fundamentals of music

Fundamentals of MusicFundamentals of Music

KRS MurthyKRS Murthy

The Wonder of the Human Ear (and the The Wonder of the Human Ear (and the brain)brain)

• Human ear is unique, especially when combined with the Human ear is unique, especially when combined with the extraordinary processing power of the brainextraordinary processing power of the brain

• What is not linear may sound linear toWhat is not linear may sound linear tothe human ear.the human ear.

• A very good example is the fact that our brains senseA very good example is the fact that our brains sensea sound pitch with respect to other sound pitches that are a sound pitch with respect to other sound pitches that are multiplesmultiplesof the power of 2of the power of 2

• A pitch and other pitches that are two times, fourA pitch and other pitches that are two times, fourtimes, eight times … and so on (to include all powers of two) times, eight times … and so on (to include all powers of two) soundsoundsimilar, except for recognizing that they are all part of a similar, except for recognizing that they are all part of a frequencyfrequencyscale.scale.

• They are called harmonics in Physics.They are called harmonics in Physics.• The frequency space between a frequency F and 2F is called The frequency space between a frequency F and 2F is called

an octave.an octave.• The wonder that our ears can uniquely recognize this fact The wonder that our ears can uniquely recognize this fact

helps us to enjoy (or intuitively `understand') music.helps us to enjoy (or intuitively `understand') music.

Silence and SoundSilence and Sound• Sound is not alone; silence is its companion.Sound is not alone; silence is its companion.• We would not differentiate or recognize that there is sound, unless We would not differentiate or recognize that there is sound, unless

it is punctuated by silence.it is punctuated by silence.• The reason is that our eye-brain combination is a very good The reason is that our eye-brain combination is a very good

differential amplifier. differential amplifier. • Therefore, we need silence for resetting our `differential amplifier'.Therefore, we need silence for resetting our `differential amplifier'.• Every time the sound is punctuated by silence, our ear-brain Every time the sound is punctuated by silence, our ear-brain

differential amplifier is able to sense the `ups and downs'.differential amplifier is able to sense the `ups and downs'.• In fact, there is really nothing like silence in nature! In fact, there is really nothing like silence in nature! • There are all type of activities in the universe all the timeThere are all type of activities in the universe all the time• It includes the earth, the local geography / space weIt includes the earth, the local geography / space we

live in with sound ambiance constantly existing.live in with sound ambiance constantly existing.• Our ear-brain combination has been gifted to conveniently Our ear-brain combination has been gifted to conveniently

`ignore' the background sound as noise`ignore' the background sound as noise• All of us do not even realize that is always some background All of us do not even realize that is always some background

sound / noise, but think that there is silence.sound / noise, but think that there is silence.

Nonlinear ScaleNonlinear Scale• The frequency space between successive octaves The frequency space between successive octaves

keeps on increasing logarithmically (to the base keeps on increasing logarithmically (to the base of 2) as you go up the sound / music scale.of 2) as you go up the sound / music scale.

• Frequency space between 2F and F is FFrequency space between 2F and F is F• Where as the frequency space in the next octave Where as the frequency space in the next octave

is 4F-2F=2Fis 4F-2F=2F• Further octaves 8F-4F=4F, 16F-8F=8F and so on.Further octaves 8F-4F=4F, 16F-8F=8F and so on.• However. our ear-brain combination perceives the However. our ear-brain combination perceives the

sound scale or the music scale as linear even.sound scale or the music scale as linear even.

The Swaras with in an The Swaras with in an OctaveOctave• The octave is divided into many parts, obviously in a non-The octave is divided into many parts, obviously in a non-

linearlinearscale.scale.

• For example, in a piano, which is made of discrete keys, theFor example, in a piano, which is made of discrete keys, theoctave is made up of 12 keys.octave is made up of 12 keys.

• If you take any key of your choice and move up (or down) If you take any key of your choice and move up (or down) counting one key at a time (to include both white and black counting one key at a time (to include both white and black keys), you will reach the next octave when you reach keys), you will reach the next octave when you reach the13th key.the13th key.

• Remember to count the first key as 1, second key as 2, andRemember to count the first key as 1, second key as 2, andso on.so on.

• The 13th key is the starting point of the next octave. You The 13th key is the starting point of the next octave. You cancando this on an electronic keyboard, harmonium or accordion.do this on an electronic keyboard, harmonium or accordion.

Non-Linear with in and between Non-Linear with in and between the Octavesthe Octaves

• Even though I am not planning to jump into the concepts of Indian orEven though I am not planning to jump into the concepts of Indian orwestern musical scale yet, I want to illustrate a point here.western musical scale yet, I want to illustrate a point here.

• Challenging some of the assumptions / foundations ofChallenging some of the assumptions / foundations ofIndian music.Indian music.

• Let us take the Indian music scale from the perspective of the seven Let us take the Indian music scale from the perspective of the seven swarasswaras

• The saptha (means seven): sa, ri, ga, ma, pa, dha. ni, (Sa the The saptha (means seven): sa, ri, ga, ma, pa, dha. ni, (Sa the beginning of the next octave).beginning of the next octave).

• The frequency space between ri and sa is smaller than theThe frequency space between ri and sa is smaller than thefrequency space between ga and rifrequency space between ga and ri

• Which is further smaller than the frequency space between ma and ga, Which is further smaller than the frequency space between ma and ga, and so on.and so on.

