Fundamentals of Music

1
Fundamentals of Music

• KRS Murthy

2
The Wonder of the Human Ear (and the brain)

• Human ear is unique, especially when combined
  with the extraordinary processing power of the
  brain
• What is not linear may sound linear tothe human
  ear.
• A very good example is the fact that our brains
  sensea sound pitch with respect to other sound
  pitches that are multiplesof the power of 2
• A pitch and other pitches that are two times,
  fourtimes, eight times and so on (to include
  all powers of two) soundsimilar, except for
  recognizing that they are all part of a
  frequencyscale.
• They are called harmonics in Physics.
• The frequency space between a frequency F and 2F
  is called an octave.
• The wonder that our ears can uniquely recognize
  this fact helps us to enjoy (or intuitively
  understand') music.

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Silence and Sound

• Sound is not alone silence is its companion.
• We would not differentiate or recognize that
  there is sound, unless it is punctuated by
  silence.
• The reason is that our eye-brain combination is a
  very good differential amplifier.
• Therefore, we need silence for resetting our
  differential amplifier'.
• Every time the sound is punctuated by silence,
  our ear-brain differential amplifier is able to
  sense the ups and downs'.
• In fact, there is really nothing like silence in
  nature!
• There are all type of activities in the universe
  all the time
• It includes the earth, the local geography /
  space welive in with sound ambiance constantly
  existing.
• Our ear-brain combination has been gifted to
  conveniently ignore' the background sound as
  noise
• All of us do not even realize that is always some
  background sound / noise, but think that there is
  silence.

4
Nonlinear Scale

• The frequency space between successive octaves
  keeps on increasing logarithmically (to the base
  of 2) as you go up the sound / music scale.
• Frequency space between 2F and F is F
• Where as the frequency space in the next octave
  is 4F-2F2F
• Further octaves 8F-4F4F, 16F-8F8F and so on.
• However. our ear-brain combination perceives the
  sound scale or the music scale as linear even.

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The Swaras with in an Octave

• The octave is divided into many parts, obviously
  in a non-linearscale.
• For example, in a piano, which is made of
  discrete keys, theoctave is made up of 12 keys.
• 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 keys), you will reach the
  next octave when you reach the13th key.
• Remember to count the first key as 1, second key
  as 2, andso on.
• The 13th key is the starting point of the next
  octave. You cando this on an electronic
  keyboard, harmonium or accordion.

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Non-Linear with in and between the Octaves

• Even though I am not planning to jump into the
  concepts of Indian orwestern musical scale yet,
  I want to illustrate a point here.
• Challenging some of the assumptions / foundations
  ofIndian music.
• Let 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 of the next octave).
• The frequency space between ri and sa is smaller
  than thefrequency space between ga and ri
• Which is further smaller than the frequency space
  between ma and ga, and so on.
• This is progressive through out the musical
  scale.
• 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
  octave.

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Non-Linearity in Music Instruments

• We see the non-linearity in some musical
  instruments, where as we do not see them obvious
  in others.
• In 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.
• Of course, you hear it when you play.
• You will also notice it, if you look at the inner
  construction.
• The continuous non-linearity is clearly visible
  in a guitar.
• The frets in a guitar become closer to each other
  as one moves up thescale
• This is in inverse' to the sound generated as
  one moves upthe scale.
• This is because the string length required to go
  up in frequency reduces as one goes up the scale.
• If you look at the flute construction, the size
  of the flute keeps reducing (non-linearly) as you
  go up in the frequency.

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With in the Octave

• The starting point of the octave (or beginning of
  one octave scale)is called the Shadja.
• Here the Devanaagari letter for Sha' is
  different from the one used for the word
  Shankara.
• Unfortunately,English alphabets, being only 26,
  are inadequate to write Devanaagari (Sanskrit
  based) alphabets.
• An easy way for me is to give you examples from
  English words.
• The sha' type of sound in the word fiction'.
• This Sha sound is produced close to the throat
• But NOT the guttural sound you hear in Urdu and
  also NOT at closer to the tip of the tongue.

