[Type text] [Type text] [Type text] ISSN : 0974-7435 Volume 10 Issue 19 BoTechnology 2014 An Indan Journal FULL PAPER BTAIJ, 10(19, 2014 [10873-10877] Computer smulaton analyss on pano tmbre ABSTRACT Wenjng Yuan Luxun Art Academy of Yan an Unversty X an, 716000, (CHINA Computer Smulaton technque could acheve a postve effect on the analyss process of pano tmbre, whch help acheve the ultmate goal of makng the pano tmbre judgment more scentfc and ratonal. However, accordng to prevous studes, researchers do not attach much attenton to the relatonshp between waveform around fve peaks n the frequency spectrum and specfc ampltude ratos, whch wll have a relatvely drect mpact on the tmbre of the pano and makes pano tmbre analyss process wthout strong comprehensve theoretcal support and computer smulaton process less scentfc and ratonal. However, ths research ntends prmarly to dscuss the pano tone model, makes the two types of parameter nterface establshed, and provdes effectve access to parameters based on the premse of tone. Ths essay also dscusses the Fourer analyss of combnaton tone and the reconstructon of tmbre of the pano, makng the tone spectrum analyss of the pano playng and the reconstructon of the pano tone effectvely guaranteed. It also provdes a sold theory and data support to computer smulaton analyss of pano tone. Ths s the man dea of ths research process, whch can also fully reflect the specfc objectves of the study and the specfc methods, wth the am to provde a sold foundaton of theory and data to further researches. KEYWORDS Pano tmbre; Computer; Smulaton analyss; Expermental study. Trade Scence Inc.
10874 Computer smulaton analyss on pano tmbre BTAIJ, 10(19 2014 INTRODUCTION The analyss of pano tmbre can manly be realzed by means of computer smulaton. So ths process needs to buld ts model by computer, makng the two dfferent parameter nterfaces to be establshed. Ths study effectvely analyses the modelng of pano tmbre, tmbre of the parameter acquston, Fourer analyss of the tone and the reconstructon of tmbre of the pano, to nvestgate the specfc factors of the analyss of the tmber of pano and to further mprove the computer smulaton analyss MODELING OF PIANO TIMBRE In the feld of pano musc, spectrum and ampltude envelope have a decsve role on each of the tmbres, so the model of tmbre can be expressed wth the followng formula. T ( p, t A( p, t E( p, t (1 In the formula above, the meanng of p refers to the absolute ptch, whle t represents the tme. T(p,t s the concrete embodment of the sound functon, and ths s the form of basc embodment of the characterstcs of pano tmbre. However, A( p, t represents concrete number varatons of the ampltude, from whch we can see the spectral characterstc. E( p, t referred to ampltude envelope functon, as well as ts man forms of the effectve reflecton of ampltude contours. The followng dscusson focuses on the related research and exploraton of the modelng process of these two features. Establshment of spectral model The spectral model refers to the combnaton of characterstcs s frequency characterstcs n the feld of pano musc as s well-known. In the pano musc, the sound s not n a state of harmony, and the relatonshp between audo and ptch fals to show nteger relatonshps, manly because there are some dfferences among stffness [1]. For ths, durng the establshment of the tmbre model, nharmonous factors whch are not relevant are not taken nto account, thereby enablng ths model to mantan a hgh degree of smplcty, whch gves the pano sound the core of feelng. However, n the course of pano musc playng, people often do not feel the musc phase, so t s not necessary to consder ths factor n the establshment of the spectral model. The pano audo model can be reflected by the followng formula. n A( p, t c0 ( p, Asn[2 f ( p t] 1 (2 In the formula above, represents s the basc varables of the number of overtone, whle co (p, s an overtone peak ampltude s specfc coeffcent. However the basc parameter poston of the ptch durng the process s postoned as 1, and the harmoncs ampltude coeffcent can be obtaned by the pano musc sample analyss. In the formula above, A represents the peak ampltude of ptch sze. The f (p represents the ptch frequency of p. The calculaton can be obtaned by combnng the frst nternatonal pano wth ptch frequency rato between the two adjacent keys, and p s an absolute hgh encodng. The formula s shown as followed: p O K S (3 The TABLE 1 shows the relevant encodng process of 12 key sgnatures. However, t s not dffcult to see from the results that there are 15 key sgnatures, whch means that 3 of them are repeatng tones. TABLE 1 : Key sgnature codng table Key sgnature(1= C *C D * * * G * A * B Codng K 0 1 2 3 4 5 6 7 8 9-2 -1 In the formula above, S represent s relatvely hgh encodng. At the same tme, the encodng of the bass s set to 1, and the encodng of the tenor s set to 13, and the encodng of the treble s set to 25, whch allows relatvely hgh notes to rse to the half treble wth the bass and the code unts to gradually rse. Its rsng degree of encodng s 1, whch can be seen n TABLE 2.
