Thursday, September 10, 2009
Carnatic Music Lessons 1-3
If you are looking for to know and Learn Carnatic Music, This blog may help you too. Kindly give me your feedback.
Gurukula - Carnatic Music Lessons 2
Gurukula - Carnatic Music Lessons 3
Gurukula - Carnatic Music Lessons 2
Gurukula - Carnatic Music Lessons 3
songs sound...
In general, if two songs sound strikingly similar, the odds are they are based on the same set of notes and thus in the same Ragam. Their basic Ragam is identified typically by pattern recognition, if you are not willing to do detailed decomposition into the constituent keys of their scale.
The basis of Ragams is (1) the use of a restrictive number of keys in an octave (2) go up and down in the octave in a prescribed manner. (3) And yes, throw in the appropriate microtones. These generate specific melodious personalities. The term microtones presents a major difficulty in understanding the totality of the concept 'Ragam'. How exactly can one specify which microtones are involved ? What is the best way to 'notate' the millions of intermediate frequencies ? Instead of getting very analytical about 'microtones' Karnatic music just gets away by omitting a precise definition of a Ragam. In some sense, the 'Arohanam'-'Avarohanam' - this is the ascending sequence and this is the descending order defintion of a Ragam is only an 'operational definition' at best. Since the 'associated microtones' or 'Gamakam' cannot be defined numerically, it has also become fashionable to simply say that a Ragam is a 'Mood' or a feeling or an emotion, if you can even relate to such unmusical terms.
Another way to define a Ragam is by analogy or how it should 'sound' like. And compare it with an established historical 'standard' or 'primitives'. It is always much easier to sing the 'Gamakams' associated with the Ragam - produce the basic patterns - rather than Fourier analyze it. A ragam is alternatively defined in terms of its 'characteristic musical phrases'. These characteristic phrases are called 'Pakads', (in Hindustani music) literally meaning 'catch' phrases.
All these lend a certain amount of mystery to the concept of Ragam. Like blind men trying to figure out an elephant, we are supposed to only know 'a part of the personality' of a ragam. Never its wholeness. We can only know so many 'characteristic phrases' of a ragam, not a complete set of them, even if there exists such a complete set. One song may have twenty of them. Another song in the same ragam might use just ten of them, but a ten other new ones. Musicians are always trying to create newer and newer 'characteristic phrases' to bring out newer and newer aspects of the ragam. One might have thought that they would have composed every possible phrase in the Ragam Shankarabharanam. But people are still making new melodies in this centuries old Ragam ! We will perhaps never run out of tunes in this Ragam.
The easiest way to identify a ragam then is by analogy and trying to figure out if there is a recurring characteristic phrase. Figuring out a Ragam has always been a natural thing for a Karnatic music enthusiast, especially if the Ragam happens to be an obscure one. It is almost like solving a crime. Some of the ragams can be so distinctive that you can recognize them when only two or three notes are played, thanks to the characteristic microtones.
Sometimes, life is not quite simple. Our definitions of the term Ragam may be violated. Some talented musicians might introduce extraneous notes occassionally into a well-defined ragam, for nice musical effect. Such a process is called 'Misra'fying. You can have a ragam Sivaranjani played pure - this is a pentatonic ragam. Or you can have Misra Sivaranjani where you occassionally introduce a sixth or seventh note not prescribed in the definition of the ragam. Note that this requires expertise. If you or I play Sivaranjani and try to Misra-fy it, we may go so far off the original ragam that we might sound horrible - resulting in 'besur' or 'Abaswaram'.
Equally incredibly, we have other violations as well. Ragams like Sindhu Bhairavi and Kapi are often played with many more notes than just the traditional maximum of seven. On the low side, people have laid claims to Ragams with just four notes. Again, let your ears be the judge.
Play some classical sounding music and try to see if any particular Ragam thrills you. Anything that turns you off completely ? Play instrumental or light classical music at first before embarking on a heavy-duty vocal piece. Is there a piece that moves you? Puts you in a sublime mood? Helps you drive your car ? Goes well in the background when you cook?
The reason for asking these questions is to figure out a little bit about the psychoacoustics. While I do not believe that a particular Ragam could inherently be an 'Angry' Ragam or a Midnight Ragam or bring the rains or tame an elephant, Ragams could very well produce individual psycho-acoustical effects.
The basis of Ragams is (1) the use of a restrictive number of keys in an octave (2) go up and down in the octave in a prescribed manner. (3) And yes, throw in the appropriate microtones. These generate specific melodious personalities. The term microtones presents a major difficulty in understanding the totality of the concept 'Ragam'. How exactly can one specify which microtones are involved ? What is the best way to 'notate' the millions of intermediate frequencies ? Instead of getting very analytical about 'microtones' Karnatic music just gets away by omitting a precise definition of a Ragam. In some sense, the 'Arohanam'-'Avarohanam' - this is the ascending sequence and this is the descending order defintion of a Ragam is only an 'operational definition' at best. Since the 'associated microtones' or 'Gamakam' cannot be defined numerically, it has also become fashionable to simply say that a Ragam is a 'Mood' or a feeling or an emotion, if you can even relate to such unmusical terms.
Another way to define a Ragam is by analogy or how it should 'sound' like. And compare it with an established historical 'standard' or 'primitives'. It is always much easier to sing the 'Gamakams' associated with the Ragam - produce the basic patterns - rather than Fourier analyze it. A ragam is alternatively defined in terms of its 'characteristic musical phrases'. These characteristic phrases are called 'Pakads', (in Hindustani music) literally meaning 'catch' phrases.
All these lend a certain amount of mystery to the concept of Ragam. Like blind men trying to figure out an elephant, we are supposed to only know 'a part of the personality' of a ragam. Never its wholeness. We can only know so many 'characteristic phrases' of a ragam, not a complete set of them, even if there exists such a complete set. One song may have twenty of them. Another song in the same ragam might use just ten of them, but a ten other new ones. Musicians are always trying to create newer and newer 'characteristic phrases' to bring out newer and newer aspects of the ragam. One might have thought that they would have composed every possible phrase in the Ragam Shankarabharanam. But people are still making new melodies in this centuries old Ragam ! We will perhaps never run out of tunes in this Ragam.
The easiest way to identify a ragam then is by analogy and trying to figure out if there is a recurring characteristic phrase. Figuring out a Ragam has always been a natural thing for a Karnatic music enthusiast, especially if the Ragam happens to be an obscure one. It is almost like solving a crime. Some of the ragams can be so distinctive that you can recognize them when only two or three notes are played, thanks to the characteristic microtones.
Sometimes, life is not quite simple. Our definitions of the term Ragam may be violated. Some talented musicians might introduce extraneous notes occassionally into a well-defined ragam, for nice musical effect. Such a process is called 'Misra'fying. You can have a ragam Sivaranjani played pure - this is a pentatonic ragam. Or you can have Misra Sivaranjani where you occassionally introduce a sixth or seventh note not prescribed in the definition of the ragam. Note that this requires expertise. If you or I play Sivaranjani and try to Misra-fy it, we may go so far off the original ragam that we might sound horrible - resulting in 'besur' or 'Abaswaram'.
Equally incredibly, we have other violations as well. Ragams like Sindhu Bhairavi and Kapi are often played with many more notes than just the traditional maximum of seven. On the low side, people have laid claims to Ragams with just four notes. Again, let your ears be the judge.
Play some classical sounding music and try to see if any particular Ragam thrills you. Anything that turns you off completely ? Play instrumental or light classical music at first before embarking on a heavy-duty vocal piece. Is there a piece that moves you? Puts you in a sublime mood? Helps you drive your car ? Goes well in the background when you cook?
The reason for asking these questions is to figure out a little bit about the psychoacoustics. While I do not believe that a particular Ragam could inherently be an 'Angry' Ragam or a Midnight Ragam or bring the rains or tame an elephant, Ragams could very well produce individual psycho-acoustical effects.
Some other ragams
(4) Some other ragams, instead of going up or down simply, can go up or down in a zig zag manner - such as Sa-ri1-ma1-ga2-pa-ni2-dha1-sa etc. That is, you cannot simply go up in scale by merely pressing the keys, but you should spiral to the top of the scale. There are not too many such ragams, but such a meandering structure is called 'Vakram', which literally means crooked. This is an additional constraint imposed on the Ragam, besides the key selection.
(5) In some other instances, it may not be easy to define uniquely the Arohanam and Avarohanam of a ragam. Many Arohanams and Avarohanams (i.e, definitions) can exist for one ragam itself. An example of such a Ragam is Ananda Bhairavi. Of course, those Arohanams and Avarohanams will be close to each other and won't be radically apart. This situation exists especially when we try to extract the Ragam equivalent of folk melodies or alien tunes.
(6) And finally here is a confusing possibility. There can be two Ragams which have identical Arohanams and Avarohanams, but DIFFERENT MICROTONAL ASSOCIATIONS or Gamakams ! The only way to tell these two Ragams apart is to sensitize your ears to the differences to the Gamakams. Of course, you can never possibly play them on the keyboard as two different Ragams!