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Shadja The aadhaara shruthi

• However, the swara Shadja is normally abbreviated
  as sa' whilesinging and writing notations.
• 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.
• Sa is the reference swara, defining the octave
• Keep in mind that the octave is defined as soon
  as sa the starting point of the octave is defined
  or chosen.
• Twice the frequency of sa is the starting point
  of the next octave.
• In Indian music sa is called the aadhaara shruthi
• Shruthi in Sanskrit means a pitch
• In practice, the music teachers in India teach sa
  as THE SHRUTHI, leaving out the word aadhaara.
• 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 one of the
  following words shruthi, swara, note, key.
• Western musicians also refer to the starting
  point of the scale as key', to imply. "Where
  does your scale start?"

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Sanctity of the shruthi

• It is very important to understand that the sa
  can be fixed at anypoint in the frequency scale
  depending on the choice of the artist(s) /
  musician(s).
• However, the complete composition (aalaapana or
  any type of composition) should maintain 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 orconcert by the use
  of tamboora.
• 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
  issaid to have LOST THE SHRUTHI'.
• It is also considered as a disgrace by many
  artists, for their basic' inability to maintain
  their performance to a specified scale.
• 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.
• It is almost as if a gymnast were expected to
  maintain perfect' fitness and never slipout of
  the agility and routine.
• 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 framework of thecomplete
  scale.

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With in the Octave

• The octave is made up of 12 keys.
• The 12 keys / swaras are given names.
• Surprisingly and coincidently, the Western and
  the Indianscales have basically seven names
• Do Re Ma Fa So La Ti - Western Tradition
• Sa Ri Ga Ma Pa Dha Ni - Indian Tradition
• Seven English alphabets A, B, C, D, E, F, G -
  are used in the Western system
• These seven letters (representing the keys are
  called natural.'
• Total of 12 keys are named, as shown in the
  table.
• They are assigned the remaining seven either as
  Sharp (denoted by ) or Flat (denoted by a small
  letter next to the Capital letter).
• For example, F is the key higher to F
• Bb (pronounced as B Flat) is the key lower to
  B.

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Karnaatak Western Hindustaani

• Karnatak Western North Indian/Hindustani
• sa (Shadja) C sa
• Ri (Rishabha) D Flat ri komal
• R2 D Sharp ri tivra
• Ga1 (Gaandhaara) E Flat ga komal
• Ga 2 E Sharp ga tivra
• Ma 1 (Madhyama) F Flat ma komal
• Ma 2 F Sharp ma tivra
• Pa (Panchama) G panchama
• Dha 1(Dhaivatha) A Flat dha komal
• Dha 2 A Sharp dha tivra
• Ni 1 (Nishaadha) B Flat ni komal
• Ni 2 B Sharp ni tivra

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Shatshruthi samgeeta

• The ancient Indian musicologists defined an
  octave, with much finer graduations in it than
  the 12 swaras.
• Indian classical music has been conceived and
  modeled with the help of an Adhaara Shruthi
• 32 intermediate shruthis or swaras in the octave.
• This includes 6 shruthi-lets of each of the
  swaras Ri, Ga, Ma, Dha, Ni
• That is 6X5 30 plus the Sa and Pa Total 32
• For reasons unknown, Panchama, denoted as Pa or
  P, has also been deemed unique.
• Panchama does not have any shruthi-lets or
  subdivisions, unlike the other 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 swaras (meaning non-natural
  swaras).

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Present Day samgeeta

• The 6 shruthi-lets are based on the Shat-Shruthi
  Sangeetha tradition.
• Shat (pronounced like Shut') means six.
• However, it should be noted that the present day
  Indian classical music utilizes only three of the
  6 shruthi-lets
• Ri, Ga, Dha and Ni have three shruthi-lets.
• Ma has only two.
• The meLakartha system, devised and documented by
  the pioneer Venkatamakhi, uses
• S, R1, R2, R3, G1, G2, G3, M1, M2, P, D1,D2, D3,
  N1, N2, N3, S (Shadja of the upper octave).

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Melakarta System

• Venkatamakhi has systematized 72 meLakartha ragas
• These are divided into two halves of 36 raagas
• One set for M1, and the other for M2.
• Instruments like piano, electronic keyboard,
  accordion or harmonium use the Western scale
  simplification with S, R1, R2, G1, G2, M1, M2, P,
  D1, D2, N1, N2, S
• This is a total of 12 swaras (keys) including S
  upper Shadja,denoted by bold letter S
  corresponds to the upper octave.
• The diagram shows the corresponding keys for
  western scale, with C used for Shadja.
• Please note that Indian scale uses relative
  positions, unlikethe western scale using fixed
  keys.

