2. The Wonder of the Human Ear (and the brain)The Wonder of the Human Ear (and the brain)
• Human ear is unique, especially when combined with theHuman 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 to
the 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 sense
a sound pitch with respect to other sound pitches that are multiplesa sound pitch with respect to other sound pitches that are multiples
of 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, four
times, eight times … and so on (to include all powers of two) soundtimes, eight times … and so on (to include all powers of two) sound
similar, except for recognizing that they are all part of a frequencysimilar, except for recognizing that they are all part of a frequency
scale.scale.
• They are called harmonics in Physics.They are called harmonics in Physics.
• The frequency space between a frequency F and 2F is called anThe frequency space between a frequency F and 2F is called an
octave.octave.
• The wonder that our ears can uniquely recognize this fact helps usThe wonder that our ears can uniquely recognize this fact helps us
to enjoy (or intuitively `understand') music.to enjoy (or intuitively `understand') music.
3. 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 it isWe would not differentiate or recognize that there is sound, unless it is
punctuated by silence.punctuated by silence.
• The reason is that our eye-brain combination is a very good differentialThe reason is that our eye-brain combination is a very good differential
amplifier.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 differentialEvery time the sound is punctuated by silence, our ear-brain differential
amplifier is able to sense the `ups and downs'.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 `ignore' theOur ear-brain combination has been gifted to conveniently `ignore' the
background sound as noisebackground sound as noise
• All of us do not even realize that is always some background sound / noise,All of us do not even realize that is always some background sound / noise,
but think that there is silence.but think that there is silence.
4. Nonlinear ScaleNonlinear Scale
• The frequency space between successive octaves keepsThe frequency space between successive octaves keeps
on increasing logarithmically (to the base of 2) as you goon increasing logarithmically (to the base of 2) as you go
up the sound / music scale.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 is 4F-Where as the frequency space in the next octave is 4F-
2F=2F2F=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 soundHowever. our ear-brain combination perceives the sound
scale or the music scale as linear even.scale or the music scale as linear even.
5. The Swaras with in an OctaveThe Swaras with in an Octave
• The octave is divided into many parts, obviously in a non-linearThe octave is divided into many parts, obviously in a non-linear
scale.scale.
• For example, in a piano, which is made of discrete keys, theFor example, in a piano, which is made of discrete keys, the
octave 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) countingIf you take any key of your choice and move up (or down) counting
one key at a time (to include both white and black keys), you willone key at a time (to include both white and black keys), you will
reach the next octave when you reach the13th key.reach the next octave when you reach 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, and
so on.so on.
• The 13th key is the starting point of the next octave. You canThe 13th key is the starting point of the next octave. You can
do this on an electronic keyboard, harmonium or accordion.do this on an electronic keyboard, harmonium or accordion.
6. Non-Linear with in and between theNon-Linear with in and between the
OctavesOctaves
• 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 or
western 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 of
Indian music.Indian music.
• Let us take the Indian music scale from the perspective of the seven swarasLet us take the Indian music scale from the perspective of the seven swaras
• The saptha (means seven): sa, ri, ga, ma, pa, dha. ni, (Sa the beginning ofThe saptha (means seven): sa, ri, ga, ma, pa, dha. ni, (Sa the beginning of
the next octave).the next octave).
• The frequency space between ri and sa is smaller than theThe frequency space between ri and sa is smaller than the
frequency space between ga and rifrequency space between ga and ri
• Which is further smaller than the frequency space between ma and ga, andWhich is further smaller than the frequency space between ma and ga, and
so on.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 isThe frequency space between ga and ri (for example) in any octave is
smaller than the frequency space between ga and ri in the higher octave.smaller than the frequency space between ga and ri in the higher octave.
7. Non-Linearity in Music InstrumentsNon-Linearity in Music Instruments
• We see the non-linearity in some musical instruments, where as we do not see themWe see the non-linearity in some musical instruments, where as we do not see them
obvious in others.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 other.The keys look in shape and color exactly same as you go from one end to 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 one goesThis is because the string length required to go up in frequency reduces as one goes
up the scale.up the scale.