You can go ahead and create your own ragam by selecting your own five keys (or six or seven) following the above rules and name it after yourself. (But make sure it doesn't already exist !) However, if you created your own pentatonic-pentatonic ragam, you probably did not choose just the first five keys of the octave. You might have distributed the five keys such that they were spread out in the octave instead of being bunched together, just so that your ragam sounded better. In fact, such subjective criteria have given resulted in only a few Ragams being popular.
Mathematically, there are many, many ragams possible. Choosing five, six or seven keys out of possible twelve keys gives rise to a huge number of combinations. Fortunately, many of the possibilities have been deemed 'boring to the ear' by musicians throughout history. Only about six thousand or so ragams have been even cataloged and of these, only about two hundred or so are even used these days. A ragam's popularity can go up and down, depending on people's taste and the existing political climate of the Karnatic music caucus. So, it is really not a tremendous task to learn about fifty or so of the more popular ragams and be good at identifying them, if at least to impress your friends.
It is always possible to break down any song, even the non-Karnatic music songs into its constituent Swarams and define a corresponding Ragam. Even 'Baa baa black sheep' can be broken into a Ragam. Musicians more clever than we are have done such things and created Ragams out of truly Dravidian folk melodies such as 'Aadu Pambey' (the snake song) or Kavadi Sindhu songs like 'Nandavanathil or aandi' and created ragams like Ananda Bhairavi or Kurunji. Sometimes, the ragam corresponding to songs like 'Baa baa black sheep' may not have enormous scope to create a lot of 'characteristic phrases' and thus limiting creating any more songs based on the ragam.
(5) In some other instances, it may not be easy to define uniquely the Arohanam and Avarohanam of a ragam. Many Arohanams and Avarohanams (i.e, definitions) can exist for one ragam itself. An example of such a Ragam is Ananda Bhairavi. Of course, those Arohanams and Avarohanams will be close to each other and won't be radically apart. This situation exists especially when we try to extract the Ragam equivalent of folk melodies or alien tunes.
(6) And finally here is a confusing possibility. There can be two Ragams which have identical Arohanams and Avarohanams, but DIFFERENT MICROTONAL ASSOCIATIONS or Gamakams ! The only way to tell these two Ragams apart is to sensitize your ears to the differences to the Gamakams. Of course, you can never possibly play them on the keyboard as two different Ragams!
You can go ahead and create your own ragam by selecting your own five keys (or six or seven) following the above rules and name it after yourself. (But make sure it doesn't already exist !) However, if you created your own pentatonic-pentatonic ragam, you probably did not choose just the first five keys of the octave. You might have distributed the five keys such that they were spread out in the octave instead of being bunched together, just so that your ragam sounded better. In fact, such subjective criteria have given resulted in only a few Ragams being popular.
Mathematically, there are many, many ragams possible. Choosing five, six or seven keys out of possible twelve keys gives rise to a huge number of combinations. Fortunately, many of the possibilities have been deemed 'boring to the ear' by musicians throughout history. Only about six thousand or so ragams have been even cataloged and of these, only about two hundred or so are even used these days. A ragam's popularity can go up and down, depending on people's taste and the existing political climate of the Karnatic music caucus. So, it is really not a tremendous task to learn about fifty or so of the more popular ragams and be good at identifying them, if at least to impress your friends.
It is always possible to break down any song, even the non-Karnatic music songs into its constituent Swarams and define a corresponding Ragam. Even 'Baa baa black sheep' can be broken into a Ragam. Musicians more clever than we are have done such things and created Ragams out of truly Dravidian folk melodies such as 'Aadu Pambey' (the snake song) or Kavadi Sindhu songs like 'Nandavanathil or aandi' and created ragams like Ananda Bhairavi or Kurunji. Sometimes, the ragam corresponding to songs like 'Baa baa black sheep' may not have enormous scope to create a lot of 'characteristic phrases' and thus limiting creating any more songs based on the ragam.
Sa, Ri, Ga, Pa, Ni, Sa
If we used Sa, Ri, Ga, Pa, Ni, Sa then we get Ragam Hamsadhwani.
If we used Sa, Ri, Ma, Pa, Dha, Sa then we get Ragam Suddha Saveri. (The Hindustani equivalent for this scale is Rag Durga)
If you have a keyboard try to play just these keys and see if you can get a feel for the identities of these Ragams. For example, in Mohanam, the jump from Ga to Pa or for that matter Dha to upper Sa is quite characteristic. Besides Karnatic and Hindustani music, a lot of Oriental tunes are based on the scale of Mohanam!
(3) The five note scale, such as Mohanam, is called a Pentatonic Ragam. The Indian equivalent term is 'Oudava Ragam'. Similary, the six note Ragam is called Shadva Ragam in India or Sextatonic in Western terminology. And the seven note Ragam is called Septatonic or Sampoorna. While the Ragam Mohanam is pentatonic with an implicit assumption that Arohanam and Avarohanam are reverses of each other, other asymmetric possibilities are allowed.
A ragam can have five notes on the way up (in Arohanam) and seven on the way down. (Avarohanam) For example, you can have a ragam which is exactly Mohanam in terms of Arohanam (Sa ri ga pa dha sa) but is Kalyani (Sa ni dha pa ma 2 ga ri sa) on the way down. This oudava - sampoorna Ragam is called Mohanakalyani. So you can have oudava-oudava, oudava-sampoorna, sampoorna-shadva etc. combinations. (Melakarta Ragams are of course, Sampoorna-Sampoorna) Also, the Avarohanam need not be the reverse of the Arohanam. For example, you can have a ragam that goes Sa-ri1-ma1-dha1-ni2-Sa (Arohanam) and Sa-ni1-dha2-pa-ma2-ga2-Sa. (Avarohanam) A good lot of ragams are however symmetric. (The same keys used to go up the octave or down the octave)
Once you have chosen the keys, you are restricted to play only those keys, however you can play them any way you want. You can compose a phrase that goes Sa-ma1-ma1-dha1-Sa-dha2-dha2-ga2. You can skip notes if you wish.
If we used Sa, Ri, Ma, Pa, Dha, Sa then we get Ragam Suddha Saveri. (The Hindustani equivalent for this scale is Rag Durga)
If you have a keyboard try to play just these keys and see if you can get a feel for the identities of these Ragams. For example, in Mohanam, the jump from Ga to Pa or for that matter Dha to upper Sa is quite characteristic. Besides Karnatic and Hindustani music, a lot of Oriental tunes are based on the scale of Mohanam!
(3) The five note scale, such as Mohanam, is called a Pentatonic Ragam. The Indian equivalent term is 'Oudava Ragam'. Similary, the six note Ragam is called Shadva Ragam in India or Sextatonic in Western terminology. And the seven note Ragam is called Septatonic or Sampoorna. While the Ragam Mohanam is pentatonic with an implicit assumption that Arohanam and Avarohanam are reverses of each other, other asymmetric possibilities are allowed.
A ragam can have five notes on the way up (in Arohanam) and seven on the way down. (Avarohanam) For example, you can have a ragam which is exactly Mohanam in terms of Arohanam (Sa ri ga pa dha sa) but is Kalyani (Sa ni dha pa ma 2 ga ri sa) on the way down. This oudava - sampoorna Ragam is called Mohanakalyani. So you can have oudava-oudava, oudava-sampoorna, sampoorna-shadva etc. combinations. (Melakarta Ragams are of course, Sampoorna-Sampoorna) Also, the Avarohanam need not be the reverse of the Arohanam. For example, you can have a ragam that goes Sa-ri1-ma1-dha1-ni2-Sa (Arohanam) and Sa-ni1-dha2-pa-ma2-ga2-Sa. (Avarohanam) A good lot of ragams are however symmetric. (The same keys used to go up the octave or down the octave)
Once you have chosen the keys, you are restricted to play only those keys, however you can play them any way you want. You can compose a phrase that goes Sa-ma1-ma1-dha1-Sa-dha2-dha2-ga2. You can skip notes if you wish.
RAGAM
WHAT IS A 'RAGAM'? Now that we have studied the Melakarta scheme inside and out, let us go on to generate the secondary or 'janya' or derived Ragams (the rest of the Ragams, that is) based on some simple guidelines. These are only guidelines and are not hard and fast rules:
(1) A Ragam should use at least five keys in an octave and utmost seven keys in the Arohanam as well as the Avarohanam.
