Characterization of Traditional Thai Musical Scale

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th Abtract: - Thi article preent an attempt to characterize the cale of traditional Thai muic. The cale of interet i known a Thang Phiang Aw (in Thai) meaning middle pitch.

1 Characterization of Traditional Thai Muical Scale ATTAKITMONGCOL, K., CHINVETKITVANIT, R., and SUJITJORN, S. School of Electrical Engineering, Intitute of Engineering Suranaree Univerity of Technology 111 Univerity Avenue Muang Ditrict Nakhon Ratchaima THAILAND Abtract: - Thi article preent an attempt to characterize the cale of traditional Thai muic. The cale of interet i known a Thang Phiang Aw (in Thai) meaning middle pitch. The modal ditribution i applied to analyze ingle- and multi-note ound played by a middle-pitch Thai flute (klui phiang aw) and a Thai metal tenor xylophone. We find that the formant of Thai octave are in the range of Hz. The pitch-interval of Thai cale are not contant a the previou hypothei of Morton [1]. Key-Word: - Traditional Thai muic, muical ignal analyi, modal ditribution, Thang Phiang Aw, formant, pitch interval. 1 Introduction It ha been known for a very long time that the pitch of Thai muical ound i different from that of the wetern. While the wetern muical ound contain both whole tone and emi-tone, one octave of the Thai contain even whole tone. The Thai regard that their muical cale poee no emi-tone at all. Tuning of Thai muical intrument rely on the hearing capability of an experienced muician. The intrument ued a reference for tuning are uually flute, and metal xylophone. About 40 year ago, Morton [1] meaured and analyzed Thai muical cale played by everal intrument. He propoed a hypothei that Thai muical cale poeed a contant pitch interval of cent (1,200 cent divided by 7). With today advanced ignal proceing technique, and meauring intrument, reinvetigation of Thai muical cale would benefit Thai ociety, contemporary compoer and muician, and fan of eatern muic. Previouly, Iemma and Cecconi [2] tudied the harmonic repone of wind intrument. Alo in 2003, Cotantini and Caali preented their work on the recognition of muical chord note [3]. In our work, Fig. 2 A Thai metal tenor xylophone. we apply the modal ditribution (MD) [4-5] to the recorded ignal of the ound from a middle-pitch Thai flute (woodwind intrument), and a Thai metal tenor xylophone. The MD give accurate formant of the cale. Moreover, we apply the method to ome cae of multiple note played by a metal tenor xylophone. The playing technique i akin to playing chord. The reult obtained are ueful for evaluating the performance of muician. Thi article review the MD in ection 2. Reult and dicuion are given in ection 3, then followed by concluion in ection 4. Fig. 1 A middle-pitch Thai flute. 2 Modal Ditribution The technique of time-frequency ditribution of Cohen cla [6] provide a mathematical framework for the deign of kernel to analyze muical ignal. In general, Cohen cla conit of linear tranformation of the Wigner ditribution