• If you look at the flute construction, the size of the flute keeps reducing (non-linearly)If you look at the flute construction, the size of the flute keeps reducing (non-linearly)
as you go up in the frequency.as you go up in the frequency.
8. With in the OctaveWith in the Octave
• The starting point of the octave (or beginning of one octave scale)The starting point of the octave (or beginning of one octave scale)
is called the Shadja.is called the Shadja.
• Here the Devanaagari letter for `Sha' is different from the one usedHere the Devanaagari letter for `Sha' is different from the one used
for the word Shankara.for the word Shankara.
• Unfortunately,English alphabets, being only 26, are inadequate toUnfortunately,English alphabets, being only 26, are inadequate to
write Devanaagari (Sanskrit based) alphabets.write Devanaagari (Sanskrit based) alphabets.
• An easy way for me is to give you examples from English words.An easy way for me is to give you examples from English 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 atBut 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.
9. Shadja – The aadhaara shruthiShadja – The aadhaara shruthi
• 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 `son'.For English speakers, this has the same `sa' part of the sound as in `sun' or `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 octaveKeep in mind that the octave is defined as soon as sa the starting point of the octave
is defined or chosen.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 theIn 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 oneSometimes, I call the remaining swaras (for example - keys in a piano) with any one
of the following words: shruthi, swara, note, key.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?"
10. 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 any
point 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 maintain theHowever, the complete composition (aalaapana or any type of composition) should maintain the
same sasame 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 artist(s).Tamboora is a drone type of instrument providing the scale / octave reference to the 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 maintain theirIt is also considered as a disgrace by many artists, for their `basic' inability to maintain their
performance to a specified scale.performance to a specified scale.
• There are cases when some artists may `slip' (out of little lapse of control or even beingThere 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.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 classical music, byThis discipline has become a tradition (and indeed a great tradition) in Indian classical music, by
sanctifying the importance of Shadja and indeed the rigid framework of thesanctifying the importance of Shadja and indeed the rigid framework of the
complete scale.complete scale.
11. 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 FlatThey are assigned the remaining seven either as Sharp (denoted by #) or Flat
(denoted by a small letter next to the Capital letter).(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.
12. Karnaatak – Western – HindustaaniKarnaatak – Western – Hindustaani
• KarnatakKarnatak WesternWestern NorthNorth
Indian/HindustaniIndian/Hindustani
• sasa (Shadja)(Shadja) CC sasa
• 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
13. Shatshruthi samgeetaShatshruthi samgeeta
• The ancient Indian musicologists defined an octave, with much finerThe ancient Indian musicologists defined an octave, with much finer
graduations in it than the 12 swaras.graduations in it than the 12 swaras.
• Indian classical music has been conceived and modeled with the help of anIndian classical music has been conceived and modeled with the help of an
Adhaara ShruthiAdhaara 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, NiThis includes 6 shruthi-lets of each of the swaras Ri, Ga, Ma, Dha, Ni
• 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 beenFor reasons unknown, Panchama, denoted as Pa or P, has also been
deemed unique.deemed unique.
• Panchama does not have any shruthi-lets or subdivisions, unlike the otherPanchama does not have any shruthi-lets or subdivisions, unlike the other
swaras.swaras.
• Sa and Pa are called the Prakruthi swaras (meaning natural swaras).Sa and Pa are called the Prakruthi swaras (meaning natural swaras).
• The other shruthi-lets of Ri, Ga, Ma, Dha, Ni are called Vikruthi swarasThe other shruthi-lets of Ri, Ga, Ma, Dha, Ni are called Vikruthi swaras
(meaning non-natural swaras).(meaning non-natural swaras).
14. Present Day samgeetaPresent Day samgeeta
• The 6 shruthi-lets are based on the Shat-ShruthiThe 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 IndianHowever, it should be noted that the present day Indian
classical music utilizes only three of the 6 shruthi-letsclassical music utilizes only three of the 6 shruthi-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 byThe 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).