(2) The Arohanam or ascending order of the notes (or Avarohanam or descending order, for that matter) is obtained by simply taking a Melakarta scale and omitting none or one note or two notes. (Remember, the Melakarta scale has seven notes and so we can end up with seven or six or five notes in the derived scale)
For example, let us (yet again !) take Ragam Shankarabharanam. If we omit the keys 'Ma' and 'Ni' and use only the five white keys Sa, Ri, Ga, Pa, Dha then we obtain a famous Ragam called Mohanam. (Hindustani equivalent is Bhoop or Bhopali)
(Usually, the the next octave's Sa is also included for completion and hence the Arohanam will be more correctly given as Sa-ri-ga-pa-dha-Sa. Similarly, the Avarohanam is given by Sa dha pa ga ri sa. You will notice that almost all ragams start with the key Sa. Also, from now on, we will omit saying 'Ri 1' or 'Ri 2' etc. IF THERE IS NO AMBIGUITY AS TO WHICH KEY WE ARE USING.
(1) A Ragam should use at least five keys in an octave and utmost seven keys in the Arohanam as well as the Avarohanam.
(2) The Arohanam or ascending order of the notes (or Avarohanam or descending order, for that matter) is obtained by simply taking a Melakarta scale and omitting none or one note or two notes. (Remember, the Melakarta scale has seven notes and so we can end up with seven or six or five notes in the derived scale)
For example, let us (yet again !) take Ragam Shankarabharanam. If we omit the keys 'Ma' and 'Ni' and use only the five white keys Sa, Ri, Ga, Pa, Dha then we obtain a famous Ragam called Mohanam. (Hindustani equivalent is Bhoop or Bhopali)
(Usually, the the next octave's Sa is also included for completion and hence the Arohanam will be more correctly given as Sa-ri-ga-pa-dha-Sa. Similarly, the Avarohanam is given by Sa dha pa ga ri sa. You will notice that almost all ragams start with the key Sa. Also, from now on, we will omit saying 'Ri 1' or 'Ri 2' etc. IF THERE IS NO AMBIGUITY AS TO WHICH KEY WE ARE USING.
Melakarta Ragams
(i) All Melakarta Ragams from 1 to 36 use Ma 1. Those from 37 to 72 use Ma 2.
(ii) The ri ga assignment is as follows:
Ri 1 - Ga 1 Melakartas 1 through 6, 37 through 42
Ri 1 - Ga 2 Melakartas 7 through 12, 43 through 48
Ri 1 - Ga 3 Melakartas 13 through 18, 49 through 54
Ri 2 - Ga 2 Melakartas 19 through 24, 55 through 60
Ri 2 - Ga 3 Melakartas 25 through 30, 61 through 66
Ri 3 - Ga 3 Melakartas 31 through 36, 67 through 72
(iii) The dha ni assignment is as follows:
Take the Melakarta number and divide it by six and look at the remainder.
Dha 1 - Ni 1 if the remainder is 1
Dha 1 - Ni 2 if the remainder is 2
Dha 1 - Ni 3 if the remainder is 3
Dha 2 - Ni 2 if the remainder is 4
Dha 2 - Ni 3 if the remainder is 5
Dha 3 - Ni 3 if the remainder is zero
So all you have to do is take a melakarta ragam. From its name determine its number in the scheme. From the number, figure out the Arohanam and Avarohanam. Simple enough !
Again, among the 72 such major ragams, not all of them are equally popular. Some of them are quite obscure, especially the ones whose keys are not spread apart well throughout the octave. However, many musicians have composed in all 72 melakartas - Koteeswara Iyer for one. Musicians like M. S. Subbulakshmi and S. Balachandar have recorded all 72 melakartas. The Suddha Madhyamam (Suddha Madhyamam is just the official name for Ma 1) group of 36 ragams are by and large more popular than the Prati Madhyamam (Prati Madhyamam is the same as Ma 2) group. The Ma2 is supposed to be more 'negative' and 'sad' !! The more unpopular ragams are the ones like Kanakangi, which use closely spaced keys. The ragam Mayamalavagaulai on the other hand has a well spread out keys - Sa-ri1-space-ga2-ma1-space-pa-dha1-space-ni2-sa. This is the ragam all beginners are taught, essentially because such a dispersed set of notes is more easy for a beginner to learn.
>From these complete ragams, you can derive 'child ragams' omitting a key here and a key there in the arohanam or avarohanam. Some melakartas are parents of a large number of popular 'child' or 'Janya' or 'derived' ragams - melakartas like Natabhairavi, Kharaharapriya, Harikambhoji for example. We will see this in the next section.
You may wonder how just one key makes a difference. I just told you that the ragams Kalyani and Shankarabharanam have identical arohanam and avarohanam, except for the key used to produce the 'ma' syllable. You have to listen to your keyboard. Play Kalyani and Shankarabharanam on the keyboard (and even though you don't produce the 'microtones' and even though you are playing an 'eqully tempered instrument') you can tell the two apart. The ma key makes a big difference and one has to simply listen to music a lot to train one's ears.
Since melakartas have the maximum allowed seven notes in a ragam, they have an enormous scope for melody making, compared to a derived ragam which may have less than seven notes. Thus melakarta ragams are very popular in concerts. Musicians choose them for the 'heavy' part of the concert and try to exhibit their mastery.
(ii) The ri ga assignment is as follows:
Ri 1 - Ga 1 Melakartas 1 through 6, 37 through 42
Ri 1 - Ga 2 Melakartas 7 through 12, 43 through 48
Ri 1 - Ga 3 Melakartas 13 through 18, 49 through 54
Ri 2 - Ga 2 Melakartas 19 through 24, 55 through 60
Ri 2 - Ga 3 Melakartas 25 through 30, 61 through 66
Ri 3 - Ga 3 Melakartas 31 through 36, 67 through 72
(iii) The dha ni assignment is as follows:
Take the Melakarta number and divide it by six and look at the remainder.
Dha 1 - Ni 1 if the remainder is 1
Dha 1 - Ni 2 if the remainder is 2
Dha 1 - Ni 3 if the remainder is 3
Dha 2 - Ni 2 if the remainder is 4
Dha 2 - Ni 3 if the remainder is 5
Dha 3 - Ni 3 if the remainder is zero
So all you have to do is take a melakarta ragam. From its name determine its number in the scheme. From the number, figure out the Arohanam and Avarohanam. Simple enough !
Again, among the 72 such major ragams, not all of them are equally popular. Some of them are quite obscure, especially the ones whose keys are not spread apart well throughout the octave. However, many musicians have composed in all 72 melakartas - Koteeswara Iyer for one. Musicians like M. S. Subbulakshmi and S. Balachandar have recorded all 72 melakartas. The Suddha Madhyamam (Suddha Madhyamam is just the official name for Ma 1) group of 36 ragams are by and large more popular than the Prati Madhyamam (Prati Madhyamam is the same as Ma 2) group. The Ma2 is supposed to be more 'negative' and 'sad' !! The more unpopular ragams are the ones like Kanakangi, which use closely spaced keys. The ragam Mayamalavagaulai on the other hand has a well spread out keys - Sa-ri1-space-ga2-ma1-space-pa-dha1-space-ni2-sa. This is the ragam all beginners are taught, essentially because such a dispersed set of notes is more easy for a beginner to learn.
>From these complete ragams, you can derive 'child ragams' omitting a key here and a key there in the arohanam or avarohanam. Some melakartas are parents of a large number of popular 'child' or 'Janya' or 'derived' ragams - melakartas like Natabhairavi, Kharaharapriya, Harikambhoji for example. We will see this in the next section.
You may wonder how just one key makes a difference. I just told you that the ragams Kalyani and Shankarabharanam have identical arohanam and avarohanam, except for the key used to produce the 'ma' syllable. You have to listen to your keyboard. Play Kalyani and Shankarabharanam on the keyboard (and even though you don't produce the 'microtones' and even though you are playing an 'eqully tempered instrument') you can tell the two apart. The ma key makes a big difference and one has to simply listen to music a lot to train one's ears.
Since melakartas have the maximum allowed seven notes in a ragam, they have an enormous scope for melody making, compared to a derived ragam which may have less than seven notes. Thus melakarta ragams are very popular in concerts. Musicians choose them for the 'heavy' part of the concert and try to exhibit their mastery.
syllables of the Melakarta ragam
The above scheme works as follows:
(1) Assign numbers to the first two syllables of the Melakarta ragam. Example, Harikambhoji, the syllable 'Ha' is 8 and 'ra' is 2 and thus Hari is 82. The melakarta number of this ragam is obtained by simply interchanging the digits, i. e 82 becomes 28 and in fact, Harikambhoji is the 28 th melakarta ragam.
(2) A few more example, Kanakangi. Ka is 1 and Na is 0 and thus Kana is 10. Interchanging the digits we get 10 -- 01 and thus this is the first melakarta ragam.
DhheeraShankarabharanam, here Dhha is 9 and ra is 2 and thus Dhheera is 92, transposing which we get 29 which is the position of the ragam. You can see that Shankarabharanam probably existed before the scheme was invented and thus the author had to alias it to conform to his look-up table scheme. There are other such aliased ragams. The popular ragam Todi is aliased to become Hanumatodi and Kalyani is officially Mechakalyani, just so that they follow the Katayapadi naming scheme. Another example, Mayamalavagaulai, (used to be called just Malavagaulai) has Ma which is 5 and Ya which is 1 and thus yielding 51, which when inverted gives 15, which is the place in the order.