2 (WD) a given by [5] C(t, ω ; ϕ) = W ( τ, ϕ( t τ, ω ξ; t, ω)dτdξ (1) where C(t, ω ; ϕ) belong to Cohen cla. (t, ω) W i the WD of ignal (t) and ϕ ( τ, ξ; t, ω) i the kernel pecifying the linear tranformation. Thi kernel i formed from two different filter; one for cro-product uppreion in time, h ( τ ), and the other for cro-product uppreion in cae of frequency modulation, G ( ξ ) : ϕ τ, = h ( τ)g (. (2) M( When we ubtitute ϕ M( τ, from (2) into (1), it yield the ditribution M(t, ω ) [5] given by M(t, ω ) = C(t, ω; ϕ ) = W ( τ, M h (t τ)g ( ω dτdξ. (3) The expreion in (3) i the linear tranformation of the WD and i referred to a the modal ditribution or modal kernel. In cae of dicrete ampled data, the MD i baed on the dicrete peudo-wigner ditribution (DPWD) given by W (n, k) = L R = L j2πk ( ) 2L (n, )h( ) e (4) where h( ) i a function of lowpa filter and (n, R ) i the dicrete intantaneou autocorrelation function of the dicrete data equence decribed by R (n, ) = (n + ) * (n ). (5) Note that * denote the complex conjugate. Then, we pa R (n, ) through the filter window h which i the invere Fourier Tranform of h ( τ ) to obtain time-filtered intantaneou autocorrelation function ( (n, ) ) uing R,t R, t R, t P (n, ) = R (n p, )h (p). (6) p = P (n, ) in (6) i computed for ome value of n (denoted by n tep _ ize ) correponding to a tep ize that ample at a frequency of 2 ωmin. The value ωmin i the minimum frequency difference between the component band in rad/ and can be approximated from the pectrogram of ignal. The pectrogram can be obtained by computing the Short-Time Fourier Tranform (STFT) of ignal (ee Appendix). Finally, we ue time moothed intantaneou function R, t (n, ) and ubtitute h( ) with the frequency moothing window g which i invere Fourier Tranform of G ( ξ ) to compute the dicrete modal ditribution M (n, k) of the ignal uing [5] M (n, k) = L R = L, t j2πk ( ) (n, )g ( )e 2L. (7) We chooe L to be a power of 2 o that M (n, k) can be computed by uing the algorithm of powerof-two fat Fourier Tranform (FFT). Both h and g are obtained by performing autocorrelation and normalization of the Hamming window. The length of one-half of the h and g are N and R, repectively. The length N i calculated from the minimum ditance between ωmin (rad/) and the ampling rate (Hz). The total length of the DFT in (7) i 2 L where L i choen to obtain the number of bin of frequency reolution. The length R i choen to be L / 2. Thu, the relationhip between the DFT length, the ampling rate ( f) and the bin pacing (B ) i given by B = f / 4L. (8) Figure 3 how the algorithm to compute the dicrete modal ditribution. The reult can be plotted a a 3-D meh plot with the magnitude of M (n, k) in z direction. The x axi and y axi repreent time and frequency pacing, repectively. 3 Reult and Dicuion To record the ound of Thai flute and metal tenor xylophone in our experiment, our average room temperature i 27 C and relative humidity i approximately 72 %. The loudne of the ound i controlled to be in the range of db. Microphone i the electret type that ha enitivity

3 of 52 db and frequency repone in the range of 50-18,000 Hz. We ue an ocillocope to collect the data of 2,500 point and apply filtering prior to uing the STFT and MD technique. START ignal parameter initialization muical intrument becaue in the proce of making them, we do not ue any electronic device for tuning the ound; jut the expertie in litening to the ound of experienced muician. From the pectrogram of the ound produced by each intrument, we can obtain the value of ωmin for the analyi uing the MD technique. For the MD technique, the value L, ωmin and n tep _ ize are 8,192 point, Hz and 4 point, repectively. Figure 4 how the formant for the note ol of a middle-pitch Thai flute. compute h and g 1 compute R, t (n, ) 2 compute R, t (n, ) 3 compute M (n, k) ) R, t M (n, k) STOP Fig. 3 Algorithm to compute the dicrete modal ditribution. 3.1 Cae I: Single note In cae of the analyi of ingle note, we conider one octave of the ound (do re mi fa ol la i do ) produced by a middle-pitch Thai flute and a Thai metal tenor xylophone. For each recording, the ound for each intrument i produced contantly with the ampling frequency of 250 khz. Then, we apply the BP Butterworth filter with cutoff frequency of 175 Hz and 25,000 Hz to reduce the effect of background noie. For the analyi uing the STFT and MD technique, we ue the ame et of parameter with all eight different note of Thai flute and metal tenor xylophone. For the STFT technique, we compute the 17,500- point DFT. The window function i the rectangular window of length 2,000. Thee parameter are choen o that they give the frequency of the note do twice the frequency of the note do. The reult of the analyi how that the frequencie of ome note are integer. Thi i unuual for the Thai Fig. 4 Modal ditribution of a middle-pitch Thai flute for the note ol. Then, we compute the frequency ratio between the frequency of a note and the next conecutive one. We alo compute the pitch interval uing Pitch interval = Klog2 (f1 / f2 ) (cent ) (9) where K = 1, 200 [7]. In theory, the pitch interval between the note do and do i equal to 1,200 cent. Table 1 how the reult of the frequency ratio and the pitch interval of a middle pitch Thai flute. It can be een that the frequency ratio are almot the ame at 1.1 except the ratio between the note i and la which i The pitch interval are clearly not contant. In the analyi uing a metal tenor xylophone, the formant i imilar to the reult uing a Thai flute in Figure 4. The frequency ratio and the pitch interval are hown in Table 2. We can ee that the pitch interval are alo not contant. Thu, thee reult do not follow the Morton hypothei that ay the pitch interval mut be contant. Figure 5 compare the pitch interval of a middle-pitch Thai flute and a Thai metal tenor xylophone with the value from