15. 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 orInstruments like piano, electronic keyboard, accordion or
harmonium use the Western scale simplification with S, R1, R2, G1,harmonium use the Western scale simplification with S, R1, R2, G1,
G2, M1, M2, P, D1, D2, N1, N2, SG2, 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 scale, withThe diagram shows the corresponding keys for western scale, with
C used for Shadja.C used for Shadja.
• Please note that Indian scale uses relative positions, unlikePlease note that Indian scale uses relative positions, unlike
the western scale using fixed keys.the western scale using fixed keys.
16. What is a raaga?What is a raaga?
• A raga is reduced to a suite of loci of musical curvesA raga is reduced to a suite of loci of musical curves
• Based on swaras (chosen shruthis ) in specifiedBased on swaras (chosen shruthis ) in specified
ascending and descending orders.ascending and descending orders.
• The real raga is based on multitudes of musical curveThe real raga is based on multitudes of musical curve
combinationscombinations
• The curves of the raga are thus reduced to piece-wiseThe curves of the raga are thus reduced to piece-wise
linear approximations of the real / ideal musical curves.linear approximations of the real / ideal musical curves.
• Definition and profile concepts of raga is complexDefinition and profile concepts of raga is complex
17. 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 raga; forOnly one of the swara-lets or shruthi-lets may be used in a raga; for
example, only one R is used.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 variationsMurthy has developed and is currently documenting other variations
possible, with logical explanations to each of hispossible, with logical explanations to each of his
proposal.proposal.
• Murthy has also conjectured the possible reasons for the traditionalMurthy has also conjectured the possible reasons for the traditional
thinking of the musicologists who have developed with their ownthinking of the musicologists who have developed with their own
assumptions.assumptions.
18. Ascending and Descending ordersAscending and Descending orders
• Ascending and descending orders are alsoAscending and descending orders are also
defineddefined
• aarOhaNa and avarOhaNaaarOhaNa and avarOhaNa
• The number of swaras in the ascending orderThe number of swaras in the ascending order
could be different from the number in thecould 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 swaras.The descending order has the same five swaras.
• In general, ascending – descendingIn 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.
19. Linear or Non-Linear ProfileLinear or Non-Linear Profile
• Some ragas have linear ascending andSome ragas have linear ascending and
descending orders.descending orders.
• Others have non-linear or crooked (called vakraOthers have non-linear or crooked (called vakra
ragas) orders, defined as part of the raga profile.ragas) orders, defined as part of the raga profile.
• Please note that the non-linearity guidelinePlease note that the non-linearity guideline
ensures the flow characteristics / loci of theensures the flow characteristics / loci of the
vakra raga.vakra raga.
20. Characteristic Musical CurvesCharacteristic Musical Curves
• Characteristic musical curvesCharacteristic musical curves
• Defined as various combinationsDefined as various combinations
• Further the combination groups of the swarasFurther the combination groups of the swaras
are provided for guideline.are provided for guideline.
• Characteristic curves are provided as aCharacteristic curves are provided as a
guideline for the ragaguideline for the raga
• These curves are provided as recommendationsThese curves are provided as recommendations
to enable the musician to invoke the `personality'to enable the musician to invoke the `personality'
of the raga.of the raga.
21. Anchor SwarasAnchor Swaras
• Students of classical music are taught the Jeeva swaras.Students of classical music are taught the Jeeva swaras.
• Swaras of the raga are used as anchors to illustrate theSwaras of the raga are used as anchors to illustrate the
outline of the raga.outline of the raga.
• The ragas are also modeled to have prime anchors,The ragas are also modeled to have prime anchors,
called the Jeeva swaras or Vaadi swarascalled the Jeeva swaras or Vaadi swaras
• Sub-prime anchors, called the Hrasva swaras orSub-prime anchors, called the Hrasva swaras or
Samvaadi swaras.Samvaadi swaras.
• This modeling of the ragas dictates that majority of theThis modeling of the ragas dictates that majority of the
musical curves.musical curves.