Take SimhendraMadhyamam. Sa is 7 and Ma is 5 and thus Simha is 75 and the melakarta number is 57. However you must notice that the second syllable, Mha is a compound syllable combining ma and ha. In these cases, we usually take the first of the two sounds. There are some exceptions too. In Ratnangi, Ra is 2 and we take the 'Na' part of 'Thna' and arrive at the destination 02. If you used 'Th' instead of 'Na', you will get the number 62 for this melakarta, which is firmly occupied by ragam Rishabhapriya.
What are the advantages of such mathematical and almost 'hackers' kind of scheme ?
(1) The melakarta scheme does not tell you if a given ragam is a melakarta or not. If you know it is a melakarta ragam, you can find out what number it has in the sequence. For example, you can try to see what number is ragam Poorvikalyani, which is not a melakarta. This would be 21 if you consider Pa ra. (or if you considered Pa and Va it is 41) However, it is not even a melakarta ragam and you cannot use the above look-up table.
(2) Incidentally, if you look up Table IV which lists all the melakarta ragam, you will see that the two very famous ragams Shankarabharanam (called DhheeraShankarabharanam) and Kalyani (called Mechakalyani) have almost identical notes except for the Ma. Shankarabharanam uses Ma1, which is called Shuddha Madhyamam, whereas Kalyani uses Ma2 which is called Prati Madhyamam. Thus the table is divided into two groups of 36 ragams each and the only difference between the ragam on the left and the one on the right is the Ma key used. The first 36 from Kanakangi to Chalanattai are called Suddha Madhyamam ragams and the other 36 are called Prati Madhyamam ragams. Melakartas which differ from each other by 36 (Such as Harikambhoji and Vachaspati, Keeravani and Simhendramadhyamam) have the same Arohanam and Avarohanam except for the Ma.
(3) How do we figure out the Arohanam and Avarohanam or which keys to use from the name of the melakarta ragam ? If somebody tells you Keeravani, can you quickly locate the keys on a keyboard corresponding to the ragam ? You just have to look at the Table IV to see how cyclical the whole thing is. All melakarta ragams in the same group of six (i. e, 1 to 6, 7 to 12, 25 to 30 etc) have the same Sa ri ga ma. All ragams which differ from each other by six have the same Pa dha ni sa. (Karaharapriya(22), Harikambhoji(28), Hemavati(58), Nasikabhoosani(70) all have the same Pa dha ni sa, because they all leave a remainder of 4 when divided by 6)
(1) Assign numbers to the first two syllables of the Melakarta ragam. Example, Harikambhoji, the syllable 'Ha' is 8 and 'ra' is 2 and thus Hari is 82. The melakarta number of this ragam is obtained by simply interchanging the digits, i. e 82 becomes 28 and in fact, Harikambhoji is the 28 th melakarta ragam.
(2) A few more example, Kanakangi. Ka is 1 and Na is 0 and thus Kana is 10. Interchanging the digits we get 10 -- 01 and thus this is the first melakarta ragam.
DhheeraShankarabharanam, here Dhha is 9 and ra is 2 and thus Dhheera is 92, transposing which we get 29 which is the position of the ragam. You can see that Shankarabharanam probably existed before the scheme was invented and thus the author had to alias it to conform to his look-up table scheme. There are other such aliased ragams. The popular ragam Todi is aliased to become Hanumatodi and Kalyani is officially Mechakalyani, just so that they follow the Katayapadi naming scheme. Another example, Mayamalavagaulai, (used to be called just Malavagaulai) has Ma which is 5 and Ya which is 1 and thus yielding 51, which when inverted gives 15, which is the place in the order.
Take SimhendraMadhyamam. Sa is 7 and Ma is 5 and thus Simha is 75 and the melakarta number is 57. However you must notice that the second syllable, Mha is a compound syllable combining ma and ha. In these cases, we usually take the first of the two sounds. There are some exceptions too. In Ratnangi, Ra is 2 and we take the 'Na' part of 'Thna' and arrive at the destination 02. If you used 'Th' instead of 'Na', you will get the number 62 for this melakarta, which is firmly occupied by ragam Rishabhapriya.
What are the advantages of such mathematical and almost 'hackers' kind of scheme ?
(1) The melakarta scheme does not tell you if a given ragam is a melakarta or not. If you know it is a melakarta ragam, you can find out what number it has in the sequence. For example, you can try to see what number is ragam Poorvikalyani, which is not a melakarta. This would be 21 if you consider Pa ra. (or if you considered Pa and Va it is 41) However, it is not even a melakarta ragam and you cannot use the above look-up table.
(2) Incidentally, if you look up Table IV which lists all the melakarta ragam, you will see that the two very famous ragams Shankarabharanam (called DhheeraShankarabharanam) and Kalyani (called Mechakalyani) have almost identical notes except for the Ma. Shankarabharanam uses Ma1, which is called Shuddha Madhyamam, whereas Kalyani uses Ma2 which is called Prati Madhyamam. Thus the table is divided into two groups of 36 ragams each and the only difference between the ragam on the left and the one on the right is the Ma key used. The first 36 from Kanakangi to Chalanattai are called Suddha Madhyamam ragams and the other 36 are called Prati Madhyamam ragams. Melakartas which differ from each other by 36 (Such as Harikambhoji and Vachaspati, Keeravani and Simhendramadhyamam) have the same Arohanam and Avarohanam except for the Ma.
(3) How do we figure out the Arohanam and Avarohanam or which keys to use from the name of the melakarta ragam ? If somebody tells you Keeravani, can you quickly locate the keys on a keyboard corresponding to the ragam ? You just have to look at the Table IV to see how cyclical the whole thing is. All melakarta ragams in the same group of six (i. e, 1 to 6, 7 to 12, 25 to 30 etc) have the same Sa ri ga ma. All ragams which differ from each other by six have the same Pa dha ni sa. (Karaharapriya(22), Harikambhoji(28), Hemavati(58), Nasikabhoosani(70) all have the same Pa dha ni sa, because they all leave a remainder of 4 when divided by 6)
Katayapadi system...
Table V
Katayapadi system of naming the Melakarta ragams
----------------------------------------------------------------------------
Number 0 1 2 3 4 5 6 7 8 9
----------------------------------------------------------------------------
Syllable ka kha ga gha - cha chha ja jha
ta tta da dda - tha thha dha ddha
na pa pha ba bha ma
ya ra la va sha shha sa ha
----------------------------------------------------------------------------
________________________________________
Katayapadi system of naming the Melakarta ragams
----------------------------------------------------------------------------
Number 0 1 2 3 4 5 6 7 8 9
----------------------------------------------------------------------------
Syllable ka kha ga gha - cha chha ja jha
ta tta da dda - tha thha dha ddha
na pa pha ba bha ma
ya ra la va sha shha sa ha
----------------------------------------------------------------------------
________________________________________
This brings out...
This brings out another interesting aspect of the Melakarta Scheme. The names of the ragams are not arbitrary. The names contain mnemonics which spell out which keys are used in the ragam. From the name DhheeraShankarabharanam, we could figure out that it is all white keys ! (Venkatamakhin was lucky that most of the 72 ragams were not known then, so he could assign names to them or add a prefix to the existing ones. Imagine if all the ragams were to exist first and then you try to group them, you may not have such mnemonics possible) In fact, in Hindustani music, such schemes were not invented and now we have hundreds of ragams which are tough to classify using such simple mnemonics. Of course, the absence of such a comprehensive scheme is by no means a negative or a deficiency on the Hindustani musical system. In music, like in most things in life, we don't (and should not) want to make value judgements !
Let me now explain you the mnemonic or the Katayapadi System. (Thanks to R. Pichumani for the notes in this section) A look-up table is created, given in Table V that assigns syllables to numbers.
Let me now explain you the mnemonic or the Katayapadi System. (Thanks to R. Pichumani for the notes in this section) A look-up table is created, given in Table V that assigns syllables to numbers.
SOME MORE DISCUSSION...
(Skip this chapter if you want to during the first reading ! But, on other hand, the Melakarta scheme is a fascinating piece of classification. You might want to read it for the fun of it)
A scholar named Venkatamakhin invented the Melakarta scheme, way back in the seventeenth century. He was the first to comprehensively classify Ragams in a 'Periodic table' like arrangement. A complete list of the 72 Melakarta Ragams is given in Table IV with the corresponding scales. When Venkatamakhin devised his Table, only a few of the 72 Ragams were known. Using his schematization Venkatamakhin not only cataloged the existing Melakarta Ragams, but also filled in the 'gaps' by coming up with the key sequence for the rest of the Melakarta Ragams. Thus this scheme helped 'discover' new Melakarta Ragams, which in turn led to even newer derivative or child Ragams using those. Composers and performers lapped it up and made songs in the newer, hitherto unknown Ragams. In Table IV, the ragam number 29 is our friendly ragam, Shankarabharanam, although its less well-known official name DhheeraShankarabharanam is used in the table.
