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International Journal of Neural Networks ISSN: 2249-2763 & E-ISSN: 2249-2771, Volume 2, Issue 1, 2012, pp.-35-38. Available online at http://www.bioinfopublication.org/jouarchive.php?opt=&jouid=BPJ0000238

A COMPARATIVE STUDY OF CARNATIC AND HINDUSTANI SYSTEMS BY NEURAL NETWORK APPROACH

SRIMANI P.K.1 AND PARIMALA Y.G.2* 1Department of Computer Science and Maths, Bangalore-560 056, Karnataka, India. 2City Engineering College, VTU, Bangalore-560 062, Karnataka, India *Corresponding Author: Email- [email protected] Received: October 25, 2012; Accepted: November 06, 2012

Abstract- A unique Neural network approach has been used in the present investigations and a comparative study of the raga systems of Carnatic (CCM) and Hindustani classical (HCM). The paper concerns a detailed study of the melakartha- raga system of CCM, -raaga system of HCM and cognitive studies of the same based on Artificial Neural networks (ANN). For CCM, studies were confined to the 72 melakartha . For HCM 101 ragas were considered. Relative frequencies of notes in the scales were used as inputs. 100% accuracy was obtained for the melakartha system of CCM for several network topologies while highest accuracy was about 80% in case of HCM. Several networks, namely MLP, PCA, GFF, LR, RBF, TLRN were analyzed and consolidate report was generated. Keywords- Carnatic , Hindustani classical music, , melakartha ragas, cognition.

Citation: Srimani P.K. and Parimala Y.G. (2012) A Comparative Study of Carnatic and Hindustani Raga Systems by Neural Network Ap- proach. International Journal of Neural Networks, ISSN: 2249-2763 & E-ISSN: 2249-2771, Volume 2, Issue 1, pp.-35-38.

Copyright: Copyright©2012 Srimani P.K. and Parimala Y.G. This is an open-access article distributed under the terms of the Creative Com- mons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.

Introduction with variants- R, G, M, D, N. CCM defines 3 variants each for R, G, D and N and 2 for M (16 variations but 12 swarasthanas or semi- consists of 2 forms- Hindustani and Carnatic tones due to overlap of 4 semitones) [Table-3]. music. CCM has its origin in [17,18]. HCM is said to have come from Persia and adopted mostly in the Northern parts of In HCM, 2 variants are defined for each of the 5 notes, (12 semi- India [15,16]. HCM follows a 20-Thaat system [Table-1] while CCM tones). Semitones bear relative frequency ratio with reference note defines a 72-melakartha system [Table-2]. or adhara shruthi, S. Table 1- 10 THAATS of HCM [15,16] Ragas in CCM and HCM Systems Name of the Ragas are musical expressions which continually change with time. Notes present Carnatic equivalent That Ragas are inherently melodic and encompass other aspects such Bilawal S R G m P D N S-S N D P m G R S Dhira (29) as microtonal variations or gamakas. Ragas are formed by different S R G M P D N S-S N D P M G R S Mecha (65) permutations of the notes. Such ragas are innumerable due to the S R G m P D n S –S n D P m G R S (28) immense possibilities of combinations of swaras. The raga classifi- S r G m P d N S –S N d P m G r S (15) cation and features in the 2 systems are compared in [Table-4]. S r G M P d N S –S N d P M G r S Kamavardhini (51) Artificial Neural Network (ANN) Marwa S r G M P D N S –S N D P M G r S (53) A neural network is constructed by highly interconnected pro- S r g m P d n S –S n d P m g r S Hanuma (08) cessing units (r neurons) which perform simple mathematical oper- S R g m P d n S-S n d P m g R S (20) ations. A neural network can be trained to perform a particular S R g m P D n S –S n D P m g R S (22) function by adjusting the values of the connections (weights) be- Todi S r g M P d N S-S N d P M g r S Subhapantuvarali (45) tween elements, so that a given input results in a specific target output. The network is adjusted, based on a comparison of the Notes (Swaras), Semitones (Swarasthanas) in CCM and HCM output and target, until the network output matches the target [1-4]. Swaras are formed by the combination of fundamental frequencies ANN Approach to understanding Raga Classification in CCM and their overtones and are by themselves pleasing to the ears. 7 and HCM notes defined in both the forms are S,R,G,M,P,D,N,. They are clas- sified into Prakruti swaras-without variants- S and P; vikruti swaras- Based on the existing theories in both the forms of music we find