• During the expounding and rendition of the raga, theDuring the expounding and rendition of the raga, the
raaga should be centered around three importantraaga should be centered around three important
anchors:anchors:
• The Aadhara shruthi or the Shadja shruthi, the Vaadi andThe Aadhara shruthi or the Shadja shruthi, the Vaadi and
the Samvaadi swaras.the Samvaadi swaras.
22. NYAASA SWARANYAASA SWARA
• Nyaasa swara is the swara with which you finish an aalapana.Nyaasa swara is the swara with which you finish an aalapana.
• Generally in aalapana, the nyaasa swara will be either Shadja orGenerally in aalapana, the nyaasa swara will be either Shadja or
Panchama.Panchama.
• In raagas like Hindola, which does not have Panchama, it may beIn raagas like Hindola, which does not have Panchama, it may be
Madhyama also.Madhyama also.
• Aalapana is composed of many units.Aalapana is composed of many units.
• During the elaboration of the raaga, the different phrases convergeDuring the elaboration of the raaga, the different phrases converge
in a nyaasa swara. In other compositions like songs or kritis, thein a nyaasa swara. In other compositions like songs or kritis, the
swara with which the composition is finished is the nyaasa swara.swara with which the composition is finished is the nyaasa swara.
• Broadly 'Nyaasa' means finish.Broadly 'Nyaasa' means finish.
• Venkatamakhi, the author of Chaturdhandi Prakaashikam terms itVenkatamakhi, the author of Chaturdhandi Prakaashikam terms it
as Vidari and Mukthaayias Vidari and Mukthaayi
• Especially to connote the last part of the presentation of the raaga,Especially to connote the last part of the presentation of the raaga,
applicable to aalaapana and compositions / songs.applicable to aalaapana and compositions / songs.
23. GamakaGamaka
• The transgression from a swara to the next one in theThe transgression from a swara to the next one in the
scale during rendition and expounding of the raga shouldscale during rendition and expounding of the raga should
not be simply with the help of linear movement.not be simply with the help of linear movement.
• Instead, the transgression should be performedInstead, the transgression should be performed
employing a variety of musical curves.employing a variety of musical curves.
• The transgression curves employed should ensure thatThe transgression curves employed should ensure that
the raga is clearly distinguishable from other ragas withthe raga is clearly distinguishable from other ragas with
similar loci.similar loci.
• In fact, all the ragas are defined with distinction ofIn 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 GamakasThese transgressions are called Gamakas
24. Varjya SwarasVarjya Swaras
• The only requirement is that theThe only requirement is that the
transgression between the swaras shouldtransgression between the swaras should
ensure that the locus of the musical curveensure that the locus of the musical curve
does not dwell on Varjya swaradoes not dwell on Varjya swara
• This is the swara to be avoided as definedThis is the swara to be avoided as defined
for the raga.for the raga.
25. Suite of Musical LociSuite of Musical Loci
• Profile of the raga comes to life by capablyProfile of the raga comes to life by capably
employing a suite of loci of musical curvesemploying a suite of loci of musical curves
provided as guidelines by examples and carriedprovided as guidelines by examples and carried
on by tradition used to expound the raga.on by tradition used to expound the raga.
• It should be noted that musicians haveIt should be noted that musicians have
improvised and discovered through explorationsimprovised and discovered through explorations
the different characteristics of ragas through outthe different characteristics of ragas through out
the past centuries, albeit some resistance fromthe past centuries, albeit some resistance from
traditionalists.traditionalists.
26. 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 areEven though most of the musicians do not understand / practice, and are
unable to reinforce the scientific basics to their students.unable to reinforce the scientific basics to their students.
• So the integrity of the musical knowledge, and its transmission toSo the integrity of the musical knowledge, and its transmission to
succeeding generations, has suffered from poorly realized and observedsucceeding generations, has suffered from poorly realized and observed
foundations.foundations.