________________________________________
Table IV
The 72 Melakarta Ragams and their scales
--------------------------------------------------------------------------
# Name Ri ga Dha ni # Name Ri ga Dha ni
Suddha Madhyamam (M1) Prati Madhyamam (M2)
----------------------------------------------------------------------------
1 Kanakanki R1 G1 D1 N1 37 Salagam R1 G1 D1 N1
2 Ratnangi R1 G1 D1 N2 38 Jalarnavam R1 G1 D1 N2
3 Ganamurti R1 G1 D1 N3 39 Jhalavarali R1 G1 D1 N3
4 Vanaspati R1 G1 D2 N2 40 Navaneetam R1 G1 D2 N2
5 Manavati R1 G1 D2 N3 41 Pavani R1 G1 D2 N3
6 Tanarupi R1 G1 D3 N3 42 Raghupriya R1 G1 D3 N3
7 Senavati R1 G2 D1 N1 43 Gavambodhi R1 G2 D1 N1
8 Hanumatodi R1 G2 D1 N2 44 Bhavapriya R1 G2 D1 N2
9 Dhenuka R1 G2 D1 N3 45 Subhapantuvarali R1 G2 D1 N3
10 Natakapriya R1 G2 D2 N2 46 Shadvigamargini R1 G2 D2 N2
11 Kokilapriya R1 G2 D2 N3 47 Suvarnangi R1 G2 D2 N3
12 Rupavati R1 G2 D3 N3 48 Divyamani R1 G2 D3 N3
13 Gayakapriya R1 G3 D1 N1 49 Dhavalambari R1 G3 D1 N1
14 Vakulabharanam R1 G3 D1 N2 50 Namanarayani R1 G3 D1 N2
15 Mayamalavagoulai R1 G3 D1 N3 51 Kamavardhini R1 G3 D1 N3
16 Chakravaham R1 G3 D2 N2 52 Ramapriya R1 G3 D2 N2
17 Suryakantam R1 G3 D2 N3 53 Gamanasrama R1 G3 D2 N3
18 Hatakambhari R1 G3 D3 N3 54 Viswambhari R1 G3 D3 N3
19 Jhankaradhwani R2 G2 D1 N1 55 Syamalangi R2 G2 D1 N1
20 Natabhairavi R2 G2 D1 N2 56 Shanmukhapriya R2 G2 D1 N2
21 Keeravani R2 G2 D1 N3 57 Simhendramadhyamam R2 G2 D1 N3
22 Kharaharapriya R2 G2 D2 N2 58 Hemavati R2 G2 D2 N2
23 Gourimanohari R2 G2 D2 N3 59 Dharamavai R2 G2 D2 N3
24 Varunapriya R2 G2 D3 N3 60 Nitimati R2 G2 D3 N3
25 Mararanjani R2 G3 D1 N1 61 Kantamani R2 G3 D1 N1
26 Charukesi R2 G3 D1 N2 62 Rishabhapriya R2 G3 D1 N2
27 Sarasangi R2 G3 D1 N3 63 Latangi R2 G3 D1 N3
28 Harikambhoji R2 G3 D2 N2 64 Vachaspati R2 G3 D2 N2
29 Dheerasankarabharanam R2 G3 D2 N3 65 Mechakalyani R2 G3 D2 N3
30 Naganandini R2 G3 D3 N3 66 Chitrambhari R2 G3 D3 N3
31 Yagapriya R3 G3 D1 N1 67 Sucharitra R3 G3 D1 N1
32 Ragavardhini R3 G3 D1 N2 68 Jyotiswarupini R3 G3 D1 N2
33 Gangeyabhusani R3 G3 D1 N3 69 Dhatuvardhini R3 G3 D1 N3
34 Vagadheeswari R3 G3 D2 N2 70 Nasikabhusani R3 G3 D2 N2
35 Sulini R3 G3 D2 N3 71 Kosalam R3 G3 D2 N3
36 Chalanattai R3 G3 D3 N3 72 Rasikapriya R3 G3 D3 N3
A scholar named Venkatamakhin invented the Melakarta scheme, way back in the seventeenth century. He was the first to comprehensively classify Ragams in a 'Periodic table' like arrangement. A complete list of the 72 Melakarta Ragams is given in Table IV with the corresponding scales. When Venkatamakhin devised his Table, only a few of the 72 Ragams were known. Using his schematization Venkatamakhin not only cataloged the existing Melakarta Ragams, but also filled in the 'gaps' by coming up with the key sequence for the rest of the Melakarta Ragams. Thus this scheme helped 'discover' new Melakarta Ragams, which in turn led to even newer derivative or child Ragams using those. Composers and performers lapped it up and made songs in the newer, hitherto unknown Ragams. In Table IV, the ragam number 29 is our friendly ragam, Shankarabharanam, although its less well-known official name DhheeraShankarabharanam is used in the table.
________________________________________
Table IV
The 72 Melakarta Ragams and their scales
--------------------------------------------------------------------------
# Name Ri ga Dha ni # Name Ri ga Dha ni
Suddha Madhyamam (M1) Prati Madhyamam (M2)
----------------------------------------------------------------------------
1 Kanakanki R1 G1 D1 N1 37 Salagam R1 G1 D1 N1
2 Ratnangi R1 G1 D1 N2 38 Jalarnavam R1 G1 D1 N2
3 Ganamurti R1 G1 D1 N3 39 Jhalavarali R1 G1 D1 N3
4 Vanaspati R1 G1 D2 N2 40 Navaneetam R1 G1 D2 N2
5 Manavati R1 G1 D2 N3 41 Pavani R1 G1 D2 N3
6 Tanarupi R1 G1 D3 N3 42 Raghupriya R1 G1 D3 N3
7 Senavati R1 G2 D1 N1 43 Gavambodhi R1 G2 D1 N1
8 Hanumatodi R1 G2 D1 N2 44 Bhavapriya R1 G2 D1 N2
9 Dhenuka R1 G2 D1 N3 45 Subhapantuvarali R1 G2 D1 N3
10 Natakapriya R1 G2 D2 N2 46 Shadvigamargini R1 G2 D2 N2
11 Kokilapriya R1 G2 D2 N3 47 Suvarnangi R1 G2 D2 N3
12 Rupavati R1 G2 D3 N3 48 Divyamani R1 G2 D3 N3
13 Gayakapriya R1 G3 D1 N1 49 Dhavalambari R1 G3 D1 N1
14 Vakulabharanam R1 G3 D1 N2 50 Namanarayani R1 G3 D1 N2
15 Mayamalavagoulai R1 G3 D1 N3 51 Kamavardhini R1 G3 D1 N3
16 Chakravaham R1 G3 D2 N2 52 Ramapriya R1 G3 D2 N2
17 Suryakantam R1 G3 D2 N3 53 Gamanasrama R1 G3 D2 N3
18 Hatakambhari R1 G3 D3 N3 54 Viswambhari R1 G3 D3 N3
19 Jhankaradhwani R2 G2 D1 N1 55 Syamalangi R2 G2 D1 N1
20 Natabhairavi R2 G2 D1 N2 56 Shanmukhapriya R2 G2 D1 N2
21 Keeravani R2 G2 D1 N3 57 Simhendramadhyamam R2 G2 D1 N3
22 Kharaharapriya R2 G2 D2 N2 58 Hemavati R2 G2 D2 N2
23 Gourimanohari R2 G2 D2 N3 59 Dharamavai R2 G2 D2 N3
24 Varunapriya R2 G2 D3 N3 60 Nitimati R2 G2 D3 N3
25 Mararanjani R2 G3 D1 N1 61 Kantamani R2 G3 D1 N1
26 Charukesi R2 G3 D1 N2 62 Rishabhapriya R2 G3 D1 N2
27 Sarasangi R2 G3 D1 N3 63 Latangi R2 G3 D1 N3
28 Harikambhoji R2 G3 D2 N2 64 Vachaspati R2 G3 D2 N2
29 Dheerasankarabharanam R2 G3 D2 N3 65 Mechakalyani R2 G3 D2 N3
30 Naganandini R2 G3 D3 N3 66 Chitrambhari R2 G3 D3 N3
31 Yagapriya R3 G3 D1 N1 67 Sucharitra R3 G3 D1 N1
32 Ragavardhini R3 G3 D1 N2 68 Jyotiswarupini R3 G3 D1 N2
33 Gangeyabhusani R3 G3 D1 N3 69 Dhatuvardhini R3 G3 D1 N3
34 Vagadheeswari R3 G3 D2 N2 70 Nasikabhusani R3 G3 D2 N2
35 Sulini R3 G3 D2 N3 71 Kosalam R3 G3 D2 N3
36 Chalanattai R3 G3 D3 N3 72 Rasikapriya R3 G3 D3 N3
Rule 1: Always...
Rule 1: Always select the first white key ! The 'Sa'.