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What is a raaga?

• A raga is reduced to a suite of loci of musical
  curves
• Based on swaras (chosen shruthis ) in specified
  ascending and descending orders.
• The real raga is based on multitudes of musical
  curve combinations
• The curves of the raga are thus reduced to
  piece-wise linear approximations of the real /
  ideal musical curves.
• Definition and profile concepts of raga is
  complex

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Salient points of raaga

• Swaras (5, 6 or 7 taken at a time).
• 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 for example, only one R is used.
• This rule is based on the current tradition.
• Murthy has developed and is currently documenting
  other variations possible, with logical
  explanations to each of hisproposal.
• Murthy has also conjectured the possible reasons
  for the traditional thinking of the musicologists
  who have developed with their own assumptions.

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Ascending and Descending orders

• Ascending and descending orders are also defined
• aarOhaNa and avarOhaNa
• The number of swaras in the ascending order could
  be different from the number in the descending
  order.
• For example, Mohana (Bhoopali in Hindusthani) has
  five swaras in the ascending order
• The descending order has the same five swaras.
• In general, ascending descending combinations
  could be 7-7, 6-6, 5-5, 7-6, 7-5, 6-7, 6-5, 5-7
  or 5-6.

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Linear or Non-Linear Profile

• Some ragas have linear ascending and descending
  orders.
• Others have non-linear or crooked (called vakra
  ragas) orders, defined as part of the raga
  profile.
• Please note that the non-linearity guideline
  ensures the flow characteristics / loci of
  thevakra raga.

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Characteristic Musical Curves

• Characteristic musical curves
• Defined as various combinations
• Further the combination groups of the swaras are
  provided for guideline.
• Characteristic curves are provided as aguideline
  for the raga
• These curves are provided as recommendationsto
  enable the musician to invoke the personality'
  of the raga.

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Anchor Swaras

• Students of classical music are taught the Jeeva
  swaras.
• Swaras of the raga are used as anchors to
  illustrate the outline of the raga.
• The ragas are also modeled to have prime anchors,
  called the Jeeva swaras or Vaadi swaras
• Sub-prime anchors, called the Hrasva swaras or
  Samvaadi swaras.
• This modeling of the ragas dictates that majority
  of the musical curves.
• During the expounding and rendition of the raga,
  the raaga should be centered around three
  important anchors
• The Aadhara shruthi or the Shadja shruthi, the
  Vaadi and the Samvaadi swaras.

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NYAASA SWARA

• Nyaasa swara is the swara with which you finish
  an aalapana.
• Generally in aalapana, the nyaasa swara will be
  either Shadja orPanchama.
• In raagas like Hindola, which does not have
  Panchama, it may be Madhyama also.
• Aalapana is composed of many units.
• During the elaboration of the raaga, the
  different phrases converge in a nyaasa swara. In
  other compositions like songs or kritis, the
  swara with which the composition is finished is
  the nyaasa swara.
• Broadly 'Nyaasa' means finish.
• Venkatamakhi, the author of Chaturdhandi
  Prakaashikam terms it as Vidari and Mukthaayi
• Especially to connote the last part of the
  presentation of the raaga, applicable to
  aalaapana and compositions / songs.

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Gamaka

• The transgression from a swara to the next one in
  the scale during rendition and expounding of the
  raga should not be simply with the help of linear
  movement.
• Instead, the transgression should be performed
  employing a variety of musical curves.
• The transgression curves employed should ensure
  that the raga is clearly distinguishable from
  other ragas with similar loci.
• In fact, all the ragas are defined with
  distinction of characteristic transgression loci
  between its swaras.
• These transgressions are called Gamakas

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Varjya Swaras

• The only requirement is that the transgression
  between the swaras should ensure that the locus
  of the musical curve does not dwell on Varjya
  swara
• This is the swara to be avoided as defined for
  the raga.

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Suite of Musical Loci

• Profile of the raga comes to life by capably
  employing a suite of loci of musical curves
  provided as guidelines by examples and carriedon
  by tradition used to expound the raga.
• It should be noted that musicians have improvised
  and discovered through explorations the different
  characteristics of ragas through out the past
  centuries, albeit some resistance from
  traditionalists.