BTAIJ, 10(19 2014 Wenjng Yuan 10875 TABLE 2 : Relatve ptch codng table Scales 1 2 3 4 5 6 7 Encodng of the bass 1 3 5 6 8 10 12 Encodng of the tenor 13 15 17 18 20 22 24 Encodng of the treble 25 27 29 30 32 34 26 Establshment of the ampltude envelope In the course of playng one note by the pano, the basc process of sound producton s made up of three stages: the frst s sound, followed by attenuaton, and the last s the process of passng. The establshment of the ampltude envelope can be reflected byby followng formula. However, the curve changes wthn the cycle of ampltude envelope can be fully seen n Fgure 1. k1t, t (0, t 1 E( p, t k2t k2t2 E2, t (t 1,t 2 E2 exp[ ( t t 2 ], t (t 2,T e (4 From the formula above you can see, E (p,t s a basc functon of the ampltude envelope, and T e represents the basc cycle of the envelope. In ths research study, by the correspondng expermental procedure of the establshment of ampltude envelope model, n a beat, E1,E2 represent the ampltude envelope coeffcents of the t1,t2 respectvely, whle k E / t, k E E / t t. A represents the the k1,k2 represents the slope of the two precedng paragraphs. In ths 1 1 1 2 2 1 2 1 recesson factor n the thrd paragraph by an easer descrpton. The tme coeffcent can by defned. c_t1,c_t2 respectvely c _ / c _ / can be set up. In ths represents the tme coeffcent. Therefore, the two equatons condtons of t1 t1 Te, t 2 t 2 t1 Te study, ts ampltude envelope parameter can be set as c_t 1, c_t 2, E 1, E 2, and A. However, n the case of the process of playng the pano, ptch dfference among ptches can cause dfferent ampltude envelope parameters. Fgure 1 : Ampltude envelope curve of the pano TIMBRE OF THE PARAMETER ACQUISITION Ths study above has effectvely establshed the tmbre model and from the establshment, two dfferent types of parameters n nterface can be obtaned. The frst type s the spectral parameters and the other type s envelope parameters. Two dfferent types of parameters can be represented as C o (p,and c_t 1 c_t 2 E 1 E 2. However, after these two parameters have been obtaned, the tone of the pano can be obtaned too. Howeve n the process of acqurng envelope parameters, the specfc method can be acheved by the waveform mages. Its man prncple s based on sound samples to gve a vald recept, enablng the waveform effects to be expressed through vsual form and envelope parameters to be approprately estmated. For access to spectrum parameters, method s to effectvely collect pano musc samples, and to effcently analyze based on Dscrete Cosne Transform method, whch enables to gve a sequence of spectrum parameters a clear embodment. Collecton of pano musc samples In general process of collectng musc, the method of collectng samples s the recordng, but n the musc recordng, the nevtable nose wll appear so there wll be errors n the followng analyss, whch wll exert correspondng negatve mpacts. However n musc recordng, f ultra-low nose recordngs are used, the nvestment of human, materal and fnancal resources wll ncrease. The pano musc collecton method s concrete way of curng analyss, allowng musc samples to get
10876 Computer smulaton analyss on pano tmbre BTAIJ, 10(19 2014 professonal treatment, whch allows the pano musc of the sample collecton process to reflect the low nose musc samples [3]. In the pano keyboard, there are 88 buttons wth 52 whte key and 36 black keys. But for the proporton between two adjacent keys n the pano keyboard, the pano musc collecton largely focuses on the sample of the whte keys. And the sample of the black keys s collected by alternatvely collectng the sample of the whte keys. Sound samples collected are C1-B1 C-B c-b c1-b1 c2-b2 c3-b3 and c4-b4 respectvely. And these sounds do not nclude the sound varatons. So