Rule 2: Always select the Pa key. This is a convenient midpoint of the octave, sort of.
Rule 3: Select one of the two Ma keys (Ma1 or Ma2 - note that one of them is black and the other one is white) Once selected, this key is your 'Ma'.
Rule 4: Select ANY two keys out of the four keys in the lower tetrachord. (From Keys 2, 3, 4 and 5) Once selected, the first of these two keys will be your 'Ri' and the second your 'ga'.
Rule 5: Select ANY two keys out of the four keys in the upper tetrachord. (From keys 9, 10, 11 and 12) Once selected, the first of the two keys will be your 'dha' and the second will be your 'ni'. This rule is exactly like Rule 4.
Once all the seven keys are chosen, you have your complete sa ri ga ma pa dha ni.
Let us see how many Melakartas or scales we can build this way. By Rule 4, you can choose two keys out of four in SIX different ways going by the elementary combination theory. Similary, going by Rule 5, we can choose two keys out of four in SIX different ways. By Rule 3, you can choose one key out of two in TWO different ways. So we get
SIX times SIX times TWO = Seventy Two Melakartas or Melakarta ragams.
And they are all unique.
By definition, the Melakarta Ragams are symmetric with respect to going up in octave or down. Saying the same thing more technically, in Melakarta Ragams, the Arohanam and the Avarohanams are simply reversed. The sequence Sa ri ga ma pa dha ni is Arohanam. The reversed sequence Sa ni dha pa ma ga ri is Avarohanam. The Melakarta Ragams are also called 'Sampoorna ragams' or Complete ragams.
Interestingly, even the Melakarta selection algorithm allows us to choose all seven white keys, the same as the Western C Major scale. In Karnatic music, we call the resulting Melakarta ragam as Shankarabharanam. (You may have even heard of this ragam) In Hindustani music, the set of all white keys is called the 'Bilaval thaat', one of the major building blocks of Hindustani musical system.
Let us now go back to Table II and see why notation 1 makes sense. For example, you can pick up any two keys from the keys 2, 3, 4 and 5 and still call the first one of those as Ri and the second one as Ga. If you chose keys 2 and 5 then, you will sing out 'ri' when you strike key 2 and 'ga' when you strike key 5. On the other hand, if you chose keys 3 and 4 you will say 'ri' for key 3 and 'ga' for key 4. Finally if you chose keys 2 and 3, then key 3 will be a 'ga' (and not 'ri') in this situation. The rule is, the first key used among these four keys is a 'ri' and the second one is 'ga' no matter which absolute position the keys are located at. Keys 3 and 4 have the dubious honor of being a ri or a ga depending on the situation. These arguments are also valid in the upper tetrachord and in the choice of 'dha' and 'ni'. Now perhaps we can understand why three keys were designated as 'ri' or 'ga' or 'dha' or ni.
A caveat. I am using the word 'Ragam' in a loose sense here. A Ragam is not just a scale or a bunch of keys - it is more than that. Remember, I told you over and over and over that microtones are everything in Indian classical music and keys in a keyboard are simply digitized approximations. The seven white keys alone are not enough to give the resulting music the flavor of ragam 'Shankarabharanam' - it is those seven keys PLUS all the associated microtones (I know, I am being vague, but there is no simple way to get around it !) which constitute the 'Shankarabharanam' ragam. In fact, you may hear shades of Shankarabharanam when someone plays the Western C Major or Hindustani Bilaval. But the 'shades' are different for C Major and Bilaval and Shankarabharanam. C Major does not have any gamakam, Bilaval has some and Shankarabharanam has another set of gamakams. It is important to listen to some music and figure out if you can identify an artiste go through gamakams. A simple rolling of the tongue, subtle jumps and modulation or vibrattos are all indicative of gamakams.
Also, if you are the type that questions authority, you may equally well question the Melakarta selection rules. Why should we include Pa always and why can't we include BOTH the Ma1 and Ma2 keys in the same scale ? In Hindustani music there are ragams which use both the Ma keys, although it is a no-no in Karnatic. (once you become more advanced you will see that even in Karnatic music some pieces use both the Mas)
Finally, we should notice a fundamental difference between the Western system of scale building compared to the Melakarta scheme. In the Western classical music, you started off on a specific key, used the algorithm to generate the next key, which in turn led you to the third key of the scale and so forth. You sequentially generated the keys one after another by just shifting a whole tone or half a tone. By a curious coincidence even the Ilikkramam algorithm in Silappadhikaram is a similar 'Mode shifting' or 'tone shifting' algorithm. By contrast, the Melakarta scheme is a brutally mathematical scheme where you selected 7 keys out of a possible 12 keys, subject to certain constraints - here you figured out the frequency relationship between the keys much later. One important consequence: In the Western scale system, the keys in a scale are not more than a 'whole tone' apart, i. e, in any Major or Minor scale, you 'skip' at the maximum just one key. Whereas in Melakarta scheme, you can choose Key 1, Key 2, Key 3, Key 7, key 8, key 11 and key 12 by the algorithm. (This corresponds to Ragam Raghupriya) Notice the big gap between key 3 and key 7 (between the 'ga' and 'ma') where we skipped over three keys (This amounts to skipping two whole tones or four semitones). Also, we skipped two keys between 'pa' and 'dha'. (keys 8 and 11) Such large 'Intervals' ('Interval' is yet another musical term !) can produce 'unpleasant' listening experience. And although Raghupriya is a legitimate Ragam, it is about as popular as rain during a picnic.
Rule 2: Always select the Pa key. This is a convenient midpoint of the octave, sort of.
Rule 3: Select one of the two Ma keys (Ma1 or Ma2 - note that one of them is black and the other one is white) Once selected, this key is your 'Ma'.
Rule 4: Select ANY two keys out of the four keys in the lower tetrachord. (From Keys 2, 3, 4 and 5) Once selected, the first of these two keys will be your 'Ri' and the second your 'ga'.
Rule 5: Select ANY two keys out of the four keys in the upper tetrachord. (From keys 9, 10, 11 and 12) Once selected, the first of the two keys will be your 'dha' and the second will be your 'ni'. This rule is exactly like Rule 4.
Once all the seven keys are chosen, you have your complete sa ri ga ma pa dha ni.
Let us see how many Melakartas or scales we can build this way. By Rule 4, you can choose two keys out of four in SIX different ways going by the elementary combination theory. Similary, going by Rule 5, we can choose two keys out of four in SIX different ways. By Rule 3, you can choose one key out of two in TWO different ways. So we get
SIX times SIX times TWO = Seventy Two Melakartas or Melakarta ragams.
And they are all unique.
By definition, the Melakarta Ragams are symmetric with respect to going up in octave or down. Saying the same thing more technically, in Melakarta Ragams, the Arohanam and the Avarohanams are simply reversed. The sequence Sa ri ga ma pa dha ni is Arohanam. The reversed sequence Sa ni dha pa ma ga ri is Avarohanam. The Melakarta Ragams are also called 'Sampoorna ragams' or Complete ragams.
Interestingly, even the Melakarta selection algorithm allows us to choose all seven white keys, the same as the Western C Major scale. In Karnatic music, we call the resulting Melakarta ragam as Shankarabharanam. (You may have even heard of this ragam) In Hindustani music, the set of all white keys is called the 'Bilaval thaat', one of the major building blocks of Hindustani musical system.
Let us now go back to Table II and see why notation 1 makes sense. For example, you can pick up any two keys from the keys 2, 3, 4 and 5 and still call the first one of those as Ri and the second one as Ga. If you chose keys 2 and 5 then, you will sing out 'ri' when you strike key 2 and 'ga' when you strike key 5. On the other hand, if you chose keys 3 and 4 you will say 'ri' for key 3 and 'ga' for key 4. Finally if you chose keys 2 and 3, then key 3 will be a 'ga' (and not 'ri') in this situation. The rule is, the first key used among these four keys is a 'ri' and the second one is 'ga' no matter which absolute position the keys are located at. Keys 3 and 4 have the dubious honor of being a ri or a ga depending on the situation. These arguments are also valid in the upper tetrachord and in the choice of 'dha' and 'ni'. Now perhaps we can understand why three keys were designated as 'ri' or 'ga' or 'dha' or ni.
A caveat. I am using the word 'Ragam' in a loose sense here. A Ragam is not just a scale or a bunch of keys - it is more than that. Remember, I told you over and over and over that microtones are everything in Indian classical music and keys in a keyboard are simply digitized approximations. The seven white keys alone are not enough to give the resulting music the flavor of ragam 'Shankarabharanam' - it is those seven keys PLUS all the associated microtones (I know, I am being vague, but there is no simple way to get around it !) which constitute the 'Shankarabharanam' ragam. In fact, you may hear shades of Shankarabharanam when someone plays the Western C Major or Hindustani Bilaval. But the 'shades' are different for C Major and Bilaval and Shankarabharanam. C Major does not have any gamakam, Bilaval has some and Shankarabharanam has another set of gamakams. It is important to listen to some music and figure out if you can identify an artiste go through gamakams. A simple rolling of the tongue, subtle jumps and modulation or vibrattos are all indicative of gamakams.
