LGAA: a Lattice-Gas Automata with Aggregation for Composing Guqin Music

Joumal of Donghua University( Eng. Ed. )Vol. 29, No. 2(2012)LGAA: a Lattice-Gas Automata with Aggregation for Composing Guqin MusicZHOU Chang-le(周昌乐),2,L0Lam-an(吕兰兰)2·, DING Xiao-jun(丁晓君)2, GUAN Yin(关胤)…2I School of information Science and Technology, Xiamen Universit, Xiamen 361005, China2 Fujian Key Laboratory of the Brain-like intelligent Systems, Xlamen University, Xiamen 361005. ChinaAbstract: Guqin music has been viewed as the symbel of Chinese new modeh--lattice-gas automata with aggregation( LGaa)ismusic. Using artificial intellgence approaches to study Guqin proposed to generate emotional Guqin melody. In order to makegemert mdld i ased on the there of atti a e halar automata algorithrm. The whole flow chart is shown in Fig pain finallyvalue. For the characteristics of guqin tablature, a new model ofit sound more natural, we use a balance rule to adjust it.h database, theywere made smoother by a balance principle which was followed byalmost all Chinese traditional music. Afer that, composition muscould be regarded as a knapsack problem, and the smooth musicseaments were seGuqin piece equaled the optimal solution to the knapsack problem.L GAAmh:下pobcIn the end, five musicians were invited to judge the results by twcriteria and they afl agreed that the automatic generated pieces ofKey words: lattice-gas; composition; Gugin; aggregation; knapsackCLC number: TPn9]Document code AArticle n:16725220(2012)2013905IntroductionFig. I The flow chart of Guqin music compositionGuqin is the oldest Chinese stringed instrument, a symof Chinese music. It was the preferred musical instrument of the 1 Model Descriptionrenowned philosopher Confucius. In Chinese traditional culturea well-educated scholar was expected to master four arts 1.1 The model of lattice-gas cellular automataincluding Qin, Q, Shu, Hua, where Qin represented Guqin. In(LGCA)classical age, Guqin was the most revered Chinese musicalThe first LGCA was proposed by Hardy, Pomeau, and deinstrument and a symbol of high culture. However, only about pazzis[is). It is named hPP after the initials of the three3 000 pieces of Guqin music have been handed down, and fewerauthors. HPP is a two-dimensional LGCA model over a squarenan 2 000 people can play it nowadays. Our research is to lattice. The vectors c, (i=1, 2, 3, 4)connecting the nearestAlgorithmic music uncovers a new direction in musical neighbors(Fg. 2) are called lattice vectors or lattice velocities.composition.Recently. there have been four basic categories of More precisely, the lattice velocities are given by the latticevectors divided by the time step At which is always set to l. Soalgorithms available for music composition . 4:(a)stochastic lattice vectors and lattice velocities have different dimensions butprocesses( probability functions, Markov chains )13. ):(b) the same mumerical values. The meaning of c, can be easilytheory)I):(c)rule-based(L-systems, formal grammars) recognized from the respective context. At each site( node)( d) evolution method genetic algorithms, cellneighbor. These cells may be empty or occupied by at most oneautomata)[+IB). Each of these processes has its own unique particle. This exclusion principle is characteristic for all LGCA.characteristics, but they are not easily adaptable to theFigure 3 shows that different particles move along the maincomposition of Chinese traditional music, especially Guqin direction of lattice. For example, the state s(r, 1)=(1011)inmusic. Unlike westem notation specifying pitch and tempotime t and lattice r means that three particles enter into oneChinese Guqin music adopts tablature, which records where and lattice simultaneity along the direction of 1, 3, 4how to play every note. The abundance and variety of guqintablature make the general cell automata model infeasible.However, lattice-gas models, which have a completely discretphase space and time and therefore may be viewed as made ofBoolean molecules". The simplest case is the HardyPomeau, and de Pazzis model( HPP)which has an underlyingregular, square, two-dimensional lattice with unit linlngths.). At each vertex, there are up to four particlesin light of the features of Guqin-the particular system of score中国煤化工eperformance and fingering, based on the lattice-gas model,aCNMHGReceived date: 2011 08-29ndation items: National Natural Science Foundations of China(No. 60975076, No. 61075058)140oumal of Donghua University(Eng. Ed.)Vol. 29, No. 2(2012)1.2 The model of LGAAThis paper builds the model of LGAAof LGCA and diffusion limited aggregation(DLA). DLA wasproposed by Witten and Sander in early 1980s 20)Aggregation is an important growth mechanism. Particles willconglutinate when they collide into each other, and finally thestructure of fractal is formed. In this paper, when the collisionhappens, particles will aggregate if they meet the followingthree rules:(1) the fingering of right hand is continuous;(2)the fingering of left hand