the musc can be valdly edted, as s shown n Fgure 2. Fgure 2 : Syllable musc After the vald edt of the scale scores, the orgnal MIDI fles and WAV format fles can be effectvely conversed and stored. Analyss of pano musc samples In analyss of the musc samples, ts man purpose s to effectvely obtan the spectrum parameters, and the method that s selected s DCT method. After the effectve arrangement of the muscal spectrum, the spectrum wll be processed by DCT calculaton and analyss, whch enables the nature of the muscal spectrum to be fully reflected. The algorthm manly contans four steps: Frst one s the effectve projecton of the wdth of gene frequency n the spectrum, whose equaton s S(1 f ( p / f, f F / (2 N, and t s a sample spectrum represented by ts own frequency [4]. Second t s to effectvely obtan the samples numbers of the overtone, wth S( S(1 to be reflected. And d n the S( wll be determned, whch can be obtaned by the formula of [ S( S(1 / 2, S( S(1 / 2]. Next step s to fnd out the maxmum value and mnmum value of Ac(u n the feld of D, to ensure that the DCT coeffcents of tmes of overtone are small by the specfc formula A'( A' max A' mn. The last s the calculaton of the ampltude peak of tmes of overtones, wth the basc formula of C 0 ( p, A '( / A '(1. THE SOUND OF FOURIER ANALYSIS AND RECONSTRUCTION OF PIANO TIMBRE Spectral analyss of pano musc playng In the computer smulaton analyss of pano tmbre, n order to ensure the analyss to be more scentfc and representatve, the sngle factors among dfferent ranges of multple panos have been effectvely analyzed n ths experment, wth a large amount of materals and dverse settngs n the aspect of playng, whch leads to dfferences between playng dynamcs and playng types. However, the sound of the pano that has been collected has been transformed effectvely, so that the tme doman waveform and frequency doman waveform can be fully reflected. The analyss method s the method of Fourer analyss. The specfc dscusson can be conducted and ts specfc process s shown as followed. 1 Frst of all, by the correspondng calculaton, the pano frequency of a that can be obtaned s 430 Hz, whch results n a slght gap wth the theory of value of f a1. The man reason for ths gap s because a certan gap between the accordatura and standard sound among each strng n the pano. It also s the fundamental reason for the frequency dfferences [5]. The second s to effectvely obtan the fundamental frequency or frequency doman range around 100 ponts wthn the frequency range. The phase nformaton can be fully reflected at the tme, and the other value s set as 0. In ths case, the tme doman waveform can be effectvely recovered, whch n turn makes relevant basc characterstcs, such as the ptch n the orgnal playng of the pano and values to be effectvely obtaned and to provde a sold foundaton for the analyss of spectrum n the playng of the pano. The last s to effectvely obtan the waveform around the headmost fve peaks wthn 100 ponts of the frequency doman waveform and then convert t nto tme doman waveform. The specfc comparson between two knds of waveforms confrms that there s no specfc change between the two waveforms whch n turn makes relevant basc characterstcs, such as the ptch n the orgnal playng of the pano and values to be effectvely obtaned. After that, the specfc rato of the fve peaks n the frequency doman wll be changed, whch makes echo or reverberaton condtons created, and proves the change of tone from ths occurs. However, the mean value around the harmonc frequency ranges from one to fve does not make any changes, but only the waveforms around harmonc frequency ranges from one to fve can be effectvely changed. Therefore, the changes of sound waveform ampltude are greatly obvous.