• This is progressive through out the musical scale.This is progressive through out the musical scale.• The frequency space between ga and ri (for example) in any octave is The frequency space between ga and ri (for example) in any octave is

smaller than the frequency space between ga and ri in the higher smaller than the frequency space between ga and ri in the higher octave.octave.

Non-Linearity in Music Non-Linearity in Music InstrumentsInstruments• We see the non-linearity in some musical instruments, where as we do not We see the non-linearity in some musical instruments, where as we do not

see them obvious in others.see them obvious in others.• In a piano, the keys are equally spacedIn a piano, the keys are equally spaced• The keys look in shape and color exactly same as you go from one end to The keys look in shape and color exactly same as you go from one end to

the other.the other.• Of course, you hear it when you play.Of course, you hear it when you play.• You will also notice it, if you look at the inner construction.You will also notice it, if you look at the inner construction.• The `continuous non-linearity is clearly visible in a guitar.The `continuous non-linearity is clearly visible in a guitar.• The frets in a guitar become closer to each other as one moves up theThe frets in a guitar become closer to each other as one moves up the

scalescale• This is in `inverse' to the sound generated as one moves upThis is in `inverse' to the sound generated as one moves up

the scale.the scale.• This is because the string length required to go up in frequency reduces as This is because the string length required to go up in frequency reduces as

one goes up the scale.one goes up the scale.• If you look at the flute construction, the size of the flute keeps reducing If you look at the flute construction, the size of the flute keeps reducing

(non-linearly) as you go up in the frequency.(non-linearly) as you go up in the frequency.

With in the OctaveWith in the Octave

• The starting point of the octave (or beginning of one octave The starting point of the octave (or beginning of one octave scale)scale)is called the Shadja.is called the Shadja.

• Here the Devanaagari letter for `Sha' is different from the one Here the Devanaagari letter for `Sha' is different from the one used for the word Shankara.used for the word Shankara.

• Unfortunately,English alphabets, being only 26, are inadequate Unfortunately,English alphabets, being only 26, are inadequate to write Devanaagari (Sanskrit based) alphabets.to write Devanaagari (Sanskrit based) alphabets.

• An easy way for me is to give you examples from English An easy way for me is to give you examples from English words.words.

• The `sha' type of sound in the word `fiction'. The `sha' type of sound in the word `fiction'. • This `Sha sound is produced close to the throatThis `Sha sound is produced close to the throat• But NOT the guttural sound you hear in Urdu and also NOT at But NOT the guttural sound you hear in Urdu and also NOT at

closer to the tip of the tongue.closer to the tip of the tongue.

Shadja – The aadhaara Shadja – The aadhaara shruthishruthi• However, the swara Shadja is normally abbreviated as `sa' whileHowever, the swara Shadja is normally abbreviated as `sa' while

singing and writing notations.singing and writing notations.• For English speakers, this has the same `sa' part of the sound as in `sun' or For English speakers, this has the same `sa' part of the sound as in `sun' or

`son'.`son'.• I may use the capital letter S or the small letter s in an exchangeable fashion.I may use the capital letter S or the small letter s in an exchangeable fashion.• Sa is the reference swara, defining the octaveSa is the reference swara, defining the octave• Keep in mind that the octave is defined as soon as sa the starting point of the Keep in mind that the octave is defined as soon as sa the starting point of the

octave is defined or chosen.octave is defined or chosen.• Twice the frequency of sa is the starting point of the next octave.Twice the frequency of sa is the starting point of the next octave.• In Indian music sa is called the aadhaara shruthiIn Indian music sa is called the aadhaara shruthi• Shruthi in Sanskrit means a pitchShruthi in Sanskrit means a pitch• In practice, the music teachers in India teach sa as THE SHRUTHI, leaving out the In practice, the music teachers in India teach sa as THE SHRUTHI, leaving out the

word aadhaara.word aadhaara.• I have a tendency to keep using the term aadhaara shruthi to refer to sa.I have a tendency to keep using the term aadhaara shruthi to refer to sa.• Sometimes, I call the remaining swaras (for example - keys in a piano) with any Sometimes, I call the remaining swaras (for example - keys in a piano) with any

one of the following words: shruthi, swara, note, key.one of the following words: shruthi, swara, note, key.• Western musicians also refer to the starting point of the scale as `key', to imply. Western musicians also refer to the starting point of the scale as `key', to imply.

"Where does your scale start?""Where does your scale start?"

Sanctity of the shruthiSanctity of the shruthi

• It is very important to understand that the sa can be fixed at anyIt is very important to understand that the sa can be fixed at anypoint in the frequency scale depending on the choice of the artistpoint in the frequency scale depending on the choice of the artist(s) / musician(s).(s) / musician(s).