Also, if you are the type that questions authority, you may equally well question the Melakarta selection rules. Why should we include Pa always and why can't we include BOTH the Ma1 and Ma2 keys in the same scale ? In Hindustani music there are ragams which use both the Ma keys, although it is a no-no in Karnatic. (once you become more advanced you will see that even in Karnatic music some pieces use both the Mas)
Finally, we should notice a fundamental difference between the Western system of scale building compared to the Melakarta scheme. In the Western classical music, you started off on a specific key, used the algorithm to generate the next key, which in turn led you to the third key of the scale and so forth. You sequentially generated the keys one after another by just shifting a whole tone or half a tone. By a curious coincidence even the Ilikkramam algorithm in Silappadhikaram is a similar 'Mode shifting' or 'tone shifting' algorithm. By contrast, the Melakarta scheme is a brutally mathematical scheme where you selected 7 keys out of a possible 12 keys, subject to certain constraints - here you figured out the frequency relationship between the keys much later. One important consequence: In the Western scale system, the keys in a scale are not more than a 'whole tone' apart, i. e, in any Major or Minor scale, you 'skip' at the maximum just one key. Whereas in Melakarta scheme, you can choose Key 1, Key 2, Key 3, Key 7, key 8, key 11 and key 12 by the algorithm. (This corresponds to Ragam Raghupriya) Notice the big gap between key 3 and key 7 (between the 'ga' and 'ma') where we skipped over three keys (This amounts to skipping two whole tones or four semitones). Also, we skipped two keys between 'pa' and 'dha'. (keys 8 and 11) Such large 'Intervals' ('Interval' is yet another musical term !) can produce 'unpleasant' listening experience. And although Raghupriya is a legitimate Ragam, it is about as popular as rain during a picnic.
First key - Choose any...
Second key - Skip the adjacent key to the right, choose the one after that. In effect, you have moved a 'whole tone' from the first key. Remember the concept of 'whole tones' and 'semitones' from the previous chapter. And that the whole tone equals shifting two semitones.
Third key - Again, skip the adjacent key to the right, choose the second one (again, you have moved a 'whole tone')
Fourth key - select the adjacent key. (you have moved a 'half tone' or a semitone)
Fifth key - Skip the next key, but select the one after that. Onceagain, you have have moved a full tone.
Sixth key - Skip the next key and select the one after that.
Seventh key - Select the adjacent key.
In short, your frequency selection is:
Select a key and then move,
Whole tone - whole tone - half tone - whole tone - whole tone - whole tone - half tone
If you started with the usual C key, the first white key, you will see that the 'C Major scale' is simply all white keys. This is a very 'major' scale, really, with a lot of popular compositions. And in the process of introducing this algorithm, we have also defined the term 'scale', which is simply a sequence of keys. Also, the algorithm 'wraps around itself'. That is, if you started out with the F key for example, and created the F Major Scale, you will spill over to the next octave. But that is okay, because you can fill up the rest of your scale by starting out with the F key of the PREVIOUS octave. That is, with this algorithm, you will always select seven keys in an octave. A question to ask is - will we get unique sequences using this algorithm every time we start off with a new key ? Or is there a possibility of our sequence repeating itself for two different starting keys, i.e, is the C Major scale different from D Major and are there twelve unique Major scales ? (I will leave this as an exercise for the very enthusiastic reader !)
Similarly, other algorithms can also be defined. One other choice is called the Minor scale - which is in reality a generic name for three different algorithms. One of them goes as
Whole - half - whole - whole - half - whole - whole (with the freedom to choose the first key)
I am not giving the selection rules for the other two 'Minor' algorithms. Again there are twelve keys we can select as our first key and therefore we can generate twelve sequences per Minor algorithm and there are three such 'Minor' algorithms, bringing a grand total of twelve times three, thirty six possible Minor scales. But we discover that many of the scales repeat themselves and in reality the number of unique 'scales' are fewer than thirty six Minor plus twelve Major scales.
Coming back to Indian system, even the ancient Tamil literary work, Silappadhikaram talks of an algorithm called 'Ilikramam', fascinating as it sounds. The rules of Ilikramam are quite similar to the selection of Major and Minor scales. It is really fun to work out this algorithm and derive a bunch of scales. (If you are more interested in this, refer to Prof. Ramanathan's book in the Reference section) In fact, nothing stops you at this point to go ahead and create your own selection rules to choose seven keys out of the twelve in the octave.
But let us turn our attention to Karnatic music. (Also, at this point, I will depart from talking about Indian classical music in general and stick only to South Indian music. Wherever relevant, references will be made to Hindustani music)
In Karnatic music, a very famous algorithm exists to select the keys in an octave, which forms the basis of important scales, which are called the 'Melakarta Scheme'. The Melakarta scheme selection algorithm is as follows: Please refer to Fig. 3 or Table II)
Third key - Again, skip the adjacent key to the right, choose the second one (again, you have moved a 'whole tone')
Fourth key - select the adjacent key. (you have moved a 'half tone' or a semitone)
Fifth key - Skip the next key, but select the one after that. Onceagain, you have have moved a full tone.
Sixth key - Skip the next key and select the one after that.
Seventh key - Select the adjacent key.
In short, your frequency selection is:
Select a key and then move,
Whole tone - whole tone - half tone - whole tone - whole tone - whole tone - half tone
If you started with the usual C key, the first white key, you will see that the 'C Major scale' is simply all white keys. This is a very 'major' scale, really, with a lot of popular compositions. And in the process of introducing this algorithm, we have also defined the term 'scale', which is simply a sequence of keys. Also, the algorithm 'wraps around itself'. That is, if you started out with the F key for example, and created the F Major Scale, you will spill over to the next octave. But that is okay, because you can fill up the rest of your scale by starting out with the F key of the PREVIOUS octave. That is, with this algorithm, you will always select seven keys in an octave. A question to ask is - will we get unique sequences using this algorithm every time we start off with a new key ? Or is there a possibility of our sequence repeating itself for two different starting keys, i.e, is the C Major scale different from D Major and are there twelve unique Major scales ? (I will leave this as an exercise for the very enthusiastic reader !)
Similarly, other algorithms can also be defined. One other choice is called the Minor scale - which is in reality a generic name for three different algorithms. One of them goes as
Whole - half - whole - whole - half - whole - whole (with the freedom to choose the first key)
I am not giving the selection rules for the other two 'Minor' algorithms. Again there are twelve keys we can select as our first key and therefore we can generate twelve sequences per Minor algorithm and there are three such 'Minor' algorithms, bringing a grand total of twelve times three, thirty six possible Minor scales. But we discover that many of the scales repeat themselves and in reality the number of unique 'scales' are fewer than thirty six Minor plus twelve Major scales.
Coming back to Indian system, even the ancient Tamil literary work, Silappadhikaram talks of an algorithm called 'Ilikramam', fascinating as it sounds. The rules of Ilikramam are quite similar to the selection of Major and Minor scales. It is really fun to work out this algorithm and derive a bunch of scales. (If you are more interested in this, refer to Prof. Ramanathan's book in the Reference section) In fact, nothing stops you at this point to go ahead and create your own selection rules to choose seven keys out of the twelve in the octave.
But let us turn our attention to Karnatic music. (Also, at this point, I will depart from talking about Indian classical music in general and stick only to South Indian music. Wherever relevant, references will be made to Hindustani music)
In Karnatic music, a very famous algorithm exists to select the keys in an octave, which forms the basis of important scales, which are called the 'Melakarta Scheme'. The Melakarta scheme selection algorithm is as follows: Please refer to Fig. 3 or Table II)
Wednesday, September 9, 2009
THE CONCEPT OF A SCALE
LET US MAKE A TUNE! (THE CONCEPT OF A SCALE)
We have learnt about the keyboard, labeled the various keys under the Eastern and Western schemes and even quarreled about whether it should have 12 keys or 22 to an octave. We now know that these keys are like the alphabets in creating music. How then do we compose music?
Before we answer this question, let us see if we can say something about the structure of a 'tune' or the 'melody' itself. If we listen to any musical piece such as 'Jana gana mana' or 'Roop tera mastana', we notice that their second lines and subsequent lines are not just mindless imitation or repetition of the first lines. There is an elaboration of a theme as the song unfolds. You could listen to any line of 'Roop tera mastana' and feel that it is connected to the first line, in a musical sense. If someone played a musical phrase from the song at random, the odds are you would guess that it is from 'Roop tera mastana'. And it may sound trivial, but you also notice that 'Roop tera mastana' does not at all sound like 'Jana gana mana'. There is a character, a structure and an identity to the song, however vague the concept may sound. (note the pun on the word 'sound' !) If you have grasped this abstract concept, you have almost understood the concept of a 'Ragam' (or 'raga' or 'rag') because a Ragam is also an embodiment of a particular musical identity.