4 Morton hypothei. We can ee that the pitch interval of the metal xylophone are cloer to the one from Morton hypothei than the pitch interval of the Thai flute are. (1, cent) i more different from the theoretical one (1,200 cent) than the pitch interval for the metal tenor xylophone (1, cent) i. Table 1 ratio and pitch interval of a middle-pitch Thai flute. One octave of Thai muical note (Hz) do re mi fa ol la i do ratio (unitle) Pitch interval (cent) Table 2 ratio and pitch interval of a Thai metal tenor xylophone. One octave of Thai muical note (Hz) do re mi fa ol la i do ratio (unitle) Pitch interval (cent) When we compare the frequencie of the ame note produced by both intrument, we can ee that they are not exactly the ame. Thi i becaue the proce of tuning for each intrument relie on the expertie in litening to the ound of experienced muician. Thu, there might caue ome error. Furthermore, the frequencie produced by Thai flute are enitive to temperature and humidity. Thu, the change of room temperature and humidity from the environment when the intrument i tuned may caue the change of frequency. Thi alo explain why the pitch interval of one octave for Thai flute Fig. 5 Pitch interval of a middle-pitch Thai flute, a Thai metal tenor xylophone and Morton. 3.2 Cae II: Multi-note We play a Thai flute to produce ound of multinote. Three different way of playing are conidered: (i) making la, ol, and fa ound by blowing the flute three time rapidly, (ii) making high-pitch mi, re, and do by blowing the flute jut once, and (iii) making fa, and ol ound alternately by blowing the flute continuouly. Recording the ound ued 10 khz ampling frequency. We apply a HP Butterworth filter with 100 Hz cutoff frequency to the recorded ignal. To analyze thee ignal need the MD of which parameter are tabulated in Table 3. Table 3 Parameter of MD technique for analyzing multi-note. Parameter L ω min * n tep _ ize Note (point) (Hz) (point) la, ol, and fa 4, mi, re, and do 4, fa, and ol 4, * determined from pectrogram of correponding ignal. Figure 6 illutrate the magnitude pectrum plotted againt time and frequency for the cae (i) of blowing the flute three time rapidly. The 3-D plot i a typical diplay of the MD reult. The difference in magnitude of the plot indicate the uneven preure of the wind blown. It might reflect that to keep the ound level evenly i very difficult with thi playing technique.

Fig. 6 Modal ditribution of a middle-pitch Thai flute for the note la, ol, and fa. Figure 7 how a typical diplay of MD reult for the cae (ii) mentioned above.

So, the loudne of the lat note (do ) played i the leat. Figure 8 indicate that the ound of fa and ol appear alternately according to the playing technique.

The playing technique i called kep, i.e. the two playing tick hit two different key imultaneouly. Thi playing technique ( kep ) i imilar to playing chord.

The following are MD parameter: L= 8,192 point, ωmin = 164.80 Hz and n tep _ ize = 4 point, repectively. Figure 9 how the reult obtained from the MD for thi cae.