International Journal of Neural Networks ISSN: 2249-2763 & E-ISSN: 2249-2771, Volume 2, Issue 1, 2012

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A Comparative Study of Carnatic and Hindustani Raga Systems by Neural Network Approach

that an extensive scientific process of classification method exists [13-15]. The present work is motivated by the interesting features in which has already been analyzed by the authors and results obtained in the previous works of the authors [5-15]. In using neural network models and very accurate results have been this work ANN approach has been used for the first time on HCM obtained using various network topologies, for 72 melakartha ragas system. A comparative analysis has been done using ANN for of CCM and also unique features of theses ragas due to tonic shift ragas of CCM and HCM systems. Table 2- 72 Melakarthas of CCM Showing The 12 Chakras, Melakartha Number, Name And Scale [17,18] ShuddhaMadhyamamela (M1) Variant notes Prathi Madhyama mela (M2) Mela No Chakra No /Name Melakartha Name R G D N Mela No Chakra No /Name Melakartha Name 1 1/ 1 1 1 1 37 7/ sAlaga 2 I 1 1 1 2 38 R jalArnava 3 N Ganamurthi 1 1 1 3 39 I JAlavarAli 4 D Vanaspathi 1 1 2 2 40 S navanIta 5 U Manavathi 1 1 2 3 41 H 6 Tanarupi 1 1 3 3 42 I Raghupriya 7 2/ 1 2 1 1 43 8/ gavAmbhodi 8 N Hanumathodi 1 2 1 2 44 V 9 E 1 2 1 3 45 A 10 T 1 2 2 2 46 S shadvidhamArgini 11 R 1 2 2 3 47 U suvarNAngi 12 A 1 2 3 3 48 13 3/ 1 3 1 1 49 9/B dhavalAmbari 14 A Vakulabharana 1 3 1 2 50 R nAmanArAyani 15 G Mayamalavagowla 1 3 1 3 51 A kAmavardhini 16 N Chakravaka 1 3 2 2 52 H Ramamanohari 17 I Suryakantha 1 3 2 3 53 M Gamanashrama 18 hATakambhari 1 3 3 3 54 A Vishvambari 19 4/ Jhenkaradhwani 2 2 1 1 55 10/ shyAmalAngi 20 V naTabhairavi 2 2 1 2 56 D 21 E 2 2 1 3 57 I simhEndramadhyama 22 D Kharaharapriya 2 2 2 2 58 S hEmavathi 23 A Gowrimanohari 2 2 2 3 59 H Dharmavathi 24 Varunapriya 2 2 3 3 60 I nIthimathi 25 5/ mAraranjini 2 3 1 1 61 11/ kAnthAmani 26 B chArukeshi 2 3 1 2 62 R 27 A 2 3 1 3 63 U lathAngi 28 N harikAmboji 2 3 2 2 64 D 29 A DhIrashankarabharan 2 3 2 3 65 R mEchakalyAni 30 2 3 3 3 66 A 31 6/ 3 3 1 1 67 12/A 32 R 3 3 1 2 68 D jyotiswarUpini 33 I gAngeyabhushini 3 3 1 3 69 I dhAthuvardhini 34 T vAgadhiswari 3 3 2 2 70 T nAsikabhushini 35 U 3 3 2 3 71 Y kOsala 36 3 3 3 3 72 A Table 3- Comparative Table Showing the Semitones in CCM and Data Sets HCM [15-18] The data sets for the present investigations consisted of the ragas Rel. freq. CCM-16 variants, 12 semitones HCM-12 semitones defined in the respective systems. In CCM only the melakartha ratio ragas were taken for input data sets. The frequencies of notes and Shadja-S 1 Shadj-S semitones of melakrtha ragas were determined from the relative Suddha Rishabha-R1 256/243 Komal Rishabh-r frequency ratios. Data sets consisted of 72 scales each with 7 at- Chatusruti Rishabha-R2/Shuddha gandhara-G1 09-Aug Suddh Rishabh-R tributes pertaining to the ascending of the scale. For HCM, 101 Shatshruthi Rishabha-R3/Sadharana Gandhara- 192/162 Komal Gandhar-g scales were used and normalised for equal number of attributes for G2 each scale. Attributes chosen were 10 each for ascending(aroha) Antara Gandhara-G3 81/64 Suddh Gandhar-G and descending (avaroha) and 20 for their combined analysis. Suddha Madhyama-M1 04-Mar Suddh Madhyam-m Prati Madhyama-M2 729/512 Teevra Madhyam-M Methodology -P 03-Feb Pancham-P Various ANN topologies were used for investigations- Multilayer Suddha Dhaivata-D1 128/81 Komal -d percepteron (MLP), Principle Component analysis (PCA), Radial Chatusruti Dhaivata-D2/Shuddha Nishadha-N1 27/16 Suddh Dhaivat-D Basis Function (RBF), Probabilistic Neural Network (PNN), Classifi- Shatshruthi Dhaivata-D3 /Kaisika Nishada-N2 16-Sep Komal Nishad-n cation Support Vector Machine (SVM), Generalized Feed forward Kakali Nishada-N3 243/128 Suddh Nishad-N (GFF), Time-delay (TDNN), Time-lag Recurrent (TLRN), Recurrent

