Mihir Sarkar

Analyzing & Synthesizing Gamakas: a Step Towards Modeling Ragas in Carnatic Music

Introduction If we are to model ragas on a computer, we must be able to include a model of gamakas. Gamakas are ornaments (quite different from the embellishments of western music) that form an integral part of Carnatic music. They are characterized by microtonal oscillations and variations. What are ragas? Unlike the western concept of scale, ragas are difficult to characterize. A raga is a musical concept or system that comprises, among other things, a scale, gamakas, characteristic phrases, and visiting notes. “Raga is a vast ocean of latent potential, waiting to be realized” (Allen, 1998). Why am I interested in modeling ragas? A computer model of Indian ragas has several applications:

• A framework for the computational representation of Carnatic music. • An archival system and a knowledge repository for Carnatic music • A research, educational and composition tool.

Modeling gamakas are a first step in modeling ragas. After a brief presentation of the background in which this work is grounded, I propose to analyze gamakas in an audio recording of a vocal artist. Then I synthetically reproduce the recorded sequence based on the previous analysis. Finally I lay out the path for future work. Background Music Technology Current music technology still relies heavily on note-based concepts such as MIDI (Music Instrument Digital Interface) inspired by western music. Although the MIDI format provides techniques like pitch bend that could be used to model gamakas, it has several flaws: the interface is not standardized across equipment manufacturers; moreover the range (minimum and maximum limits) and resolution (quantization) are limited. Even if these techniques can be used to model gamakas, they do not provide enough control to the musicians to adequately reproduce a particular pitch contour; what is more the pitch variations have to be programmed from scratch. An attempt has been made to play gamakas on a computer (Carnatic2000 website), but the source code is not available for extension (adding different types of gamakas), and the system lacks a user interface.

Gamakas Several authors have attempted to classify gamakas. The number of categories ranges from 23 to 15 to 10 to 3 (Swift, 1990; Allen, 2004). The present work does not attempt to provide fixed templates for gamakas, but rather to provide an extensible language to create and play tunes with the inclusion of any type of user-defined gamaka. Analysis I analyzed an excerpt from the recording of raga Hamsadvani (ascending and descending scales) sung in the context of the Pagavari varnam (singer Kamala Ramamurthy recorded by Richard Wolf in Madurai, Tamil Nadu India, 1985.) Raga Hamsadvani comprises the following notes: C D E G B C’ (up) / C’ B G E D C (down). To analyze the recording, I created a pitch-tracker patch on Max/MSP using the pitch~ object (Jehan). The collected samples were then imported into Matlab for alignment and plotting. I performed an analysis on the pitch contour after having aligned each musical entity (swara). The estimated pitch is scaled according to the MIDI pitch number to maintain linearity. The following graphs plot the pitch contour of the raga. The gamakas are clearly visible.

Fig. 1: Pitch contour of swaras in raga Hamsadvani (ascending and descending scales) The resulting curve for the “NI” may be an artifact from the pitch tracker object. A confirmation would require additional analysis from other sources. Synthesis I used the Csound programming environment to model gamakas. I took advantage of function-tables (look-up tables) to create cubic spline curves that match the analyzed pitch contour for each note. The sound engine currently generates only pure sine waves in my program. Each gamaka is considered as a separate instrument (in Csound terminology), and can therefore be triggered anytime in the score file. The following table describes various representations of the note entities that I used in the synthesis process.

Note (Carnatic) Note (Western) Frequency (Hz) MIDI pitch SA C 261.626 54 RI D 293.665 56 311.127 57 GA E 329.628 58 349.228 59 369.994 60 PA G 391.955 61 NI B 493.883 65 SA’ C’ 523.251 66

Fig. 2: Relation between note entities

Although the model for the gamakas is based on the contours extracted previously, the synthesized pitch contour is still a relatively gross approximation of the original. It was especially difficult to model the “NI” (see above).

Fig. 4: Coarse pitch contour of the synthesized raga

Future Work Based on the initial baseline developed here, several improvements come to mind:

• Introduce “nano-oscillations” that stem from the imperfections of the human voice, and accounts for its warmth.

• Introduce variables for easy access to the modeling parameters such as the oscillation rate, or the duration of a slide.

• A finer analysis is required for some gamakas (like the “NI” mentioned above). • In the current model, each note is played as a distinct entity. An improved model

would consider the continuous transitions between notes when relevant. • Provide a model for gamakas that span across several notes, taking into account

the varying spectrum. • Model amplitude variations along with pitch variations. • Provide a Graphical User Interface for users to interact with the model, and

create their own gamakas. Contributions Through this work, I made the following contributions:

• Analyzed the gamakas of raga Hamsadvani in the context of arohana (ascending scale) and avarohana (descending scale)

• Analyzed the requirements to model gamakas on a computer.

• Wrote a computer program to synthesize a first-order approximation of gamakas.

• Laid out a list of items to further this work. References Allen, Matthew. 1998. “Tales Tunes Tell: Deepening the Dialogue between ‘Classical’ and ‘Non-Classical’ in the Music of India.” Yearbook for Traditional Music 30: 22-52. Boulanger, R., Ed., 2000, The Csound Book: Perspectives in Software Synthesis, Sound Design, Signal Processing, and Programming, Cambridge, Mass.: The MIT Press. Swift, Gordon. 1990. “South Indian ‘Gamaka’ and the Violin.” Asian Music 21(2): 71-89. Viswanathan, T. and Matthew Harp Allen. 2004. Music in South India: Experiencing Music, Expressing Culture. New York: Oxford University Press. Websites: http://carnatic2000.tripod.com Csound: http://csounds.com Max/MSP: http://cycling74.com Matlab: http://csounds.com