• In addition, the tradition of classical music has failed to utilize many usefulIn addition, the tradition of classical music has failed to utilize many useful
techniques available in the modern world.techniques available in the modern world.
• For example, two-dimensional graphs used in many facets of modern worldFor example, two-dimensional graphs used in many facets of modern world
have not been attempted for documenting, and as teaching aids, of Indianhave not been attempted for documenting, and as teaching aids, of Indian
classical music.classical music.
• An X-Y plot with time on the X-axis, and frequency on the Y-axis would beAn X-Y plot with time on the X-axis, and frequency on the Y-axis would be
very helpful for students to visualize the ascending / descendingvery helpful for students to visualize the ascending / descending
orders, musical curves and comparison of ragas.orders, musical curves and comparison of ragas.
• Talas can also be very well displayed on graphs. Computers, musicTalas can also be very well displayed on graphs. Computers, music
synthesizers, and electronic keyboards with MIDI interface will be verysynthesizers, and electronic keyboards with MIDI interface will be very
handy in such endeavors.handy in such endeavors.
27. Current Music TeachingCurrent Music Teaching
• Teachers of Indian classical music have beenTeachers of Indian classical music have been
following the tradition of teaching the musicalfollowing 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 onIn effect, the teaching tradition is based on
piece-wise linear approximation of the musicalpiece-wise linear approximation of the musical
curves.curves.
• The ragas are also taught with the AadharaThe ragas are also taught with the Aadhara
Shruthi used as the paramount anchor for theShruthi used as the paramount anchor for the
raga.raga.
28. Another ApproachAnother Approach
• An alternate approach would be to introduce the students toAn alternate approach would be to introduce the students to
a "toola "tool
kit" of musical curves with out any apparent Aadhara Shruthi.kit" of musical curves with out any apparent Aadhara Shruthi.
• The curves would be taught as Shruthi-independentThe curves would be taught as Shruthi-independent
repertoire, to be used in various combinations to sing or playrepertoire, to be used in various combinations to sing or play
music.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 student isThe theoretical foundations are taught after the student is
taught the skills to reproduce musical curves, and also aftertaught the skills to reproduce musical curves, and also after
gaining the ability to creatively expound withgaining the ability to creatively expound with
the foundations of the "tool kit".the foundations of the "tool kit".
29. Invoke the child in youInvoke the child in you
• To illustrate the approach, let us understand the way a child learnsTo illustrate the approach, let us understand the way a child learns
language.language.
• A child learns to speak by imitating sounds, words andA child learns to speak by imitating sounds, words and
expressions from other children and adults.expressions from other children and adults.
• We do not teach the child alphabets of a language first, and thenWe 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 anyThe child would be able to speak fluently, before it learns any
alphabets.alphabets.
• Script is used as a communication tool in school, work andScript 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 similarIf we can imagine the words and phrases of a language to be similar
to musical curves and their combinations in the world of music, myto musical curves and their combinations in the world of music, my
suggested approach becomes clear.suggested approach becomes clear.
30. Murthy’s DiagramMurthy’s Diagram
• This illustration in the diagram uses a clock analogy toThis illustration in the diagram uses a clock analogy to
demonstrate a number coding concept for the raagas.demonstrate a number coding concept for the raagas.
• The lower Shadja is denoted by 0 (Zero), where as theThe lower Shadja is denoted by 0 (Zero), where as the
higher Shadja is denoted by 12.higher Shadja is denoted by 12.
• Raagas are coded for the swaras in the raaga with theRaagas are coded for the swaras in the raaga with the
number difference between the adjacent swaras.number difference between the adjacent swaras.
• Murthy has created this with only two each of R, G, M, D,Murthy has created this with only two each of R, G, M, D,
and N to make it easy for playing keyboard orand N to make it easy for playing keyboard or
harmonium.harmonium.
• An expanded version can be created for a ShatSruthiAn expanded version can be created for a ShatSruthi
system, a system with SIX each of R, G, M, D and N,system, a system with SIX each of R, G, M, D and N,
with one Panchama.with one Panchama.
