Spectral analysis of Gamaka Swaras of Indian music

Karuna Nagarajan, Heisnam Jina Devi, N V C Swamy* & H R Nagendra

Swami Vivekananda Yoga Anusandhana Samsthana (Deemed University), Bangalore 19, KarnatakaE-mail: nvcswamy@rediffmai1.com

Received 6 April 2005; revised 24 April 2006

In Indian classical music, there are a huge number of modes (Ragas). There are also pieces (Ragamala or Ragamalikai inwhich modulations are employed. In both Hindustani & Carnatic (Karnataka) music, songs are usually preceded by animprovised unmeasured prelude (A lap), which is sometimes extensive. Individual pieces are shorter in Camatic music, sorecitals are constructed by selecting items in contrasting ragas. Gamaka Swaras, the subtle decorations of musical notes,usually referred to as the shaking of notes or vibration of Swaras come in various forms. Gamaka plays a very essential rolein Indian music. Spectral analysis of the seven notes of Indian music has been reported. The work reported in the paper is acontinuation of that work, extending it to Gamaka Swaras. Report of the preliminary study giving a glimpse into spectralintricacies of Arohana Gamaka has also been discussed.

Keywords: Gamaka Swaras, Indian music, Karnataka music, Spectral analysis

IPC Int. CI.8: G06F17/20, GIOG3/00, GIOLl9102

IndianJournal of Traditional KnowledgeVol.5(4), October 2006, pp. 439-444

Gamaka Swaras are subtle decorations of musicalnotes, usually referred to as the shaking of notes orvibration of Swaras. They come in various forms andare incorporated into Ragas, giving each note aunique characteristic and delicate beauty. Gamakaplays a very essential role in Indian music, whetherHindustani or Karnataka, classical or otherwise. It iseven considered the very essence of music, withoutwhich music tends to become flat, pale andunaesthetic. Recently, the Spectral analysis of theseven notes of Indian Music has been reported. 1 Thework reported in the paper is a continuation of theearlier work, extending it to Gamaka Swaras. Thereare various types of Gamakas in use.' GamakaSwaras of the ascending scale of the RagaMayamalavagowla, which uses the seven notes in asequence and is the basis for the commencement oftraining in Karnataka music of southern India, hasbeen discussed. Indian music owes its origin to theSamaveda24

. The evolution of Music from theSamaveda has been the subject of study by manyscholars and a good number of literatures areavailable on this subject. Some of them give a bird'seye view of the development of music down the agesuntil it reached its current form".

*Corresponding author

Indian music is one of the oldest musical traditionsin the world and its origin go back to Vedas (ancientIndian scripts). Many different legends have grownup concerning the origin and development of Indianclassical music. Indian music has developed within avery complex interaction between different peoples ofdifferent races and cultures. The basis for Indianmusic is Sangeet. Sangeet is a combination of threeart forms: vocal, instrumental and dance. Althoughthese three art forms were originally derived from thesingle field of stagecraft, today these three forms havedifferentiated into complex and highly refinedindividual art forms. Indian music is based upon: Ragand Tal. Rag is the melodic form while Tal is therhythmic. Rag may be roughly equated with theWestern term mode or scale. There is a system ofseven. notes, which are arranged in a means not unlikeWestern scales. Tal (rhythmic form) is also verycomplex. Many common rhythmic patterns exist.They revolve around repeating patterns of beats. Allof this makes up the complex and exciting field ofIndian classical music. Its understanding easilyconsumes an entire lifetime.

Speech and sound analysis, on the other hand, is ofrecent origin. The impetus for this came from thefamous work of Fourier, leading to the study ofsound patterns by splitting them into sinusoidal and

440 INDIAN J TRADITIONAL KNOWLEDGE, VOL 5, NO.4, OCTOBER 2006

co-sinusoidal components, now called Fourieranalysis or spectral analysis. However, the analysis ofhuman voice itself commenced only about half-a-century ago, with the invention of the SoundSpectrograph in 1946. Today, it has become a highlydeveloped technical domain.'

The analysis of sound patterns is usually doneeither in the frequency domain or in the time domain.The former gives information about the distribution ofthe energy of sound over a range of frequencies. Forhuman voices, the range is 20-20,000 Hz. However,the contribution above 8,000 Hz. is usually negligible.In the case of slow speech, the shape of the vocal tractremains steady up to about 200 millisec. Hence, it isthe usual practice to do time domain studies in therange of 30-100 millisec. Frequency domain analysisleads to the energy spectrum, where the initialwaveform is Fourier-analysed. This has the handicapof losing information about variations with time.Therefore, it is the usual practice to supplement thespectrum by a Spectrogram, which is a plot offrequency as a function of time. The spectrogramconsists of a set of horizontal lines of varyingthickness and intensity, which are an index of theenergy level. In this sense, the spectrogram is aparametric representation, with the energy as theparameter. Between them, the energy spectrum andthe corresponding spectrogram provide enoughinformation for the analysis of the sound pattern.t"

MethodologyThe experimental procedure consisted of the

following steps: (1) recording the Gamaka Swaraswith a sensitive microphone in a quiet ambience, (2)digitizing the waveforms using a sampling rate of44100 per see, (3) analyzing the digitized data toextract the energy-frequency and frequency-timespectra, and (4) identifying the predominantfrequencies through spectrograms. The procedure forrecording was essentially the same as describedearlier'. Even though the human voice normally doesnot use frequencies higher than 8000 Hz., it was stilldecided to digitize the signals with a sampling rate of44100 per second for the sake of fidelity. Trialsshowed that with a threshold level of 7500 Hz., thespectrograms showed very clear lines, easy foranalysis. Using a higher threshold made the lines toothin and difficult to analyze.