5 Fig. 6 Modal ditribution of a middle-pitch Thai flute for the note la, ol, and fa. Figure 7 how a typical diplay of MD reult for the cae (ii) mentioned above. The magnitude of the plot indicate that the loudne of the ound decreae in order. Mi i the loudet note played. Thi correpond to the playing technique of blowing the flute only once. So, the loudne of the lat note (do ) played i the leat. Figure 8 indicate that the ound of fa and ol appear alternately according to the playing technique. The pectrum of the fa appear a the main while the peak pectrum of the ol appear alternately. We alo analyze the ound of do and fa played by the metal tenor xylophone. The playing technique i called kep, i.e. the two playing tick hit two different key imultaneouly. Thi playing technique ( kep ) i imilar to playing chord. The recorded ignal i ampled uing 100 khz ampling rate. The ampled ignal i paed through a BP Butterworth filter having it corner frequencie of 175 Hz and 25,000 Hz. The following are MD parameter: L= 8,192 point, ωmin = Hz and n tep _ ize = 4 point, repectively. Figure 9 how the reult obtained from the MD for thi cae. The pectrum of the note do i omewhat lower than that of the fa. Thi mean that the player hit the tick with uneven force. Fig. 7 Modal ditribution of a middle-pitch Thai flute for the note mi, re, and do. Fig. 8 Modal ditribution of a middle-pitch Thai flute for the note fa, and ol. Fig. 9 Modal ditribution of a Thai metal tenor xylophone for the note do, and fa played by kep technique. 4 Concluion We attempt to characterize the traditional Thai muical cale via uing the modal ditribution (MD). Our work i elementary in that we analyze the ound played by a Thai flute and a metal tenor xylophone in order to find out the formant of the Thai octave. The middle pitch Thai octave or thang phiang aw ha it formant in between Hz. Table 1 and 2 give the detail. The correponding pitch interval are in the range of cent. They are not contant a the previou claim made by Morton [1]. The application of the MD analyi technique to the multi-note cae i preented. The MD technique give excellent reult indicating correct appearance of each note correponding to each different playing

6 technique. We expect our future work extended in the area of analyzing the pecial technique played by ome oloit, recognition of muical pattern, a well a, developing ome device to ait the beginner of Thai muical intrument. 5 Appendix Spectrogram of ignal x ( X STFT (k, n) ) that can be computed by uing MATLAB toolbox i defined by R 1 m = 0 j2πkm ( ) N X (k, n) = x(n m)w(m) e (10) STFT where w i a window equence of length R and N i a DFT length [8]. 6 Acknowledgment The author thank Thailand Toray Science Foundation (TTSF) for upporting thi reearch work and Suranaree Univerity of Technology, (SUT) for a partial funding. Reference: [1] D. Morton, The Traditional Muic of Thailand, Univerity of California Pre, [2] U. Iemma, and F. Cecconi, Harmonic Repone of Wind Intrument via BEM, WSEAS multi conference on ICAMSL-ICAI-MCBC-MCBE, Tenerife, Spain, Dec 19-21, [3] G. Cotantini, and D. Caali, Recognition of Muical Chord Note, WSEAS multi conference on MCBC-MCBE-ICAI-ICAMSL, Tenerife, Spain, Dec 19-21, [4] W. Pielemeier, G. Wakefield, and M. Simoni, Time- Analyi of Muical Signal, Proceeding of the IEEE, Vol.84, No.9, 1996, pp [5] W. Pielemeier, and G. Wakefield, A High- Reolution Time- Repreentation for Muical Intrument Signal, The Journal of the Acoutical Society of America, Vol.99, No.4, 1996, pp [6] L. Cohen, Time- Ditribution: A Review, Proceeding of the IEEE, Vol.77, No.7, 1989, pp [7] A. Wood, The Phyic of Muic, John Wiley & Son, [8] S. Mitra, Digital Signal Proceing: A computer-baed approach, McGraw-Hill/Irwin, 2001.

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