31. 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 itsThe students may imagine and comprehend that the raaga (and its
profile remainsprofile remains
intact) is same in the lower and upper octaves also, just that the scaleintact) is same in the lower and upper octaves also, just that the scale
is different.is different.
• The diagram shows the corresponding keys for western scale, with CThe diagram shows the corresponding keys for western scale, with C
used for Shadja.used for Shadja.
• Please note that Indian scale uses relative positions, unlike thePlease 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 S,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 aonly five notes S, R2, G2, P, D, S (Higher Octave) are used. It is a
raaga with same swaras in ascending and descending orders.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 S
0 2 2 3 2 3 (12)0 2 2 3 2 3 (12)
32. Shruthi PallataShruthi Pallata
• Please note that the total of the codes is alwaysPlease note that the total of the codes is always
12.12.
• Therefore we only need to code swaras otherTherefore we only need to code swaras other
than Shadja! Mohana can be coded or noted asthan Shadja! Mohana can be coded or noted as
022323 or simply 2232 leaving out the S022323 or simply 2232 leaving out the S
(Shadja) boundaries.(Shadja) boundaries.
• After doing Aadhaara Sruthi pallata (or rotation inAfter doing Aadhaara Sruthi pallata (or rotation in
the clockwise by one next swara), you can getthe clockwise by one next swara), you can get
the following combination of ragas: 2323the following combination of ragas: 2323
(SR2M1PN1); 3232 (SG1M1D1N1); 3223(SR2M1PN1); 3232 (SG1M1D1N1); 3223
(SG1M1PN1) (back to the starting point).(SG1M1PN1) (back to the starting point).
33. PHYSICS BEHIND MUSICPHYSICS BEHIND MUSIC
• It is very important to understand that the ratio of theIt is very important to understand that the ratio of the
frequenciesfrequencies
(pitch) for any swara in an octave (scale) or Sthaayee(pitch) for any swara in an octave (scale) or Sthaayee
and theand the
respectve swara in the lower ocative (scale) or Sthaayeerespectve swara in the lower ocative (scale) or Sthaayee
is TWOis TWO
• In other words, the frequency doubles from one octaveIn other words, the frequency doubles from one octave
(Sthaayee) to the higher octave (Sthaayee)(Sthaayee) to the higher octave (Sthaayee)
• It is very important to realize that the frequency scale isIt is very important to realize that the frequency scale is
NOT linear.NOT linear.
• This means that the arithmetic frequency differencesThis means that the arithmetic frequency differences
between any key and its next key keeps on increasing asbetween any key and its next key keeps on increasing as
you move up the scale or pitch.you move up the scale or pitch.
34. Human Ear and Non-LinearityHuman Ear and Non-Linearity
• Human ear does not realize the non-linearity of the scale. Therefore,Human ear does not realize the non-linearity of the scale. 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 moreFor example, is divided into parts to make up R1 and R2 (or more
parts in the case of shatshruthi system).parts in the case of shatshruthi system).
• Similarly, we may feel that Gaandhaara, Dhaivatha and NishaadhaSimilarly, we may feel that Gaandhaara, Dhaivatha and Nishaadha
are made of two or more parts, and that the Madhyama is made intoare made of two or more parts, and that the Madhyama is made into
two parts - Shudha and Prathi Madhyama (M1 and M2).two parts - Shudha and Prathi 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 as
distinct 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 distinctIn summary, the twelve swaras, played on a keyboard, are distinct
from each other, except for the non-linear frequency nature of thefrom each other, except for the non-linear frequency nature of the
musical scale.musical scale.
35. Nyaasa SwaraNyaasa Swara
• Examples: In aalaapana of raaga Abhogi, the artist endsExamples: In aalaapana of raaga Abhogi, the artist ends
phrases inphrases in
Madhyama: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, if theSimilarly, D (Dhaivatha) will be the nyaasa swara, if the
phrases endphrases end
in D, like:in D, like:
• GMDSD, SRGSRSD,MDSDMGRGMD,GRSRDSDMD...GMDSD, SRGSRSD,MDSDMGRGMD,GRSRDSDMD...