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(RN). Data sets consisting of the input attributes, and decision -validation & 20% -testing. 1/2 hidden layers, on-line/ batch pro- outputs were constructed for CCM and HCM systems. cessing, Levenberg-Marquardt (LM) /momentum learning rules were used. No of epochs were 1000. MSE, correlation and accura- Number of exemplars were 72 for CCM and 101 for HCM. ANNs cy reports and summary of best networks are shown in [Tables-1] were built, 70% of input samples were used for training, 10%-cross to [Tables-5], [Tables-6]. Table 4- Comparative Table Showing Raga Classification Schemes N CCM and HCM No CCM SYSTEM [17,18] HCM SYSTEM [15,16] 1 Uses Melakartha-Janya raga system Uses Thaat-raaga system (Table1) Melakartha ragashave same notes in ascending & descending in order of frequencies, 2 Thaats are only scales are major ragas Thaats are defined through popular full scale ragas & named after them, are 10 in Melakarthas arise from permutation of the 10 variant semitones giving exactly 72 3 number. combinations (Table 3) *They are 10 of the 72 melakarthas of CCM 4 Melakartha ragas are rendered elaborately and form most important ragas of CCM Thaats are never rendered Janya ragas are born out of the parent raga called melakartha or janaka or sampoor- 5 Raagas belong to particular thaat na Janya ragas classified into a) Upanga: have notes of parent raga only-3 types namely: i. No janya raga concept. i) Oudhava (5 notes) ii) Shadhava (6 notes), iii) Vakra (notes appearing not in order) ii. Ragas are mixture of sampoorna, Oudhav, Shadav vakra and Bhashanga and are 6 b) Bhashanga: having one or more notes not present in the parent raga (may be not explicitly defined and categorized. Oduhava, shadhava, vakra, swaranthya and/or sampoorna) c) Swaranthya-which iii. Subtle differences in meend, or vadi swar gives rise to new raga. clearly begin and end at certain notes that define the range of the raga iv. Swaranthya ragas are not defined Raga classification is abstract- based on time of singing, vadi swar, mood or ra- Precise classification for all types of ragas Eg. Raga Mayamalavagoula (15th) is 7 sa.Raga need not have the notes of its thaat, eg AhirBhairav (has D) belongs to Bhairav of HCM and chakravaka (16th) is AhirBhairav of HCM. Bhairav thaat(with d) No. of oudhav shadhav ragas are precisely known. No. of vakra, 8 Not clearly defined Bhashanga,Swaranthya ragas are infinite 9 New ragas created, belong to any one of the mela Some new ragas do not belong to existing thaat but other melas of CCM