• However, the complete composition (aalaapana or any type of composition) should However, the complete composition (aalaapana or any type of composition) should maintain the same samaintain the same sa

• Most of the times, the complete concert is performed using the same sa.Most of the times, the complete concert is performed using the same sa.• This sa is maintained, rather `religiously' throughout the composition orThis sa is maintained, rather `religiously' throughout the composition or

concert by the use of tamboora.concert by the use of tamboora.• Tamboora is a drone type of instrument providing the scale / octave reference to the Tamboora is a drone type of instrument providing the scale / octave reference to the

artist(s).artist(s).• If the artist looses the aadhaara shruthi or actually `falls off' the scale, the artist isIf the artist looses the aadhaara shruthi or actually `falls off' the scale, the artist is

said to have `LOST THE SHRUTHI'.said to have `LOST THE SHRUTHI'.• It is also considered as a disgrace by many artists, for their `basic' inability to It is also considered as a disgrace by many artists, for their `basic' inability to

maintain their performance to a specified scale.maintain their performance to a specified scale.• There are cases when some artists may `slip' (out of little lapse of control or even There are cases when some artists may `slip' (out of little lapse of control or even

being physically and vocally tired) and consider that as a shame.being physically and vocally tired) and consider that as a shame.• It is almost as if a gymnast were expected to maintain `perfect' fitness and never slipIt is almost as if a gymnast were expected to maintain `perfect' fitness and never slip

out of the agility and routine.out of the agility and routine.• This discipline has become a tradition (and indeed a great tradition) in Indian This discipline has become a tradition (and indeed a great tradition) in Indian

classical music, by sanctifying the importance of Shadja and indeed the rigid classical music, by sanctifying the importance of Shadja and indeed the rigid framework of theframework of thecomplete scale.complete scale.

With in the OctaveWith in the Octave

• The octave is made up of 12 keys. The octave is made up of 12 keys. • The 12 keys / swaras are given names.The 12 keys / swaras are given names.• Surprisingly and coincidently, the Western and the IndianSurprisingly and coincidently, the Western and the Indian

scales have basically seven names:scales have basically seven names:• Do Re Ma Fa So La Ti - Western TraditionDo Re Ma Fa So La Ti - Western Tradition• Sa Ri Ga Ma Pa Dha Ni - Indian TraditionSa Ri Ga Ma Pa Dha Ni - Indian Tradition• Seven English alphabets –Seven English alphabets –

A, B, C, D, E, F, G - are used in the Western systemA, B, C, D, E, F, G - are used in the Western system• These seven letters (representing the keys are called `natural.' These seven letters (representing the keys are called `natural.' • Total of 12 keys are named, as shown in the table.Total of 12 keys are named, as shown in the table.• They are assigned the remaining seven either as Sharp (denoted by #) or They are assigned the remaining seven either as Sharp (denoted by #) or

Flat (denoted by a small letter next to the Capital letter).Flat (denoted by a small letter next to the Capital letter).• For example, F# is the key higher to FFor example, F# is the key higher to F• Bb (pronounced as B Flat) is the key lower to B.Bb (pronounced as B Flat) is the key lower to B.

Karnaatak – Western – Karnaatak – Western – Hindustaani Hindustaani • Karnatak Karnatak WesternWestern North Indian/HindustaniNorth Indian/Hindustani

• sa sa (Shadja)(Shadja) C C sa sa • Ri (Rishabha)Ri (Rishabha) D FlatD Flat ri komalri komal• R2R2 D SharpD Sharp ri tivrari tivra• Ga1 (Gaandhaara)Ga1 (Gaandhaara) E FlatE Flat ga komalga komal• Ga 2Ga 2 E SharpE Sharp ga tivraga tivra• Ma 1 (Madhyama)Ma 1 (Madhyama) F FlatF Flat ma komalma komal• Ma 2Ma 2 F SharpF Sharp ma tivrama tivra• Pa (Panchama)Pa (Panchama)GG panchamapanchama• Dha 1(Dhaivatha)Dha 1(Dhaivatha) A FlatA Flat dha komaldha komal• Dha 2Dha 2 A SharpA Sharp dha tivradha tivra• Ni 1 (Nishaadha)Ni 1 (Nishaadha) B FlatB Flat ni komalni komal• Ni 2Ni 2 B SharpB Sharp ni tivrani tivra

Shatshruthi samgeetaShatshruthi samgeeta

• The ancient Indian musicologists defined an octave, with much The ancient Indian musicologists defined an octave, with much finer graduations in it than the 12 swaras.finer graduations in it than the 12 swaras.

• Indian classical music has been conceived and modeled with the Indian classical music has been conceived and modeled with the help of an Adhaara Shruthihelp of an Adhaara Shruthi

• 32 intermediate shruthis or swaras in the octave.32 intermediate shruthis or swaras in the octave.• This includes 6 shruthi-lets of each of the swaras Ri, Ga, Ma, Dha, This includes 6 shruthi-lets of each of the swaras Ri, Ga, Ma, Dha,

NiNi• That is 6X5 = 30 plus the Sa and Pa – Total 32That is 6X5 = 30 plus the Sa and Pa – Total 32• For reasons unknown, Panchama, denoted as Pa or P, has also For reasons unknown, Panchama, denoted as Pa or P, has also

been deemed unique.been deemed unique.• Panchama does not have any shruthi-lets or subdivisions, unlike Panchama does not have any shruthi-lets or subdivisions, unlike

the other swaras.the other swaras.• Sa and Pa are called the Prakruthi swaras (meaning natural Sa and Pa are called the Prakruthi swaras (meaning natural

swaras).swaras).• The other shruthi-lets of Ri, Ga, Ma, Dha, Ni are called Vikruthi The other shruthi-lets of Ri, Ga, Ma, Dha, Ni are called Vikruthi

swaras (meaning non-natural swaras). swaras (meaning non-natural swaras).