The recording was done for a total of 5 male voicesand 5 female voices, choosing the ascending scale of

the raga Mayamalavagowla of Karnataka music andwas supervised and checked for fidelity by the firstauthor, a trained singer of Karnataka classical music.The seven notes were sung in the ascending order,giving long runs to each note. Three criteria wereused for selecting the best recordings - steadiness ofthe pitch, perfection of the notes and breath control ofthe reciter leading to the steadiness of the voice.Based on these criteria, three male and three femalerecordings were selected for further study. The mostimportant segment of the recording is the exactlocation in the waveform of the Gamaka Swaras. Theidentification was done as follows: The signal wasexpanded in the time scale and the cursor was movedfrom one end of the waveform to the other, using theplay icon in the Sound Forge software. The musicalnotes were scanned with the help of a headphone.Wherever the Gamaka note was heard, the cursor wasstopped to note down the precise location in thewaveform. This position was highlighted and thatportion of the waveform was used for further analysis.In this manner, the position before the Gamaka,during the Gamaka, after the Gamaka and thetransition from one note to the next were identified.

ResultsThe results are presented in the form of sample

waveforms, short-time window patterns, sampleenergy-frequency spectra and sonograms of the sevennotes as well as of the transitions. The waveform ofthe seven notes with Gamaka for a female voice(Fig. 1) and that for a male voice (Fig. 2) has beenpresented. The analysis reported is based on allwaveforms recorded, but only two of them aredisplayed to give an idea as to what the waveformslook like. A short-time window pattern for a femalevoice (Fig. 3) and that for a male voice (Fig. 4) havebeen displayed. These patterns demonstrate theperiodic nature of the signals, indicating that norandom analysis is needed. Sample energy-frequencyspectra are shown in figs 5 & 6. Fig. 5 shows thespectrum for the note Sa of a female voice duringGamaka. The same spectrum for a male voice isdisplayed in Fig. 6. A sample set of sonograms hasbeen displayed (Figs 7-14). The sonogram for allseven notes for a female voice (Fig. 7) and that for amale voice (Fig. 8) have been displayed. There are inall seven transitions between the notes and thesonogram of these transitions for the female voice(Fig. 9) and that for the male voice (Fig. 10). Lastly,

NAGARAJAN et al.: SPECTRAL ANALYSIS OF GAMAl«A SWARAS OF INDIAN MUSIC 441

Fig. 1 Female voice waveform

Fig 3 Short-time window pattern for female voice

9 ====================================~wFig. 5 Female sa during gamaka - energy spectrum

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Fig. 7 Sonogram for all the seven notes: female voice

TimeFig. 2 Male voice waveform

TimeFig. 4 Short-time window pattern for male voice

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Fig. 8 Sonogram for all the seven notes: male voice

442 INDIAN J TRADITIONAL KNOWLEDGE, VOL 5, NO.4, OCTOBER 2006

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Fig 9 Sonogram for the seven transitions femalesa

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Fig 11 Seven notes before gamaka: female voice•••

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Fig 13 Seven notes after gamaka: female voice

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the sonograms for the seven notes before Gamaka forthe female voice in (Fig. 11) and the male voice in(Fig. 12) and the corresponding sonograms for theseven notes after Gamaka (Figs 13-14) have also beendisplayed. Of the total 390 figures, only samplefigures to illustrate the kind of data analysis, whichhas been used to draw the conclusions, have beenpresented."

DiscussionMusical notes are periodic in nature and differ from

noise, which is non-periodical. It is the periodic

""1.~NfUl .,......... ~----<===0 .,.Fig 10 Sonogram for the seven transitions male

sa n ga rMI P8 h nI

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o BIIFig 12 Seven notes before gamaka: male voice

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Fig 14 Seven notes after gamaka: male voice

nature of the musical notes, which makes them sopleasant to hear even for long periods of time. Noise,on the other hand, creates mental disturbances leadingto discomfort. This is a common experience. Theadvantage of musical notes is their periodicity, whichmakes working with them and their analysis muchsimpler. Therefore, before working on any musicalwaveform for its periodicity, not only to ensure itsfidelity but also to see that there is no intrusion byexternal or internal noise is checked. With this end inview, all recorded waveforms (Figs 1-2), werechecked for periodicity by taking several 100 millisec

NAGARAJAN et al.: SPECTRAL ANAL YSIS OF GAMAKA SWARAS OF INDIAN MUSIC 443

windows. It is said that the human voice finds itdifficult to be stable beyond a time period of 200millisec. But during the study, all the singers werewell trained and could hold their voice steady.Nevertheless, windows of 100 millisec were used toensurethat all the waveforms were periodic.