• The swara at which the aalaapana ends finally is alsoThe swara at which the aalaapana ends finally is also
called a Nyaasa swara.called a Nyaasa swara.
• Similarly, the swara at which a kriti, keerthana or anySimilarly, the swara at which a kriti, keerthana or any
compositioncomposition
ends is the nyasa swara.ends is the nyasa swara.
36. Western and Indian ScaleWestern and Indian Scale
• The table gives approximate comparisons between theThe table gives approximate comparisons between the
Western scale and the two Indian scales, with theirWestern scale and the two Indian scales, with their
names.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 asYou should read the table as "if we choose to use C as
Sa".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; PaRi =Rishabha; Ga = Gaandhaara; Ma = Madhyama; Pa
= Panchama; Dha =Dhaivatha; Ni = Nishaadha.= Panchama; Dha =Dhaivatha; Ni = Nishaadha.
37. Special Gift of the Human EarSpecial Gift of the Human Ear
• We recognize sound / music patterns or curves which are really logarithmicallyWe recognize sound / music patterns or curves which are really logarithmically
magnified as one goes up the scale as `linear'.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 a
magnified version. Let us think of an analogy. A mountain rangemagnified version. Let us think of an analogy. A mountain range
starting from a point close to a viewer and spread away from thestarting from a point close to a viewer and spread away from the
viewer with many mountains of different sizes may look similar inviewer with many mountains of different sizes may look similar in
shape. 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 of
pattern recognition and especially `automatic' size and shapepattern recognition and especially `automatic' size and shape
adjustment is probably the ability of the brain common to processingadjustment is probably the ability of the brain common to processing
information from all our sense organs like ear, eye, tongue, skin andinformation from all our sense organs like ear, eye, tongue, skin and
nose. Thanks for the gift of the brain's differential amplifier likenose. Thanks for the gift of the brain's differential amplifier like
post processing, for otherwise, we could not function in this worldpost processing, for otherwise, we could not function in this world
as 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 the
sound and silence, punctuating each other, and also the frequencysound and silence, punctuating each other, and also the frequency
curves mapped from a logarithmic scale to a liner scale; the resultcurves mapped from a logarithmic scale to a liner scale; the result
is music. Music is nothing but dancing sound variations; many timesis music. Music is nothing but dancing sound variations; many times
it is a choreography of multitudes of sounds (tones – the personalityit is a choreography of multitudes of sounds (tones – the personality
of the sound) in the pasture of our ear-brain platform / stage.of the sound) in the pasture of our ear-brain platform / stage.
48. More thaatsMore thaats
• There are problems whenever one is talking about theThere are problems whenever one is talking about the
number ofnumber of thaatsthaats..
• Generally only ten are acknowledged; twenty are inGenerally only ten are acknowledged; twenty are in
common usage.common usage.
• 32 are possible given present concepts of scale32 are possible given present concepts of scale
construction.construction.
• This has created a lot of confusion in north IndianThis has created a lot of confusion in north Indian
pedagogy.pedagogy.
• Three common scales which are not part of the tenThree common scales which are not part of the ten
thaatsthaats areare AhirAhir BhairavBhairav,, CharukesiCharukesi, or, or KiruvaniKiruvani..
50. Mohana - BhoopMohana - Bhoop
Raga Mohana
Raga : 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
51. Mohana - BhoopMohana - Bhoop
• RasaRasa: Vira, Kroda, Challenge: Vira, Kroda, Challenge
Time:Time:NightNight
• Jeeva SwaraJeeva Swara: R, G, D: R, G, D
Amsa Swaras:Amsa Swaras: G, PG, P
Graha Swaras :Graha Swaras : G, P, DG, P, D
• Special Considerations:Special Considerations: Gamakas for all swaras.Gamakas for all swaras.
Found in Chinese, Japanese and Swedish musicFound 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 -> Udayaravichandrika D -> Udayaravichandrika