Present Day samgeetaPresent Day samgeeta

• The 6 shruthi-lets are based on the Shat-Shruthi The 6 shruthi-lets are based on the Shat-Shruthi Sangeetha tradition.Sangeetha tradition.

• Shat (pronounced like `Shut') means six.Shat (pronounced like `Shut') means six.• However, it should be noted that the present day However, it should be noted that the present day

Indian classical music utilizes only three of the 6 Indian classical music utilizes only three of the 6 shruthi-letsshruthi-lets

• Ri, Ga, Dha and Ni have three shruthi-lets.Ri, Ga, Dha and Ni have three shruthi-lets.• Ma has only two.Ma has only two.• The meLakartha system, devised and documented by The meLakartha system, devised and documented by

the pioneer Venkatamakhi, uses:the pioneer Venkatamakhi, uses:• S, R1, R2, R3, G1, G2, G3, M1, M2, P, D1,S, R1, R2, R3, G1, G2, G3, M1, M2, P, D1,

D2, D3, N1, N2, N3, S (Shadja of the upper octave). D2, D3, N1, N2, N3, S (Shadja of the upper octave).

Melakarta SystemMelakarta System

• Venkatamakhi has systematized 72 meLakartha ragasVenkatamakhi has systematized 72 meLakartha ragas• These are divided into two halves of 36 raagasThese are divided into two halves of 36 raagas• One set for M1, and the other for M2.One set for M1, and the other for M2.• Instruments like piano, electronic keyboard, accordion or Instruments like piano, electronic keyboard, accordion or

harmonium use the Western scale simplification with S, R1, harmonium use the Western scale simplification with S, R1, R2, G1, G2, M1, M2, P, D1, D2, N1, N2, SR2, G1, G2, M1, M2, P, D1, D2, N1, N2, S

• This is a total of 12 swaras (keys) including S; upper Shadja,This is a total of 12 swaras (keys) including S; upper Shadja,denoted by bold letter S corresponds to the upper octave.denoted by bold letter S corresponds to the upper octave.

• The diagram shows the corresponding keys for western The diagram shows the corresponding keys for western scale, with C used for Shadja.scale, with C used for Shadja.

• Please note that Indian scale uses relative positions, unlikePlease note that Indian scale uses relative positions, unlikethe western scale using fixed keys.the western scale using fixed keys.

What is a raaga?What is a raaga?

• A raga is reduced to a suite of loci of musical A raga is reduced to a suite of loci of musical curvescurves

• Based on swaras (chosen shruthis ) in specified Based on swaras (chosen shruthis ) in specified ascending and descending orders.ascending and descending orders.

• The real raga is based on multitudes of musical The real raga is based on multitudes of musical curve combinationscurve combinations

• The curves of the raga are thus reduced to piece-The curves of the raga are thus reduced to piece-wise linear approximations of the real / ideal wise linear approximations of the real / ideal musical curves.musical curves.

• Definition and profile concepts of raga is complex Definition and profile concepts of raga is complex

Salient points of raagaSalient points of raaga

• Swaras (5, 6 or 7 taken at a time).Swaras (5, 6 or 7 taken at a time).• A raga is defined by a scale of 5, 6, or 7 swaras.A raga is defined by a scale of 5, 6, or 7 swaras.• Only one of the swara-lets or shruthi-lets may be used in a Only one of the swara-lets or shruthi-lets may be used in a

raga; for example, only one R is used. raga; for example, only one R is used. • This rule is based on the current tradition.This rule is based on the current tradition.• Murthy has developed and is currently documenting other Murthy has developed and is currently documenting other

variations possible, with logical explanations to each of hisvariations possible, with logical explanations to each of hisproposal.proposal.

• Murthy has also conjectured the possible reasons for the Murthy has also conjectured the possible reasons for the traditional thinking of the musicologists who have traditional thinking of the musicologists who have developed with their own assumptions.developed with their own assumptions.

Ascending and Descending Ascending and Descending ordersorders• Ascending and descending orders are also Ascending and descending orders are also

defineddefined• aarOhaNa and avarOhaNaaarOhaNa and avarOhaNa• The number of swaras in the ascending order The number of swaras in the ascending order

could be different from the number in the could be different from the number in the descending order.descending order.

• For example, Mohana (Bhoopali in Hindusthani) For example, Mohana (Bhoopali in Hindusthani) has five swaras in the ascending orderhas five swaras in the ascending order

• The descending order has the same five The descending order has the same five swaras.swaras.

• In general, ascending – descending In general, ascending – descending combinations could be 7-7, 6-6, 5-5, 7-6, 7-5, 6-combinations could be 7-7, 6-6, 5-5, 7-6, 7-5, 6-7, 6-5, 5-7 or 5-6.7, 6-5, 5-7 or 5-6.

Linear or Non-Linear ProfileLinear or Non-Linear Profile

• Some ragas have linear ascending and Some ragas have linear ascending and descending orders.descending orders.

• Others have non-linear or crooked (called Others have non-linear or crooked (called vakra ragas) orders, defined as part of the vakra ragas) orders, defined as part of the raga profile.raga profile.

• Please note that the non-linearity guideline Please note that the non-linearity guideline ensures the flow characteristics / loci of ensures the flow characteristics / loci of thethevakra raga.vakra raga.