The signals can be analyzed by the energy-frequency spectrum and the frequency-timesonogram. The former gives a static picture and thelatter gives a dynamic picture. Both therepresentations are equally useful if the spectra areindependent of time. But where the energy spectravarywith time, the sonogram representation is moreuseful, since it gives information about variationswith time, which tend to get masked in the energyspectra. In the current study, the focus of attentionwasthe Gamaka, which represents minute variationsin the voice resorted to by musicians to bring outemotions more effecti vel y. Therefore, sonogramswereconsidered to be more appropriate medium forthestudy and hence they have been used primarily fordrawing the conclusions. While studying thesonograms, the abscissa represents time and theordinate the frequency, with the energy level servingas a parameter. The lowest line represents thefundamental frequency and successive lines areharmonics. Shades of grey serve to identify the levelofenergy. The darker the line, the higher the energy.It is also seen that there is hardly any energy betweenthelines, since the signal is periodic and composed ofharmonic frequencies, which are integral multiples ofthe fundamental. Black and white sonograms havebeen used rather than coloured ones, since theyhighlight the variations more clearly.

The frequency of the signal is a function of timeandhence the sonogram lines are expected to be bentand not straight, which would be the case if thefrequency is independent of time. The time variationof the frequency was clearly seen (Figs 7-14)contrasted with sonograms for the notes withoutGamaka. In the Gamaka way of singing, there is atransition from one note to another, which is expectedto be smooth (Figs 9-14). The largest time variationwasto be found within the window of the signal at thepointof Gamaka itself (Figs 9-10). The magnitude ofthese variations depends upon the way the singerintroduces Gamaka into the singing of the notes,which varies among the various schools or Gharanas(according to the North Indian style of classicalmusic). The male voice is usually richer in timbre

than the female voice and thus displays a largernumber of harmonics or lines in the sonograms. Thisis borne out by comparing Figs 7, 9, 11 and 13,respectively with Figs 8, 10, 12 and 14. Certainstriking features of the signals were observed. Someof them are common to both the male and the femalevoices. There are seven transitions involved inthe signal, namely sa to ri, ri to ga, ga to ma, ma topa, pa to dha, dha to ni and finally ni to sa. TheGamaka for the first and the last transitions areusually not emphasized by singers. Gamaka usuallystarts with ri. It is also mild for ga and emphatic forma. Similar is the case for pa and dha, the latter beingvibrated more predominantly. The note ni is also sungwith mild Gamaka.

A study of the spectrograms in their totalityrevealed that in all cases the spectrograms for sa andpa are almost flat, whereas those for the other notesshowed predominant time variation. It appears as ifthe notes form a staircase, alternate notes representingthe rise and the tread. In this sense, the word A rohana,meaning ascent, is indeed appropriate.

ConclusionMale voices have a richer timbre, which many a

time, plays the same role as Gamaka. Hence, there isno need for the male voice to use or emphasizeGamaka. The female voice on the other hand, with ashallower timbre, needs to emphasize Gamaka more,to bring out the same effect. This has been noticed inthe recitation of Mantras also. In the case of any flatnote, the fundamental frequency remains unchangingwith time. However, it is also a function of the pitch.When the human voice moves over the ascendingscale of notes, the fundamental frequency graduallyincreases. This is irrespective of whether the voice ismale or female. The notes with Gamaka appear toform a staircase, with the alternate notes representinga rise or the step, thus justifying the use of thetechnical word Arohana. This is a preliminary studygiving a glimpse into the spectral intricacies ofArohana Gamaka. A more detailed study would haveto take into account the actual variations in thefrequency during Gamaka, the peak frequencyreached and its relation to the transition between thenotes. The study has been undertaken and the resultswill be reported later.

AcknowledgementAuthors thank Sri Natesh Babu and Sri Heisnam

Bison Singh for their help in the use of the Sound

Forge Software. Authors are grateful to all those wholeant their voices for the Gamaka recordings.

References1 Chandrasekharan J, Heisnam Jina Devi, Swamy N V C &

Nagendra H R, Spectral analysis of Indian Musical notes,Indian J Traditional Knowledge, 4(2) (2005) 127-131.

2 Prajnanananda Swami, Music of the Nations, (RamakrishnaVedanta Math, Kolkata), 1973.

3 Chandrasekharan J, Spectral Analysis of Indian MusicalNotes, MSc Dissertation, Swami Vivekananda Yoga

Anusandhana Samsthana, Bangalore, 2004.4 Nagarajan Karuna, Spectral Analysis of Gamaka Swaras,

MSc Dissertation, Swami Vivekananda Yoga AnusandhanaSamsthana, Bangalore, 2005.

5 Furui S & Soudhi M, Advances in Speech Signal Processing,(Marcel Dekker), 1992.

6 Flanagan J, Speech Analysis, Synthesis and Perception,(Springer Verlag) 1972.

7 Heisnam Jina Devi, Swamy N V C & Nagendra H R,Spectral Analysis of Vedic Mantra-Ornkara, Indian JTraditional Knowledge, 3(2) (2004) 154-161.

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