Table 5- Comparative Results for Various Ann Topologies for CM [13] and HCM Systems Results-CCM-72 melas Results-HCM-aroha-avaroha Model Name Training Cross Validation Testing Training Cross Validation Testing MSE Correct MSE Correct MSE Correct MSE Correct MSE Correct MSE Correct MLP-1-O-M 0.0002245 54.90% 0.0002865 42.86% 0.0003721 53.33% 0.0002245 54.90% 0.0002865 42.86% 0.0003721 53.33% LR-0-B-M 0.0013303 100.00% 0.0015955 100.00% 0.0026225 100.00% 0.0013303 100.00% 0.0015955 100.00% 0.0026225 100.00% LR-0-B-L 3.80E-33 100.00% 5.44E-33 100.00% 2.28E-33 100.00% 3.80E-33 100.00% 5.44E-33 100.00% 2.28E-33 100.00% MLP-1-B-L 0.0005298 60.78% 0.0007574 57.14% 0.0003308 46.67% 0.0005298 60.78% 0.0007574 57.14% 0.0003308 46.67% PNN-0-N-N 0.0012962 100.00% 0.0018533 100.00% 0.002353 100.00% 0.0012962 100.00% 0.0018533 100.00% 0.002353 100.00% RBF-1-B-L 0.0001445 27.45% 0.0001083 14.29% 0.0013391 33.33% 0.0001445 27.45% 0.0001083 14.29% 0.0013391 33.33% GFF-1-B-L 1.37E-21 35.29% 1.96E-21 14.29% 1.81E-21 33.33% 1.37E-21 35.29% 1.96E-21 14.29% 1.81E-21 33.33% MLPPCA1BL 0.0019863 70.59% 0.003071 100.00% 0.0028401 80.00% 0.0019863 70.59% 0.003071 100.00% 0.0028401 80.00% SVM-0-N-N 0.0038795 98.04% 0.0121926 100.00% 0.0262371 93.33% 0.0038795 98.04% 0.0121926 100.00% 0.0262371 93.33% TDNN-1-B-L 0.1249603 78.43% 0.2087963 71.43% 0.2065678 66.67% 0.1249603 78.43% 0.2087963 71.43% 0.2065678 66.67% TLRN-1-B-L 0.2554014 0.00% 0.2645641 0.00% 0.2738686 0.00% 0.2554014 0.00% 0.2645641 0.00% 0.2738686 0.00% RN-1-B-L 0.1943998 72.92% 0.1618133 85.71% 0.4412331 46.67% 0.1943998 72.92% 0.1618133 85.71% 0.4412331 46.67% MLP-2-B-L 0.007688 72.92% 0.0014991 100.00% 0.2368255 60.00% 0.007688 72.92% 0.0014991 100.00% 0.2368255 60.00% MLP-1-B-M 3.35E-05 56.25% 7.67E-05 42.86% 5.63E-05 40.00% 3.35E-05 56.25% 7.67E-05 42.86% 5.63E-05 40.00% MLP-2-O-M 0.002565 97.92% 0.0021378 100.00% 0.007056 93.33% 0.002565 97.92% 0.0021378 100.00% 0.007056 93.33% MLP-2-B-M 0.0223987 91.67% 0.0094351 100.00% 0.0161087 100.00% 0.0223987 91.67% 0.0094351 100.00% 0.0161087 100.00% MLPPCA1OM 0.0009251 87.50% 0.0008452 100.00% 0.0010845 73.33% 0.0009251 87.50% 0.0008452 100.00% 0.0010845 73.33% MLPPCA1BM 0.2350577 0.00% 0.2328904 0.00% 0.3633121 0.00% 0.2350577 0.00% 0.2328904 0.00% 0.3633121 0.00% GFF-1-O-M 0.0003181 68.75% 0.0014483 57.14% 0.0014248 53.33% 0.0003181 68.75% 0.0014483 57.14% 0.0014248 53.33% GFF-1-B-M 0.0016211 95.83% 0.0007143 100.00% 0.0072221 86.67% 0.0016211 95.83% 0.0007143 100.00% 0.0072221 86.67% RBF-1-O-M 0.0246457 100.00% 0.0261598 100.00% 0.0311684 100.00% 0.0246457 100.00% 0.0261598 100.00% 0.0311684 100.00% RBF-1-B-M 0.1013581 100.00% 0.1064778 100.00% 0.1070609 100.00% 0.1013581 100.00% 0.1064778 100.00% 0.1070609 100.00% TDNN-1-O-M 0.0004125 93.75% 0.0003583 85.71% 0.0002338 93.33% 0.0004125 93.75% 0.0003583 85.71% 0.0002338 93.33% TDNN-1-B-M 0.0066683 87.50% 0.0099334 100.00% 0.0083518 93.33% 0.0066683 87.50% 0.0099334 100.00% 0.0083518 93.33% RN-1-O-M 0.0208484 95.83% 0.002136 100.00% 0.0449767 86.67% 0.0208484 95.83% 0.002136 100.00% 0.0449767 86.67% RN-1-B-M 0.0033325 95.83% 0.0023256 100.00% 0.026649 100.00% 0.0033325 95.83% 0.0023256 100.00% 0.026649 100.00% TLRN-1-O-M 0.005773 95.83% 0.0076466 85.71% 0.0147633 100.00% 0.005773 95.83% 0.0076466 85.71% 0.0147633 100.00% TLRN-1-B-M 0.0002235 100.00% 0.0002636 100.00% 0.0011377 100.00% 0.0002235 100.00% 0.0002636 100.00% 0.0011377 100.00%