has to be convenient, and the spanbetween the neighbor"hui" position is not allowed too wide(3)the interval between the neighbor pitch is not too far.Otherwise, they will diffuse in opposite directions. Theevolution opcrator s is defined in Eq. (1)Fig 3 The exampl of HPP particle structuree=s·c·a,(1)where s, c, and a mean streaming collision, and aggre gationThe evolution in time is deterministic and proceeds as analternation of local collisions c (only particles at the same nodeare involved)and streaming s( also called propagation)along 2 Music Segment Generationthe appropriate links to the nearest neighbors. Figure 4 gives theles of HPP:(a)a single particle is streaming:(b)and(c) 2.1 Generation by lgaashow that the collision will happen only if two particles comeFirstly, we use the algorithm Apriori-a method offrom the opposite direction. In other situations, the particlesmining, to find the frequent itemsets from the certain emotionalill penetrate each other and go straight. Then, based on the database(here, we use the emotion"sad"as an example)Boolean expression of every lattice's particle, the collisionofThen, LGaa is initialized by the random process using thetwo particles which come from the opposite direction canfrequent itemsets, So, at time I =0, the lattice bits of LGAAare set randomly, The states are fully described by the boolean(1010)→(0101),(0101)→(1010).fields n 4,r,), where the index i runs from 1 to 4 respectivelylestates don't change. In the streaming state, a singleindicating the four directions. n, is the occupation number whiclle l changes to the right neighbor cell. Particle 2 changes may be 0 or 1; is the( discrete)time; and r, is the coordinateto the down neighbor cell, and so on.of the nodes. The transition probability is N,=P- (1-p)"P=l/4,j=l,2,3, 4. The transition direction can bedescribed as d(t, k)=max N,, i=l, 2, 3, 4, which meansthe particle k's transition direction at time f. At time t +1, iftwo( the direction is opposite)or more particles enter into onenode simultaneity, and they obey the rules in section 1.2, theation will happeIn our experiment, the averaged particle density per site is3. 1. The total lattice size is 50 x 50. and the total evolutiontime is also 50. Figure 5 shows the evolution of LGAA in the排Guqin music composition. The particles marked by circles inFigs.5(a)and(b)reflect theof aggregation betweenthe neighbor evolutions, Figures 5(c)and(d) represent theevolution results of the tenth and fiftieth, respectivelyObviously, with the increase of iteration, the distributingnsity of particles becomes”钐TTimc t+125Fig 4 HPP rulesIn LGCA, boundary conditions are very easy toimplement. The lattice can be seen as a spherical, for example中国煤化工:pif the lattice size is m xn, and i=l, l z, and it amounts to adding item u, to the勻勾勾五正So we can use the following recurrence for finding the勻勻兀宮芍笠羹芍勻勻凹0 or=0,英卺芭;查妻歪罪置v[i-1, j].Ⅵi,门签老于与巴.芍勻勻昱3+,听ii>0叫dj≥x冠句内;专岂唐写.已巨手引考犭自写巴mdynamic programming to solve this integering problem is now straightforward. The method is巨.莊;蕭主距;新毛escribed in algorithm knapsack(Fig. 8)Input: A set of items U=1u,, "2,"",", with sizes z,,自等异艺.;2,…, and values y1,"2,…, v. and a knapsack龚最芑.写勻匀医京,當並舁竿立爸勻Output: The maximum value of the function 2 v, subject奇勻!自芑,爸;与Ato 24 sC for some subsets of items 2CU.;季自亓主卺写岂写13. for i+0 to n14.v;,0]-0區巴勻勻患自琶,签老与矮舜,;犭:自写16. for j+0 to cl7.Ⅵ0,j+0漪;兀亐安岂写,,♀18. end for19.fori+0to丌Fig 9 A complete Piece of music20. for j+0 to c2L.Vi,j←vi-1,j2.ifx;≤henvLi,]+maxl v[i,jl,vi-1,j-z]+y,23. end foretum v[n, C輯菲些From the algorithm above, we know that the optimalsolution to the knapsack problem is just time e(nC) and spacee(C). In the process of composition, the length of a piece oflusic( the number of Jian- zi-pu) can be seen as the capacity ofknapsack, and assumed as C= 250, which means that themaximum of Jian-zi-pu in a piece of music is 250. Let z, be the目佳睡size of music segment i, then we use the statistic methodcompute the six emotional features of every melody t(i, k). (k=1, 2,", 6), the weight of melody i can be obtained by Eq丰中r輯自,=∑(i,k)Finally, using the algorithm knapsack( Fig. 8)obtain a complete piece of music as Fig 9. Moreover, Fig. 10shows the corresponding pitch sequence, which is extracted中国煤化工 quence of Fig9from Fig 9CN MHGto judge the success of4 Conclusions and Future Worksthe fingering is smooth; (2)whether tablature is simple anAccording to the features of Guqin music, a new model of easy to remember. They all agree that fingering is smooth,butLGAA to generate emotional Guqin music based on lian-zi-pu the tablature is not simple enough for a performer to rememberJoumal of Donghua University( Eng. Ed. )Vol. 29, No. 2(2012)143The problem lies in the fact that we don't consider it in theA-R Editions Inc. 2000: 1-287formation of melody. It is only considered in the adjustment [9]Arize C. Automata Bending: Applications of Dynamicprocess. The future work should operate in this direction. 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