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Scientific Approach

• The theoretical foundations of Indian classical
  music are veryscientific in nature.
• Even though most of the musicians do not
  understand / practice, and are unable to
  reinforce the scientific basics to their
  students.
• So the integrity of the musical knowledge, and
  its transmission to succeeding generations, has
  suffered from poorly realized and observed
  foundations.
• In addition, the tradition of classical music has
  failed to utilize many useful techniques
  available in the modern world.
• For example, two-dimensional graphs used in many
  facets of modern world have not been attempted
  for documenting, and as teaching aids, of Indian
  classical music.
• An X-Y plot with time on the X-axis, and
  frequency on the Y-axis would bevery helpful for
  students to visualize the ascending /
  descendingorders, musical curves and comparison
  of ragas.
• Talas can also be very well displayed on graphs.
  Computers, music synthesizers, and electronic
  keyboards with MIDI interface will be very handy
  in such endeavors.

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Current Music Teaching

• Teachers of Indian classical music have been
  following the tradition of teaching the musical
  scale, and ragas based on discrete swaras.
• In effect, the teaching tradition is based on
  piece-wise linear approximation of the musical
  curves.
• The ragas are also taught with the Aadhara
  Shruthi used as the paramount anchor for the
  raga.

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Another Approach

• An alternate approach would be to introduce the
  students to a "toolkit" of musical curves with
  out any apparent Aadhara Shruthi.
• The curves would be taught as Shruthi-independent
  repertoire, to be used in various combinations to
  sing or play music.
• The tool kit is used to make the student
  functional.
• The theoretical foundations are taught after the
  student is taught the skills to reproduce musical
  curves, and also after gaining the ability to
  creatively expound withthe foundations of the
  "tool kit".

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Invoke the child in you

• To illustrate the approach, let us understand the
  way a child learnslanguage.
• A child learns to speak by imitating sounds,
  words andexpressions from other children and
  adults.
• We do not teach the child alphabets of a language
  first, and then words with meanings, and then
  sentences.
• 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 alphabets.
• Script is used as a communication tool in school,
  work and throughout life.
• If we can imagine the words and phrases of a
  language to be similar to musical curves and
  their combinations in the world of music, my
  suggested approach becomes clear.

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Murthys Diagram

• This illustration in the diagram uses a clock
  analogy to demonstrate a number coding concept
  for the raagas.
• The lower Shadja is denoted by 0 (Zero), where as
  the higher Shadja is denoted by 12.
• Raagas are coded for the swaras in the raaga with
  the number difference between the adjacent
  swaras.
• Murthy has created this with only two each of R,
  G, M, D, and N to make it easy for playing
  keyboard or harmonium.
• An expanded version can be created for a
  ShatSruthi system, a system with SIX each of R,
  G, M, D and N, with one Panchama.

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Mohana Example

• I have shown the middle, lower and upper octaves.
• The students may imagine and comprehend that the
  raaga (and its profile remainsintact) is same in
  the lower and upper octaves also, just that the
  scale is different.
• The diagram shows the corresponding keys for
  western scale, with C used for Shadja.
• Please note that Indian scale uses relative
  positions, unlike the western scale using fixed
  keys.Example of Mohana (Bhoopali) is shown
  belowOut 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 a raaga
  with same swaras in ascending and descending
  orders.Mohana or Bhoopali RaagaS R2 G2 P D
  S0 2 2 3 2 3 (12)

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Shruthi Pallata

• Please note that the total of the codes is always
  12.
• Therefore we only need to code swaras other than
  Shadja! Mohana can be coded or noted as 022323 or
  simply 2232 leaving out the S (Shadja)
  boundaries.
• After doing Aadhaara Sruthi pallata (or rotation
  in the clockwise by one next swara), you can get
  the following combination of ragas
  2323(SR2M1PN1) 3232 (SG1M1D1N1) 3223
  (SG1M1PN1) (back to the starting point).

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PHYSICS BEHIND MUSIC

• It is very important to understand that the ratio
  of the frequencies(pitch) for any swara in an
  octave (scale) or Sthaayee and therespectve
  swara in the lower ocative (scale) or Sthaayee is
  TWO
• In other words, the frequency doubles from one
  octave (Sthaayee) to the higher octave (Sthaayee)
• It is very important to realize that the
  frequency scale is NOT linear.
• This means that the arithmetic frequency
  differences between any key and its next key
  keeps on increasing as you move up the scale or
  pitch.