Result and discussion dent from present results, for e.g., The classification approach based on ANN could be applied very a. Although HCM uses a 12-note system with similar frequencies, effectively and efficiently on CCM, whereas on HCM it was quite number of major full scales that are accepted are only 10 unlike difficult since the built-in logic in HCM is not that consistent as evi- 72 melakarthas of CCM.

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A Comparative Study of Carnatic and Hindustani Raga Systems by Neural Network Approach

b. The ragas of HCM are characterized by several abstract fea- cation of ragas into their chakras and iii) their location within tures: i)thaats are never sung whereas melakartha ragas are chakras. gave 100% results for LR-0-B-M, LR-0-B-L, PNN-0-N- extensively elaborated ii) there is clear distinction between N, TLRN-1-B-M, RBF-1-O-M, RBF-1-B-M. melakartha and janya ragas in CCM while in HCM exhaustive d. For HCM, several investigations were performed :i) purely on classification of all ragas into such categories is not found iii) ascending scale ii) purely on descending scale iii) on full scale- aroha and avaroha are not always sampoorna or having exact- i.e., both aroha & avaroha. Nu. of attributes were normalized ly 7 notes iv)more than 2 raagas can have exactly the same for meaningful comparison [Tables-5] [Tables-6] show compar- scale but probably differ only in features like duration of holding ative results for various ANN topologies, best performing NNs. a certain note, meend, vadi swar, auspicious time of singing i) SVM gives best results of 97% for training, 30% for CV and the raga, produced, as noted earlier. 40% for testing for only ascending. ii) For descending, GFF is c. In CCM, the sets trained using the different networks and relat- the best NN- giving 64.7% for training, 30%-CV and 35%- ed parameters were tested to obtain outputs indicating :i) testing, iii) For full-scale, MLPPCA-1-B-L gives best accuracies whether a given raga is shuddha madhyama or prathi madh- of 81%-training, 40%-CV and 35%-testing. yama mela,- This gave 100% accuracy for all NNs; ii) classifi- Table 6- Results of Best Performing Networks for CCM and HCM CCM -72 mela HCM-aroha-avaroha-101 ragas Model Name: LR-0-B-M (Linear Regression) Model Name: MLPPCA-1-B-L (MLP with PCA) Training Cross Val. Testing Training Cross Val. Testing # of Rows 48 7 14 # of Rows 68 10 20 MSE 0.000102 9.06E-05 0.000103 MSE 0.026337 0.117244 0.150796 Correlation (r) 0.999902 0.999957 0.999861 Correlation (r) 0.803248 #DIV/0! -0.02437 # Correct 51 7 14 # Correct 55 4 7 # Incorrect 0 0 0 # Incorrect 15 6 13 % Correct 106.25% 100.00% 100.00% % Correct 80.88% 40.00% 35.00% HCM-aroha only HCM-avaroha only Model Name: SVM-0-N-N (Classification SVM) Model Name: GFF-1BL (Generalized Feedforward) Training Cross Val. Testing Training Cross Val. Testing # of Rows 68 10 20 # of Rows 68 10 20 MSE 0.037457 0.055418 0.080246 MSE 0.079795 0.113842 0.114127 Correlation (r) 0.680573 #DIV/0! 