BTAIJ, 10(19 2014 Wenjng Yuan 10877 From the experments above you can see, n prevous studes and dscusson, the waveform around the fve peaks n the spectrum and relatonshp among specfc ampltude ratos do not receve enough attenton, whch has drect mpact on the tmbre of the pano [6]. Reconstructon of the pano tmbre Human ear judges the tone heght by the fundamental frequency. The analyss of the actual performance data and the waveforms, can tell that the sound energy proporton from the fundamental wave n the frequency doman to fve tmes harmonc wave and frequency waveform n the small range of harmonc frequency reflect that the playng ptch, tmbre and the nformaton of sound energy. In the experment, the functon smulaton s desgned as the waveforms from the fundamental frequency to fve tmes harmonc frequency ranges. On the bass of the fundamental frequency of the known accordatura and the proporton of the harmonc frequency peak values from one to fve, all the musc of the pano tmber can be reconstructed successfully. Four smlar functons are selected n the experment (Cauchy functon, Gaussan functon Snc functons cosne and sne - weghted Cauchy functon to get the frequency doman waveform of the actual playng of the pano. The fourth functon s used to descrbe the fundamental frequency and frequency doublng nformaton to more approprately smulate the pano tmbre [7]. When the approprate parameter s selected, Fourer Transform doman s turned nto tme doman, and there s lttle dfference wth the pano tmbre whch s actually acqured, but ts sound effects and MIDI the tmbre of Grand Pano n MIDI are qute smlar. In the experment whch uses the Weghted Cauchy functon to get to the frequency doman waveform, Y ( j, s used to represent for the dscrete of Fourer Transform wth the dscrete tme sgnal Y ( n. Y ( j can be obtaned by the followng formula: n Y ( j Y ( j, Y ( j S ( j F ( j, 1 a A a S ( j 2 A (, 2 2 ( other (5 (6 In the formula above, refers to the fundamental frequency of the sound or the frequency multpler, s the base frequency pont or ampltude of the multpler ponts, s used to adjust the fundamental frequency or the wdth of the frequency doublng waveforms around. s a functon of sne and cosne. CONCLUSION Above all, t s the relevant research and exploraton of the computer smulaton analyss of the tmbre of pano. It manly focuses on the establshment of the model of the pano tmbre, the Fourer analyss of sound and the two parts of the reconstructon of the pano tmbre. These tmbre parameters help to establsh the process effectvely and to acheve the ultmate goal of mprovng the computer smulaton analyss. REFERENCE [1] Fu Quanwe; The collson and fuson of tradtonal and modern-muscal works n terms of dgtal musc, Muscal works, (7, 126-127 (2013. [2] L Mn; Some thoughts on the establshment of vocal musc accompanment musc lbrary, Arts Crtcsm, (6, 130-132 (2012. [3] L Yuja; The aesthetc paradox of computer musc n the dgtal age, Journal of Northwest Unversty, Phlosophy and Socal Scences Edton, 41(3, 112-116 (2011. [4] Xu Dengfeng; Computer supportng system of musc technque and ts dgtzaton, Hundred Schools n Arts, (6, 230-233 (2010. [5] Cao Xhe, Cao Yng, Sun Ln; Pano tmbre smulaton by computer orented to preschool educaton and teachng, Journal of Henan Normal Unversty, Natural Scence, 38(1, 47-50 (2010. [6] Wang Feng, Zhang Xueyng, L Bngnan; Research and dscuss of chord recognton based on PCP, Mathematcs n Practce and Theory, (5, 97-101 (2010. [7] L Juan; Study on computer aded musc producton courses for young chldren, Journal of the Chnese Socety of Educaton, (S1, 38-39 (2010.