Menggu music model .y=-05697X+0.2523 amount of nodes
y = -0.2388x - 0.4807 -3 -2.5 -2 -1.5 -1 -0.5 0 0 2 4 6 8 10 12 14 16 18 logdo/N amount of nodes Chart 4 oudegree distribution of Jiangnan music model y = -0.6451x + 0.3136 -3 -2.5 -2 -1.5 -1 -0.5 0 0 1 2 3 4 5 6 7 8 9 logdi/N amount of nodes Chart 5 indegree distribution of Menggu music model y = -0.5697x + 0.2523 -2.5 -2 -1.5 -1 -0.5 0 0 1 2 3 4 5 6 7 logdo/N amount of nodes Chart 6 outdegree distribution of Menggu music model
4. Automatic Composition 4.1 Random walk algorithm A combination of regional music and pop music should have features of them both Figure 4 shows the combined model of pop music and regional music. To make pop-regional music have more pop music tone, the pop music model have more nodes and edges than Jiangnan music model and Menggu music model by coding more pop music. Some other regional music are also included nan musIc Shanxi music Sichuan Pop music :·,· Random walk algorithm is that first randomly choose a node in the network and then connect it with its neighbor node v with possibility P=w∑wi wy is the weight of the edge between the node and node v. Then connect node v with its neighbor in the same way Using this algorithm music can be written, but it can be not pleased to hear. So add some motif influence in the algorithm for development 4.2 Development Based on Motif Motif is of great importance for melodic music. To make the song have more outstanding regional flavor, motif sources are filtered from regional music. To be more specific, only motif of tune is considered to help remove the disharmony in
4. Automatic Composition 4.1 Random Walk Algorithm A combination of regional music and pop music should have features of them both. Figure 4 shows the combined model of pop music and regional music. To make pop-regional music have more pop music tone, the pop music model have more nodes and edges than Jiangnan music model and Menggu music model by coding more pop music. Some other regional music are also included. Random walk algorithm is that first randomly choose a node in the network and then connect it with its neighbor node v with possibility: Pv=wv/Σwi wv is the weight of the edge between the node and node v. Then connect node v with its neighbor in the same way… Using this algorithm music can be written, but it can be not pleased to hear. So add some motif influence in the algorithm for development. 4.2 Development Based on Motif Motif is of great importance for melodic music. To make the song have more outstanding regional flavor, motif sources are filtered from regional music. To be more specific, only motif of tune is considered to help remove the disharmony in Jiangnan music Hunan music Shanxi music Sichuan music Menggu music Pop music
For typical motif, it has same or similar interval groups in time zone. And interval groups are available in the model of intervals. Although they are not that accurate, it is enough to show key features 4.2.1 Code mode of interval For a note a and a note B, the interval of them equals to b-a If B is higher than a in pitch, the code of the interval is the value of interval. If not, the code of the interval is the minus value of interval 4.2.2 Model of interva In the network of interval. nodes are the intervals and directed edges shows whether they are next to each other in time area. The more the interval sequence appears, the higher weight the edge is Figure 5 Interval Model of menggu Music Figure 6 Interval Model of jiangnan Music
it. For typical motif, it has same or similar interval groups in time zone. And interval groups are available in the model of intervals. Although they are not that accurate, it is enough to show key features. 4.2.1 Code Mode of Interval For a note A and a note B, the interval of them equals to | B-A |. If B is higher than A in pitch, the code of the interval is the value of interval. If not, the code of the interval is the minus value of interval. 4.2.2 Model of Interval In the network of interval, nodes are the intervals and directed edges shows whether they are next to each other in time area. The more the interval sequence appears, the higher weight the edge is. Figure 5 Interval Model of Menggu Music Figure 6 Interval Model of Jiangnan Music
In the interval model of Menggu music and Jiangnan music, the thicker the edges are, the more possible the interval of motif is included Table 3 Motif of Menggu Music 26;27;229;30;322;2 30;29;226;25;234;:35:330;29:;3 26;25;226;25;226;27;226;25:222;21;229;29;329;30;3 6 6 6 0 3 26:27:329:30;227;26:226:27:326:25229:30:233:34:3 21;22;230;29:226;26;230;29:325;26;230;29;329:29;3 22:21;230;30;226:27;229:30;226;26;233:34:334:33:3 2 6 9 7 4 26:27:321;21;227:26:230:29:226:27:234:34:3:343 0 9 7 4 21;2:221:2:226:27:221:21:227:26:225;:26:234:34:3 6 22;21;225;26;226;27;321:22;226;27;226:25:234:35:3 2 5 6 5 26:27;:3|27;26;230:29:325;26:2|33:34:325;26;234:34:3 0 9 30;29;326;25;229:30;227;26;234:34:329:30;234;35;3 6 9 Table 4 Motif of Jiangnan Music 26:25:23330233:30:2|27:26:229:26:230:29:23:30 29;26;233:30;229;27;226;23;226;25;226;25;230;29;2 5 3 「26:25:23:30280:.7:27:5:2:22:30279:7:2:30 2 6 9 7 25;:2:20:29:226:25;229:27:230:29:230:29;226:23;2 26;25;233:30;227;26;233:30;229;27;233;30;226;23;2 2 26:25:230:29;226;23;230:29:2|27;25:230;292 2 5 7 25:22:230;29;226;25;229:27;2|29:27;229;27;2 34;33;326;25;222;21;126;25;230;29;230;29;2 9 7