Characteristic Musical Characteristic Musical CurvesCurves• Characteristic musical curvesCharacteristic musical curves

• Defined as various combinationsDefined as various combinations

• Further the combination groups of the swaras Further the combination groups of the swaras are provided for guideline.are provided for guideline.

• Characteristic curves are provided as aCharacteristic curves are provided as aguideline for the ragaguideline for the raga

• These curves are provided as recommendationsThese curves are provided as recommendationsto enable the musician to invoke the to enable the musician to invoke the `personality' of the raga.`personality' of the raga.

Anchor SwarasAnchor Swaras• Students of classical music are taught the Jeeva Students of classical music are taught the Jeeva

swaras.swaras.• Swaras of the raga are used as anchors to Swaras of the raga are used as anchors to

illustrate the outline of the raga.illustrate the outline of the raga.• The ragas are also modeled to have prime The ragas are also modeled to have prime

anchors, called the Jeeva swaras or Vaadi swarasanchors, called the Jeeva swaras or Vaadi swaras• Sub-prime anchors, called the Hrasva swaras or Sub-prime anchors, called the Hrasva swaras or

Samvaadi swaras.Samvaadi swaras.• This modeling of the ragas dictates that majority This modeling of the ragas dictates that majority

of the musical curves.of the musical curves.• During the expounding and rendition of the raga, During the expounding and rendition of the raga,

the raaga should be centered around three the raaga should be centered around three important anchors:important anchors:

• The Aadhara shruthi or the Shadja shruthi, the The Aadhara shruthi or the Shadja shruthi, the Vaadi and the Samvaadi swaras.Vaadi and the Samvaadi swaras.

NYAASA SWARANYAASA SWARA• Nyaasa swara is the swara with which you finish an Nyaasa swara is the swara with which you finish an

aalapana.aalapana.• Generally in aalapana, the nyaasa swara will be either Generally in aalapana, the nyaasa swara will be either

Shadja orShadja orPanchama.Panchama.

• In raagas like Hindola, which does not have Panchama, it In raagas like Hindola, which does not have Panchama, it may be Madhyama also.may be Madhyama also.

• Aalapana is composed of many units.Aalapana is composed of many units.• During the elaboration of the raaga, the different phrases During the elaboration of the raaga, the different phrases

converge in a nyaasa swara. In other compositions like converge in a nyaasa swara. In other compositions like songs or kritis, the swara with which the composition is songs or kritis, the swara with which the composition is finished is the nyaasa swara.finished is the nyaasa swara.

• Broadly 'Nyaasa' means finish.Broadly 'Nyaasa' means finish.• Venkatamakhi, the author of Chaturdhandi Prakaashikam Venkatamakhi, the author of Chaturdhandi Prakaashikam

terms it as Vidari and Mukthaayiterms it as Vidari and Mukthaayi• Especially to connote the last part of the presentation of the Especially to connote the last part of the presentation of the

raaga, applicable to aalaapana and compositions / songs.raaga, applicable to aalaapana and compositions / songs.

GamakaGamaka

• The transgression from a swara to the next one in The transgression from a swara to the next one in the scale during rendition and expounding of the the scale during rendition and expounding of the raga should not be simply with the help of linear raga should not be simply with the help of linear movement.movement.

• Instead, the transgression should be performed Instead, the transgression should be performed employing a variety of musical curves.employing a variety of musical curves.

• The transgression curves employed should ensure The transgression curves employed should ensure that the raga is clearly distinguishable from other that the raga is clearly distinguishable from other ragas with similar loci.ragas with similar loci.

• In fact, all the ragas are defined with distinction of In fact, all the ragas are defined with distinction of characteristic transgression loci between its swaras.characteristic transgression loci between its swaras.

• These transgressions are called Gamakas These transgressions are called Gamakas

Varjya SwarasVarjya Swaras

• The only requirement is that the The only requirement is that the transgression between the swaras transgression between the swaras should ensure that the locus of the should ensure that the locus of the musical curve does not dwell on Varjya musical curve does not dwell on Varjya swaraswara

• This is the swara to be avoided as This is the swara to be avoided as defined for the raga.defined for the raga.

Suite of Musical LociSuite of Musical Loci

• Profile of the raga comes to life by capably Profile of the raga comes to life by capably employing a suite of loci of musical curves employing a suite of loci of musical curves provided as guidelines by examples and carriedprovided as guidelines by examples and carriedon by tradition used to expound the raga.on by tradition used to expound the raga.

• It should be noted that musicians have It should be noted that musicians have improvised and discovered through explorations improvised and discovered through explorations the different characteristics of ragas through the different characteristics of ragas through out the past centuries, albeit some resistance out the past centuries, albeit some resistance from traditionalists.from traditionalists.

Scientific ApproachScientific Approach• The theoretical foundations of Indian classical music are veryThe theoretical foundations of Indian classical music are very

scientific in nature.scientific in nature.• Even though most of the musicians do not understand / practice, and Even though most of the musicians do not understand / practice, and

are unable to reinforce the scientific basics to their students.are unable to reinforce the scientific basics to their students.• So the integrity of the musical knowledge, and its transmission to So the integrity of the musical knowledge, and its transmission to

succeeding generations, has suffered from poorly realized and succeeding generations, has suffered from poorly realized and observed foundations.observed foundations.

