About the author: Dr. Hassan Azad is a mathematician by profession and a senior student of sitar-nawaz Ustad Mohammad Shareef Khan. He is also a founding director of the Rauf Ansari Foundation. Learn More »

This essay is addressed to listeners of Raag music who want to go beyond being simple consumers, and to students of this music. The title is inspired by Marc Frantz’s article ‘Drawing with Awareness [MF]’. The comparison of drawing with listening is not as far fetched as one might be inclined to think.

We first learn music directly, without being aware of any note names. All of us can sing without knowing the sargam or even being aware of it; for instrumentalists, the fingers just learn to find the correct place with sufficient practice. The direct method of absorbing music and reproducing it is indeed the best method of learning. In learning the music of the subcontinent, great emphasis is also placed on knowing the names of notes. Why is it important when even professional musicians sometimes have difficulty in naming notes? For example, one will be able to sing the melody in Ustad Vilayat Khan’s Bhairveen, which is available at Patrick Moutal’s site [PM]. However, singing or transcribing its sargam will test even a professional musician. So why and when does the ability to name notes become important?

It becomes important when one wants to learn and listen with “awareness”. The desire to know and understand is a fundamental human desire. One wants to know whether Raag development is arbitrary and if not, does it follow some sort of a path. What, if any, are the principles of improvisation and composition in Indian classical music? Are these really different from principles of composition elsewhere? The answers to these questions are of great significance for the transmission of the art of improvisation to the succeeding generations. Surely, the answer must come by analysing recorded or orally transmitted works of masters.

By its very nature, a performer of ICM is a composer of sorts. By learning note recognition, it is possible to get an idea about basic principles of composition in ICM. Of course, no one can teach creativity. By analysis, one can begin to understand the intuition of great artists. We have before us the example of perspective drawing. By analysing it, now even a computer can render a three dimensional scene on the flat screen of a computer.

If one wants to listen with awareness, one has to invest a substantial time in learning note recognition. How can this be achieved? The best I can do is to share my own experiences with you. I used to take very long walks and, to occupy myself, would think about music (and mathematics). I knew several popular songs and I tried to recognize the relative pitch of the first notes of the songs. I also practiced things like SR SG SM SP SD SN SS and then RG RM RP RD RN RS RR etc to etch the various intervals in my mind. After some time I could make out the notes in various compositions.

Once you have mastered note recognition, you will be able to answer the questions posed above. Even the simple question- Is there a relationship between the last note (or groups of notes) of one phrase and the next? – extremely illuminating.

To understand principles of improvisation, one can concentrate on what note or pattern a phrase finishes and with what note or pattern the next phrase starts with. Is there a correlation between the last note of the phrase and the beginning note of the next, or the first notes or groups of notes in one phrase and the next?

For example, if a phrase ends in Sa, it is a good idea to start the next phrase also with Sa (or its consonants) and, for contrasts, with nonconsonants. Look at the phrases in Darbari: Sa- dha ni Re- next Re Sa ni dha – next dha ni dha Sa ni Re, dha Re Re – Dha ga Ma Re Sa Re ___ Re Sa.

You will begin to see that the performers are guided subconsciously by principles of consonances and contrasts, repetitions, silences – which are indeed universal principles of composition.

There are elements of repetitions – recapitulation – omitting notes, substituting other notes, inversions etc. In a musical mind, this happens instinctively, but it certainly helps the student to be aware of this while improvising.

The variation in Raag music comes from colouring the notes differently – this is what a shurti does- hearing the same phrase in the mind differently with microtones, meends, gamaks, variation in volume, cross rhythms…

Once you have mastered note recognition, you will be able to find your own answer to the question: Where are our Mozarts and Beethovens? From the analysis of the recorded music of Ustads Imdad Khan, Inayat Khan, and Vilayat Khan, it seems that composition in Raag Music is incremental and our Mozarts and Beethovens are ever present with us. It is their sense of balance, contrasts and a stream of ever new ideas and nuances which distinguishes them from the average performer.

The immense treasures available on the Internet will also become available for you to analyze and learn and teach from and to test your theories. You will have a fund of first rate taans and compositions to transcribe, to play and sing. You will derive immense pleasure from recognizing germs of new ideas and their evolution. You can see and hear all this in play in the transcription given in the appendix and the ones done earlier on the Virsa site.