0.104384 Correlation (r) 0.122027 -0.12496 -0.12781 # Correct 66 3 8 # Correct 44 3 7 # Incorrect 4 7 12 # Incorrect 26 7 13 % Correct 97.06% 30.00% 40.00% % Correct 64.71% 30.00% 35.00%

Conclusion [6] Srimani P.K. (2004) World Conf. Ved. Sci. Vig. India. A comparative study of CCM and HCM raga systems were made [7] Srimani P.K. (1997) Proc. World Conf., India. applying ANN topologies 72 melas of CCM and 101 ragas belong- [8] Srimani P.K., Parimala Y.G., (2009) Proc. Mahila Vijnana Sam- ing to 10 thaats of HCM were taken for analysis. CCM system, melana-5, Mangalore. being highly scientific gave expected accuracies of 100% with sev- [9] Srivatasa P.K. (1992) Research, development & improvisation eral networks, while best accuracies in HCM was limited to about of S. Ind. musical instruments-Tamboora, , , 80% for training with SVM network. The relatively poorer accura- , Sangeeta Nrtya Navarathri, Visvakala, Bangalore. cies in HCM system even after using the full scales are attributed to various aspects of HCM like i) limitations in the number of thaats ii) [10] Srivatsa P.K. (2006) Proc., Triadic Nat. Conf. want of precise formulation in attributing a given raga to a certain [11] Srimani P.K., Parimala Y.G. (2012) Int. Conf. on methods & That iii) a clear definition of the scales. We conclude that there is Models in Sc. & Tech. IETAN, Jaipur. immense scope for further research in the area of cognitive analy- sis using this unique ANN approach in the complex fields of Ind. Cl. [12] Srimani P.K. and Parimala Y.G. (2012) Int. Conf. on Intelligent music. Computational Systems, PSRC, Dubai. [13] Srimani P.K. and Parimala Y.G. (2011) Int. Conf. on Computer, References Comm. and Information Sc. and Engg., Switzerland. [1] Bishop C.M. (1995) Neural Networks for Pattern Recognition, [14] Bhatkhande V.N., Sangit Paddati H., I-IV. Oxford, Oxford Univ. Press. [15] Subba Rao B.C. and Cl H. (956) Music, 1-6. [2] Haykin S. (1994) NNs Comp Found., NY, MM. [16] Ramamurthy & Rajaratnam Deepike,2001. [3] Judd J.S. (1990) Neural Network Design and the Complexity of [17] Govinda Dikshitar “Sangraha Choodamani, 1800. Learning MA, The MIT Press. [4] Srimani P.K. (2001) Nat. Conf. Appl. Engg. & Tech., India. [5] Srimani P.K. (1998) Music for Excellence, New Delhi, India.

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