• In addition, the tradition of classical music has failed to utilize many In addition, the tradition of classical music has failed to utilize many useful techniques available in the modern world.useful techniques available in the modern world.

• For example, two-dimensional graphs used in many facets of modern For example, two-dimensional graphs used in many facets of modern world have not been attempted for documenting, and as teaching world have not been attempted for documenting, and as teaching aids, of Indian classical music.aids, of Indian classical music.

• An X-Y plot with time on the X-axis, and frequency on the Y-axis An X-Y plot with time on the X-axis, and frequency on the Y-axis would bewould bevery helpful for students to visualize the ascending / descendingvery helpful for students to visualize the ascending / descendingorders, musical curves and comparison of ragas.orders, musical curves and comparison of ragas.

• Talas can also be very well displayed on graphs. Computers, music Talas can also be very well displayed on graphs. Computers, music synthesizers, and electronic keyboards with MIDI interface will be synthesizers, and electronic keyboards with MIDI interface will be very handy in such endeavors.very handy in such endeavors.

Current Music TeachingCurrent Music Teaching

• Teachers of Indian classical music have been Teachers of Indian classical music have been following the tradition of teaching the musical following the tradition of teaching the musical scale, and ragas based on discrete swaras.scale, and ragas based on discrete swaras.

• In effect, the teaching tradition is based on In effect, the teaching tradition is based on piece-wise linear approximation of the musical piece-wise linear approximation of the musical curves.curves.

• The ragas are also taught with the Aadhara The ragas are also taught with the Aadhara Shruthi used as the paramount anchor for the Shruthi used as the paramount anchor for the raga.raga.

Another ApproachAnother Approach• An alternate approach would be to introduce the An alternate approach would be to introduce the

students to a "toolstudents to a "toolkit" of musical curves with out any apparent Aadhara kit" of musical curves with out any apparent Aadhara Shruthi.Shruthi.

• The curves would be taught as Shruthi-independent The curves would be taught as Shruthi-independent repertoire, to be used in various combinations to sing repertoire, to be used in various combinations to sing or play music.or play music.

• The tool kit is used to make the student functional. The tool kit is used to make the student functional. • The theoretical foundations are taught after the The theoretical foundations are taught after the

student is taught the skills to reproduce musical student is taught the skills to reproduce musical curves, and also after gaining the ability to creatively curves, and also after gaining the ability to creatively expound withexpound withthe foundations of the "tool kit".the foundations of the "tool kit".

Invoke the child in youInvoke the child in you

• To illustrate the approach, let us understand the way a child To illustrate the approach, let us understand the way a child learnslearnslanguage.language.

• A child learns to speak by imitating sounds, words andA child learns to speak by imitating sounds, words andexpressions from other children and adults.expressions from other children and adults.

• We do not teach the child alphabets of a language first, and then We do not teach the child alphabets of a language first, and then words with meanings, and then sentences.words with meanings, and then sentences.

• It would be a strange world if we attempted such techniques at all.It would be a strange world if we attempted such techniques at all.• The child would be able to speak fluently, before it learns any The child would be able to speak fluently, before it learns any

alphabets.alphabets.• Script is used as a communication tool in school, work and Script is used as a communication tool in school, work and

throughout life.throughout life.• If we can imagine the words and phrases of a language to be If we can imagine the words and phrases of a language to be

similar to musical curves and their combinations in the world of similar to musical curves and their combinations in the world of music, my suggested approach becomes clear.music, my suggested approach becomes clear.

Murthy’s DiagramMurthy’s Diagram• This illustration in the diagram uses a clock This illustration in the diagram uses a clock

analogy to demonstrate a number coding concept analogy to demonstrate a number coding concept for the raagas.for the raagas.

• The lower Shadja is denoted by 0 (Zero), where as The lower Shadja is denoted by 0 (Zero), where as the higher Shadja is denoted by 12. the higher Shadja is denoted by 12.

• Raagas are coded for the swaras in the raaga with Raagas are coded for the swaras in the raaga with the number difference between the adjacent the number difference between the adjacent swaras.swaras.

• Murthy has created this with only two each of R, G, Murthy has created this with only two each of R, G, M, D, and N to make it easy for playing keyboard M, D, and N to make it easy for playing keyboard or harmonium.or harmonium.

• An expanded version can be created for a An expanded version can be created for a ShatSruthi system, a system with SIX each of R, G, ShatSruthi system, a system with SIX each of R, G, M, D and N, with one Panchama.M, D and N, with one Panchama.

Mohana ExampleMohana Example• I have shown the middle, lower and upper octaves.I have shown the middle, lower and upper octaves.• The students may imagine and comprehend that the raaga (and The students may imagine and comprehend that the raaga (and

its profile remainsits profile remainsintact) is same in the lower and upper octaves also, just that the intact) is same in the lower and upper octaves also, just that the scale is different.scale is different.

• The diagram shows the corresponding keys for western scale, The diagram shows the corresponding keys for western scale, with C used for Shadja.with C used for Shadja.

• Please note that Indian scale uses relative positions, unlike the Please note that Indian scale uses relative positions, unlike the western scale using fixed keys.western scale using fixed keys.