In the interval model of Menggu music and Jiangnan music, the thicker the edges are, the more possible the interval of motif is included. Table 3 Motif of Menggu Music 26;27;2 7 29;30;3 0 22;21;2 1 30;29;2 9 26;25;2 5 34;35;3 5 30;29;3 0 26;25;2 6 26;25;2 6 26;27;2 6 26;25;2 6 22;21;2 1 29;29;3 0 29;30;3 3 26;27;3 0 29;30;2 9 27;26;2 6 26;27;3 0 26;25;2 6 29;30;2 9 33;34;3 3 21;22;2 1 30;29;2 9 26;26;2 7 30;29;3 0 25;26;2 6 30;29;3 0 29;29;3 0 22;21;2 2 30;30;2 1 26;27;2 6 29;30;2 9 26;26;2 7 33;34;3 4 34;33;3 4 26;27;3 0 21;21;2 2 27;26;2 7 30;29;2 9 26;27;2 7 34;34;3 5 33;34;3 4 21;22;2 1 21;22;2 5 26;27;2 6 21;21;2 2 27;26;2 7 25;26;2 5 34;34;3 5 22;21;2 2 25;26;2 9 26;27;3 0 21;22;2 5 26;27;2 6 26;25;2 6 34;35;3 5 26;27;3 0 27;26;2 6 30;29;3 0 25;26;2 9 33;34;3 4 25;26;2 9 34;34;3 5 30;29;3 0 26;25;2 5 29;30;2 9 27;26;2 6 34;34;3 5 29;30;2 9 34;35;3 4 Table 4 Motif of Jiangnan Music 26;25;2 2 33;30;2 9 33;30;2 9 27;26;2 3 29;26;2 5 30;29;2 6 33;30;2 9 29;26;2 5 33;30;2 9 29;27;2 7 26;23;2 2 26;25;2 2 26;25;2 3 30;29;2 7 26;25;2 2 33;30;2 9 30;27;2 6 25;22;2 9 33;30;2 9 29;27;2 7 33;30;2 9 25;22;2 1 30;29;2 7 26;25;2 2 29;27;2 7 30;29;2 7 30;29;2 7 26;23;2 2 26;25;2 2 33;30;2 9 27;26;2 3 33;30;2 9 29;27;2 7 33;30;2 9 26;23;2 2 26;25;2 2 30;29;2 7 26;23;2 2 30;29;2 7 27;25;2 5 30;29;2 7 25;22;2 1 30;29;2 7 26;25;2 3 29;27;2 7 29;27;2 7 29;27;2 7 34;33;3 0 26;25;2 2 22;21;1 9 26;25;2 3 30;29;2 7 30;29;2 7
Motifs of Menggu music and Jiangnan music are listed respectively in table 4 and table 5. The nodes are in the form of code of music model 4.2.3 Consonance and Dissonant Interval Intervals are traditionally considered either consonant or dissonant. Consonant intervals are usually described as pleasant and agreeable. Dissonant intervals are those that cause tension and desire to be resolved to consonant intervals These descriptions relate to harmonious intervals In music theory, consonances are traditionally divided into two groups: perfect and imperfect. Perfect intervals(1, 4, 5, 8)are perfect consonances, as seen in nic music of the Middle Ages. Imperfect consonances (3 and 6)are either major or minor Dissonances can be divided into sharp and soft dissonances. This division relates mainly to atonal music. Minor second and major seventh are sha dissonances In tonal music, non-diatonic intervals(diminished and augmented)are usually dissonances, but in jazz and other African-American music, the tritone is"neutral", in other words it does not require resolution to a consonance Table 5 Consonance and Dissonant Interval Perfect Consonances Imperfect Consonances Perfect Unison(1) Minor Third(3) Perfect Fifth(5) Major Third (3) Perfect Octave( 8) Minor Sixth(6) Major Sixth(6) Diatonic dissonances Chromatic dissonances (avoided entirely Perfect Fourth(4 Tritone (Diabolus in Music) Minor Second (2) Any Other Augmented or Diminished Interval Major Seventh(7) In C program, some restrictions are called to avoid chromatic dissonances and diatonic dissonances. Besides, there are also some preference of composing more motifs of regional mus
Motifs of Menggu music and Jiangnan music are listed respectively in table 4 and table 5. The nodes are in the form of code of music model. 4.2.3 Consonance and Dissonant Interval Intervals are traditionally considered either consonant or dissonant. Consonant intervals are usually described as pleasant and agreeable. Dissonant intervals are those that cause tension and desire to be resolved to consonant intervals. These descriptions relate to harmonious intervals. In music theory, consonances are traditionally divided into two groups: perfect and imperfect. Perfect intervals (1, 4, 5, 8) are perfect consonances, as seen in the polyphonic music of the Middle Ages. Imperfect consonances (3 and 6) are either major or minor. Dissonances can be divided into sharp and soft dissonances. This division relates mainly to atonal music. Minor second and major seventh are sharp dissonances. In tonal music, non-diatonic intervals (diminished and augmented) are usually dissonances, but in jazz and other African-American music, the tritone is "neutral", in other words it does not require resolution to a consonance. Table 5 Consonance and Dissonant Interval Perfect Consonances Imperfect Consonances Perfect Unison (1) Minor Third (3) Perfect Fifth (5) Major Third (3) Perfect Octave (8) Minor Sixth (6) Major Sixth (6) Diatonic Dissonances Chromatic Dissonances (can be resolved) (avoided entirely) Perfect Fourth (4) Tritone (Diabolus in Music) Minor Second (2) Any Other Augmented or Diminished Interval Major Second (2) Minor Seventh (7) Major Seventh (7) In C program, some restrictions are called to avoid chromatic dissonances and diatonic dissonances. Besides, there are also some preference of composing more motifs of regional music