I want to conclude this essay by reproducing words which were addressed to the student of Mathematics. Replacing Mathematics with Music shows how close the learning methods of these disciplines really are:

While you may have a clear idea of what a physicist or a chemist does – because you see them working in their laboratories – you may not have a very clear picture of what a professional mathematician does to discover something new. Well, the laboratory of a mathematician is the laboratory of ideas which are handed down through generations of mathematicians. The usual task of a mathematician is to combine these ideas to form new ideas, to link hitherto unrelated mathematical ideas and, of course, to have original ideas. All of this demands extreme hard work and patience but if you are mathematically talented, you will certainly have a couple of good original ideas and these ideas would be enough to earn you a respectable place in the comity of mathematicians.

Just as most of you learn to appreciate language and can recognise beautiful phrases and ideas, a trained mathematician also learns to recognise beauty in mathematics and to sift good ideas and he is guided in his researches by such largely aesthetic criteria. The joy of discovering a truly fruitful idea is something that can only be experienced; it cannot be described in words.

Acknowledgement: I thank Pete Fine for a correspondence which led to this essay.


[MF] Marc Frantz, Drawing with Awareness

[PM] Patrick Moutal’s Indian Music page

APPENDIX: A Transcription of Ustad Vilayat Khan’s Gujari Todi: click here to download it from Patrick Moutal’s page

Notation: This is just a skeletal notation meant only for learning and research. It should be read while listening to the actual music from the source. To follow this, you will need to download the Gujari Todi mp3 file with the option of speed reduction. For the purposes of analysis and study, it is recommended that you play the music at half the speed.

Naturals are denoted by capital letters, any variation thereof by small letters. The letter c denotes playing the chikari string. Notes of the lower octave (Mandir Asthaan) are indicated by a dash (‘), notes of the upper octave (Taar Asthaan) by a double dash (“). A bold letter denotes the first beat (Sum) of the cycle. The composition is in Teen Taal.

Although Pa is not allowed in Gujari Todi, it is acceptable at extremely fast speeds.

Gugari Todi:

Alaap:ScSc SN’rS /


Gaat: d-mdm/dNS”Ndmdmg/g-m/




/S”- -d-mdN N-dmd mgmm/


1st taan from (1/2 matra before) sum- in double tempo(x 2)

(1) NN dm dm gr gr SN’ Sr gr SN’ S – – – – –

2nd taan from 16th matra(x 2)

(16)SN’ rS gr SN’ Srg Srg N’S N’r Sg rS

N’r SN’ SN’ rS gr SN’

S r g m P m g r / g m P d NN d m / S” r” g”m”P” m” g” r” /

S”S” dN dN dm dm g r S_/ NNdmgmd-/ NNdmgmdNS”-/NNdmgmdNS”

– – -/(4) dm md N-dmd m g m mdS” — m-d- _ _ _ _ _ _ _ _ _ _ _ _ _

– 3rd taan-from 4th matra: (x2)

(4)d m d NS N d m g r g r S N’ S- – – – – X- – -/ – – -/

(8)S r g r S N’ / S r g m P m g r / g m P d S” N d m d m g r g r S N’ S/

– – – – – – – –

From sum : (1)S r g m P m g r /g m P d S” N d p / S” r” g” m” P” m” g” r”/ S” S” d m g

r SN’S/ S” N d m g r S N’ S / S” N d m g r S N’ S / S” N d m g r S N’ S /

(1)S”- – d- m m d N-dmd mgmdS’- d—d-d-d-

(1) m g r S – – – -/(9) S – r S- – S N’ r S- g r S – r S-g r – rS- rS-rS-gr-mg-

gamak /d d d d/d d d d/d d d d /g r S N’- r g m D n n n- d m g g m m g r S/

N’- r g m d N S”/ S” N g” r”-N d-m-g-r S/

N’-r g m d/N’-r g m d/g-m d – – m-d N S” N d m-m g m d S”-d-/- – – -/o – – – /- – – – /

X- (3)gg mm dd NN S”S” NN dd mm gg rr gg rr SS rr/

(1)N’N’N’N’ rrrr gggg mmmm dddd NNNN S”S”S”S” r”r”r”r”/(1) g” r”- r” S”-S” NX Nd_d/ g-

md- -d- g-md g-m g-md- -m d N S” N d m d m g g-m d- – -/ – –

Also read Mathematics, Arts and Real Life: Reflections on Teaching Mathematics — Hassan Azad