Example of Mohana (Bhoopali) is shown below:Example of Mohana (Bhoopali) is shown below:

Out of the 12 key octave of S R1 R2 G1 G2 M1 M2 P D1 D2 N1 N2 Out of the 12 key octave of S R1 R2 G1 G2 M1 M2 P D1 D2 N1 N2 S, only five notes S, R2, G2, P, D, S (Higher Octave) are used. It is S, only five notes S, R2, G2, P, D, S (Higher Octave) are used. It is a raaga with same swaras in ascending and descending orders.a raaga with same swaras in ascending and descending orders.

Mohana or Bhoopali RaagaMohana or Bhoopali Raaga

S R2 G2 P D SS R2 G2 P D S0 2 2 3 2 3 (12)0 2 2 3 2 3 (12)

Shruthi PallataShruthi Pallata• Please note that the total of the codes is Please note that the total of the codes is

always 12.always 12.

• Therefore we only need to code swaras Therefore we only need to code swaras other than Shadja! Mohana can be coded or other than Shadja! Mohana can be coded or noted as 022323 or simply 2232 leaving out noted as 022323 or simply 2232 leaving out the S (Shadja) boundaries.the S (Shadja) boundaries.

• After doing Aadhaara Sruthi pallata (or After doing Aadhaara Sruthi pallata (or rotation in the clockwise by one next rotation in the clockwise by one next swara), you can get the following swara), you can get the following combination of ragas: 2323combination of ragas: 2323(SR2M1PN1); 3232 (SG1M1D1N1); 3223 (SR2M1PN1); 3232 (SG1M1D1N1); 3223 (SG1M1PN1) (back to the starting point).(SG1M1PN1) (back to the starting point).

PHYSICS BEHIND MUSICPHYSICS BEHIND MUSIC• It is very important to understand that the ratio of It is very important to understand that the ratio of

the frequenciesthe frequencies(pitch) for any swara in an octave (scale) or (pitch) for any swara in an octave (scale) or Sthaayee and theSthaayee and therespectve swara in the lower ocative (scale) or respectve swara in the lower ocative (scale) or Sthaayee is TWOSthaayee is TWO

• In other words, the frequency doubles from one In other words, the frequency doubles from one octave (Sthaayee) to the higher octave (Sthaayee)octave (Sthaayee) to the higher octave (Sthaayee)

• It is very important to realize that the frequency It is very important to realize that the frequency scale is NOT linear.scale is NOT linear.

• This means that the arithmetic frequency This means that the arithmetic frequency differences between any key and its next key differences between any key and its next key keeps on increasing as you move up the scale or keeps on increasing as you move up the scale or pitch.pitch.

Human Ear and Non-Human Ear and Non-LinearityLinearity

• Human ear does not realize the non-linearity of the scale. Human ear does not realize the non-linearity of the scale. Therefore,Therefore,we may assume (or feel that) that the Rishabha swara.we may assume (or feel that) that the Rishabha swara.

• For example, is divided into parts to make up R1 and R2 (or For example, is divided into parts to make up R1 and R2 (or more parts in the case of shatshruthi system).more parts in the case of shatshruthi system).

• Similarly, we may feel that Gaandhaara, Dhaivatha and Similarly, we may feel that Gaandhaara, Dhaivatha and Nishaadha are made of two or more parts, and that the Nishaadha are made of two or more parts, and that the Madhyama is made into two parts - Shudha and Prathi Madhyama is made into two parts - Shudha and Prathi Madhyama (M1 and M2).Madhyama (M1 and M2).

• It is very important to realize that the two Madhyamas are asIt is very important to realize that the two Madhyamas are asdistinct from each other as Panchama is from lower Dhaivatha.distinct from each other as Panchama is from lower Dhaivatha.

• In summary, the twelve swaras, played on a keyboard, are In summary, the twelve swaras, played on a keyboard, are distinct from each other, except for the non-linear frequency distinct from each other, except for the non-linear frequency nature of the musical scale.nature of the musical scale.

Nyaasa SwaraNyaasa Swara• Examples: In aalaapana of raaga Abhogi, the Examples: In aalaapana of raaga Abhogi, the

artist ends phrases inartist ends phrases inMadhyama:Madhyama:

• DMGRGM,SDRSDM....RGRRSRSSDSDM...DMGRGM,SDRSDM....RGRRSRSSDSDM...M (Nadhyama) is nyaasa swara.M (Nadhyama) is nyaasa swara.

• Similarly, D (Dhaivatha) will be the nyaasa swara, Similarly, D (Dhaivatha) will be the nyaasa swara, if the phrases endif the phrases endin D, like:in D, like:

• GMDSD, SRGSRSD,MDSDMGRGMD,GRSRDSDMD...GMDSD, SRGSRSD,MDSDMGRGMD,GRSRDSDMD...• The swara at which the aalaapana ends finally is The swara at which the aalaapana ends finally is

also called a Nyaasa swara.also called a Nyaasa swara.• Similarly, the swara at which a kriti, keerthana or Similarly, the swara at which a kriti, keerthana or

any compositionany compositionends is the nyasa swara.ends is the nyasa swara.

Western and Indian ScaleWestern and Indian Scale

• The table gives approximate comparisons between The table gives approximate comparisons between the Western scale and the two Indian scales, with the Western scale and the two Indian scales, with their names.their names.