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Human Ear and Non-Linearity

• Human ear does not realize the non-linearity of
  the scale. Therefore,we may assume (or feel
  that) that the Rishabha swara.
• For example, is divided into parts to make up R1
  and R2 (or more parts in the case of shatshruthi
  system).
• Similarly, we may feel that Gaandhaara, Dhaivatha
  and Nishaadha are made of two or more parts, and
  that the Madhyama is made into two parts - Shudha
  and Prathi Madhyama (M1 and M2).
• It is very important to realize that the two
  Madhyamas are asdistinct from each other as
  Panchama is from lower Dhaivatha.
• In summary, the twelve swaras, played on a
  keyboard, are distinct from each other, except
  for the non-linear frequency nature of the
  musical scale.

35
Nyaasa Swara

• Examples In aalaapana of raaga Abhogi, the
  artist ends phrases inMadhyama
• DMGRGM,SDRSDM....RGRRSRSSDSDM...M (Nadhyama) is
  nyaasa swara.
• Similarly, D (Dhaivatha) will be the nyaasa
  swara, if the phrases endin D, like
• GMDSD, SRGSRSD,MDSDMGRGMD,GRSRDSDMD...
• The swara at which the aalaapana ends finally is
  also called a Nyaasa swara.
• Similarly, the swara at which a kriti, keerthana
  or any compositionends is the nyasa swara.

36
Western and Indian Scale

• The table gives approximate comparisons between
  the Western scale and the two Indian scales, with
  their names.
• I have shown C as an equivalent to Sa
• However, unlike the western system, a swara
  doesnot refer to a given key.
• You should read the table as "if we choose to use
  C as Sa".
• I have given the full name of the swaras
• Ri Rishabha Ga Gaandhaara Ma Madhyama Pa
  Panchama Dha Dhaivatha Ni Nishaadha.

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Special Gift of the Human Ear

• We recognize sound / music patterns or curves
  which are really logarithmically magnified as one
  goes up the scale as linear'.
• Therefore a musical curve in any octave
  isperceived similar as the one higher up in
  scale, even though it is amagnified version. Let
  us think of an analogy. A mountain rangestarting
  from a point close to a viewer and spread away
  from theviewer with many mountains of different
  sizes may look similar inshape. A small mountain
  closer may look similar in size (and shape)to a
  larger mountain farther away from the viewer.
  This ability ofpattern recognition and
  especially automatic' size and shapeadjustment
  is probably the ability of the brain common to
  processinginformation from all our sense organs
  like ear, eye, tongue, skin andnose. Thanks for
  the gift of the brain's differential amplifier
  likepost processing, for otherwise, we could not
  function in this worldas well as we are coping
  now.In summary, the brain enables us to
  appreciate the combination of thesound and
  silence, punctuating each other, and also the
  frequencycurves mapped from a logarithmic scale
  to a liner scale the resultis music. Music is
  nothing but dancing sound variations many
  timesit is a choreography of multitudes of
  sounds (tones the personalityof the sound) in
  the pasture of our ear-brain platform / stage.

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Bilawal Dhaat
39
Khamaaj Dhaat
40
Kafi Dhaat
41
Aasaavari Dhaat
42
Bhairavi Dhaat
43
Bhairav Dhaat
44
Kalyaan Dhaat
45
Maarva Dhaat
46
Poorvi Dhaat
47
ToDi Dhaat
48
More thaats

• There are problems whenever one is talking about
  the number of thaats.
• Generally only ten are acknowledged twenty are
  in common usage.
• 32 are possible given present concepts of scale
  construction.
• This has created a lot of confusion in north
  Indian pedagogy.
• Three common scales which are not part of the ten
  thaats are Ahir Bhairav, Charukesi, or Kiruvani.

49
Regions of Indian Styles
50
Mohana - Bhoop
Raga Mohana Raga MohanaMela 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 - Bhoop

• Rasa Vira, Kroda, Challenge TimeNight
• Jeeva Swara R, G, D Amsa Swaras G, P Graha
  Swaras G, P, D
• Special Considerations Gamakas for all swaras.
  Found in Chinese, Japanese and Swedish music
• Murchanakaraka Ragas         R-gt Madhyamati
                                              P -gt
  Hindolam                                        
       G -gt Sudha Saveri                          
                     D -gt Udayaravichandrika