• I have shown C as an equivalent to SaI have shown C as an equivalent to Sa• However, unlike the western system, a swara doesHowever, unlike the western system, a swara does

not refer to a given key. not refer to a given key. • You should read the table as "if we choose to use C You should read the table as "if we choose to use C

as Sa".as Sa".• I have given the full name of the swaras:I have given the full name of the swaras:• Ri =Rishabha; Ga = Gaandhaara; Ma = Madhyama; Ri =Rishabha; Ga = Gaandhaara; Ma = Madhyama;

Pa = Panchama; Dha =Dhaivatha; Ni = Nishaadha.Pa = Panchama; Dha =Dhaivatha; Ni = Nishaadha.

Special Gift of the Human Special Gift of the Human EarEar• We recognize sound / music patterns or curves which are really We recognize sound / music patterns or curves which are really

logarithmically magnified as one goes up the scale as `linear'. logarithmically magnified as one goes up the scale as `linear'. • Therefore a musical curve in any octave isTherefore a musical curve in any octave is

perceived similar as the one higher up in scale, even though it is aperceived similar as the one higher up in scale, even though it is amagnified version. Let us think of an analogy. A mountain rangemagnified version. Let us think of an analogy. A mountain rangestarting from a point close to a viewer and spread away from thestarting from a point close to a viewer and spread away from theviewer with many mountains of different sizes may look similar inviewer with many mountains of different sizes may look similar inshape. A small mountain closer may look similar in size (and shape)shape. A small mountain closer may look similar in size (and shape)to a larger mountain farther away from the viewer. This ability ofto a larger mountain farther away from the viewer. This ability ofpattern recognition and especially `automatic' size and shapepattern recognition and especially `automatic' size and shapeadjustment is probably the ability of the brain common to processingadjustment is probably the ability of the brain common to processinginformation from all our sense organs like ear, eye, tongue, skin andinformation from all our sense organs like ear, eye, tongue, skin andnose. Thanks for the gift of the brain's differential amplifier likenose. Thanks for the gift of the brain's differential amplifier likepost processing, for otherwise, we could not function in this worldpost processing, for otherwise, we could not function in this worldas well as we are coping now.as well as we are coping now.

In summary, the brain enables us to appreciate the combination of theIn summary, the brain enables us to appreciate the combination of thesound and silence, punctuating each other, and also the frequencysound and silence, punctuating each other, and also the frequencycurves mapped from a logarithmic scale to a liner scale; the resultcurves mapped from a logarithmic scale to a liner scale; the resultis music. Music is nothing but dancing sound variations; many timesis music. Music is nothing but dancing sound variations; many timesit is a choreography of multitudes of sounds (tones – the personalityit is a choreography of multitudes of sounds (tones – the personalityof the sound) in the pasture of our ear-brain platform / stage.of the sound) in the pasture of our ear-brain platform / stage.

Bilawal DhaatBilawal Dhaat

Khamaaj DhaatKhamaaj Dhaat

Kafi DhaatKafi Dhaat

Aasaavari DhaatAasaavari Dhaat

Bhairavi DhaatBhairavi Dhaat

Bhairav DhaatBhairav Dhaat

Kalyaan DhaatKalyaan Dhaat

Maarva DhaatMaarva Dhaat

Poorvi DhaatPoorvi Dhaat

ToDi DhaatToDi Dhaat

More thaatsMore thaats

• There are problems whenever one is talking There are problems whenever one is talking about the number of about the number of thaatsthaats..

• Generally only ten are acknowledged; twenty are Generally only ten are acknowledged; twenty are in common usage.in common usage.

• 32 are possible given present concepts of scale 32 are possible given present concepts of scale construction.construction.

• This has created a lot of confusion in north Indian This has created a lot of confusion in north Indian pedagogy.pedagogy.

• Three common scales which are not part of the Three common scales which are not part of the ten ten thaatsthaats are are AhirAhir BhairavBhairav, , CharukesiCharukesi, or , or KiruvaniKiruvani..

Regions of Indian StylesRegions of Indian Styles

Mohana - BhoopMohana - Bhoop

Raga MohanaRaga : Mohana

Mela: Harikambhoji - Mela 28 Other Names: Mohanam; Bhoop (Hindustani); Regupti ( Tamil Pan)

Arohana:    S R2 G2 P D2 S     || S Ri Gu Pa Dhi S Avarohana: S D2 P G2 R1 S || S Dhi Pa Gu Ra S

References: Sancharas: DP,,GPD_PGR RGPDSD GPD_S RSSDDPG GPD_

PDS DSR_GRGPGRS  DGRGSR DRSD_ PGPDSD_P GPD_PGR GRPGR_S-RSd_Pd_s

Mohana - BhoopMohana - Bhoop

• RasaRasa: Vira, Kroda, Challenge : Vira, Kroda, Challenge Time:Time:Night Night

• Jeeva SwaraJeeva Swara: R, G, D : R, G, D Amsa Swaras:Amsa Swaras: G, P G, P Graha Swaras :Graha Swaras : G, P, D G, P, D

• Special Considerations: Special Considerations: Gamakas for all swaras. Gamakas for all swaras. Found in Chinese, Japanese and Swedish music Found in Chinese, Japanese and Swedish music

• Murchanakaraka Ragas:         Murchanakaraka Ragas:         R-> Madhyamati; R-> Madhyamati;                                             P -> Hindolam;                                             P -> Hindolam;                                             G -> Sudha Saveri;                                             G -> Sudha Saveri;                                             D ->                                             D -> Udayaravichandrika Udayaravichandrika