For example, if you heard the song 'Vande maataram, Shujalaam shuphalaam...' you can tell that it has its own identity, which is different from the way 'Jana gana mana..' or 'Roop tera mastana ..' sound. This song is in fact, based on a Ragam called 'Desh'.
How do we forge such special musical identities using a keyboard ? The answer lies in choosing just a SUBSET of keys out of the twelve keys available in an octave (instead of all twelve) and sticking to just this subset of keys while making music. If you used all the keys in the keyboard to compose one song, you may not create anything with an identity. (You will see, as you understand more about music that this statement is strictly not true. There are nice-sounding musical compositions where almost all the keys are used)
Let us take an example. Let us choose just all the white keys in an octave - that is, use only seven out of the twelve keys. And let us play the keys in any order, even stay on one key for whatever length of time if we choose to do so. Let us allow ourselves to go to the white keys in the octaves below and above the standard octave as well. After a few minutes, you may sense an 'effect', a 'whole-ness' ('Gestalt'!) or a personality to the sound. If you don't believe me, have your friend play the keyboard with only the white keys. Now close your eyes and ask him (or her) to occassionally hit any black key. You can easily tell whenever the black keys are hit, because you are now sensitive to the 'structure' or 'character' produced by the seven white keys.
Is there a lower limit on how FEW keys we can choose in our subset and still get by ? If we chose a subset of just three keys (say, the first three white keys) in an octave and limit ourselves to those keys, we see that we don't have much variety to the melodies we can produce. It may sound like a drum beating. But is devoid of any special melodic personality. In general, (note that this is not an absolute law) one chooses five or six or seven keys out of the twelve keys available in an octave. More about these selection rules later. Once these keys are selected, the corresponding keys in the other octaves are also automatically selected and used in melody making.
In the context of Indian music, one has an extra degree of freedom. One can choose one set of keys to go up in frequency in the octave and choose an entirely different set to come down the octave, if we so desire. The key sequence to go up is called 'Arohanam' and the key sequence which forms the descending order is called the 'Avarohanam'. More about it later as well ! Let us now stick to 'symmetric' choices while going up or down. At the risk of sounding repetitive, let me say that you can always decide to be a non-conformist and follow none of these so-called rules and conventions. Music is after all, a creative art and the final criterion is whether it sounds pleasing.
How do we select the 'subset' of keys ? Our ancestors have done quite a bit of research on such selection rules and have come up with algorithms. Let us look at the Western music first. The 'Major' Scale is a very typical selection algorithm. This helps you select seven keys in an octave. The rules are as follows:
We have learnt about the keyboard, labeled the various keys under the Eastern and Western schemes and even quarreled about whether it should have 12 keys or 22 to an octave. We now know that these keys are like the alphabets in creating music. How then do we compose music?
Before we answer this question, let us see if we can say something about the structure of a 'tune' or the 'melody' itself. If we listen to any musical piece such as 'Jana gana mana' or 'Roop tera mastana', we notice that their second lines and subsequent lines are not just mindless imitation or repetition of the first lines. There is an elaboration of a theme as the song unfolds. You could listen to any line of 'Roop tera mastana' and feel that it is connected to the first line, in a musical sense. If someone played a musical phrase from the song at random, the odds are you would guess that it is from 'Roop tera mastana'. And it may sound trivial, but you also notice that 'Roop tera mastana' does not at all sound like 'Jana gana mana'. There is a character, a structure and an identity to the song, however vague the concept may sound. (note the pun on the word 'sound' !) If you have grasped this abstract concept, you have almost understood the concept of a 'Ragam' (or 'raga' or 'rag') because a Ragam is also an embodiment of a particular musical identity.
For example, if you heard the song 'Vande maataram, Shujalaam shuphalaam...' you can tell that it has its own identity, which is different from the way 'Jana gana mana..' or 'Roop tera mastana ..' sound. This song is in fact, based on a Ragam called 'Desh'.
How do we forge such special musical identities using a keyboard ? The answer lies in choosing just a SUBSET of keys out of the twelve keys available in an octave (instead of all twelve) and sticking to just this subset of keys while making music. If you used all the keys in the keyboard to compose one song, you may not create anything with an identity. (You will see, as you understand more about music that this statement is strictly not true. There are nice-sounding musical compositions where almost all the keys are used)
Let us take an example. Let us choose just all the white keys in an octave - that is, use only seven out of the twelve keys. And let us play the keys in any order, even stay on one key for whatever length of time if we choose to do so. Let us allow ourselves to go to the white keys in the octaves below and above the standard octave as well. After a few minutes, you may sense an 'effect', a 'whole-ness' ('Gestalt'!) or a personality to the sound. If you don't believe me, have your friend play the keyboard with only the white keys. Now close your eyes and ask him (or her) to occassionally hit any black key. You can easily tell whenever the black keys are hit, because you are now sensitive to the 'structure' or 'character' produced by the seven white keys.
Is there a lower limit on how FEW keys we can choose in our subset and still get by ? If we chose a subset of just three keys (say, the first three white keys) in an octave and limit ourselves to those keys, we see that we don't have much variety to the melodies we can produce. It may sound like a drum beating. But is devoid of any special melodic personality. In general, (note that this is not an absolute law) one chooses five or six or seven keys out of the twelve keys available in an octave. More about these selection rules later. Once these keys are selected, the corresponding keys in the other octaves are also automatically selected and used in melody making.
In the context of Indian music, one has an extra degree of freedom. One can choose one set of keys to go up in frequency in the octave and choose an entirely different set to come down the octave, if we so desire. The key sequence to go up is called 'Arohanam' and the key sequence which forms the descending order is called the 'Avarohanam'. More about it later as well ! Let us now stick to 'symmetric' choices while going up or down. At the risk of sounding repetitive, let me say that you can always decide to be a non-conformist and follow none of these so-called rules and conventions. Music is after all, a creative art and the final criterion is whether it sounds pleasing.
How do we select the 'subset' of keys ? Our ancestors have done quite a bit of research on such selection rules and have come up with algorithms. Let us look at the Western music first. The 'Major' Scale is a very typical selection algorithm. This helps you select seven keys in an octave. The rules are as follows:
Table III-22 Sruti scheme
Sruti Frequency Frequency
ratio (Hertz)
Sa 1 240
Ri 1 32/31 252.8
Ri 2 16/15 256
Ri 3 10/9 266.6
Ri 4 9/8 270
Ga 1 32/27 284.4
Ga 2 6/5 288
Ga 3 5/4 300
Ga 4 81/64 303.7
Ma 1 4/3 320
Ma 2 27/20 324
Ma 3 45/32 337.5
Ma 4 64/45 341.3
Pa 3/2 360
Dha 1 128/81 379
Dha 2 8/5 384
Dha 3 5/3 400
Dha 4 27/16 405
Ni 1 16/9 426.6
Ni 2 9/5 432
Ni 3 15/8 450
Ni 4 31/16 465
ratio (Hertz)
Sa 1 240
Ri 1 32/31 252.8
Ri 2 16/15 256
Ri 3 10/9 266.6
Ri 4 9/8 270
Ga 1 32/27 284.4
Ga 2 6/5 288
Ga 3 5/4 300
Ga 4 81/64 303.7
Ma 1 4/3 320
Ma 2 27/20 324
Ma 3 45/32 337.5
Ma 4 64/45 341.3
Pa 3/2 360
Dha 1 128/81 379
Dha 2 8/5 384
Dha 3 5/3 400
Dha 4 27/16 405
Ni 1 16/9 426.6
Ni 2 9/5 432
Ni 3 15/8 450
Ni 4 31/16 465
Table II - Karnatic...
Key # Western name Karnatic Karnatic
(Notation 1) (Notation 2)
1 C Sa S
2 C # (D b) Ri 1 R1
3 D Ri 2 (Ga 1) R2 (G1)
4 D # (E b) Ri 3 (Ga 2) R3 (G2)
5 E Ga 3 G3
6 F Ma 1 M1
7 F # (G b) Ma 2 M2
8 G Pa P1
9 G # (A b) Dha 1 D1
10 A Dha 2 (Ni 1) D2 (N1)
11 A # (B b) Dha 3 (Ni 2) D3 (N2)
12 B Ni 3 N3
________________________________________
It is also common to abbreviate the seven notes sa, ri, ga, ma, pa, dha, ni to letters S, R, G, M, P, D and N. The way to use this table is to realize that when you hit the first key of the octave (the C key) you will sing out 'Sa'. When you hit the first black key (C sharp) you will sing out 'Ri'. On the third key, you will sing out 'Ri' or perhaps a 'Ga' depending on the context. More about this 'context' later.
________________________________________
(Notation 1) (Notation 2)
1 C Sa S
2 C # (D b) Ri 1 R1
3 D Ri 2 (Ga 1) R2 (G1)
4 D # (E b) Ri 3 (Ga 2) R3 (G2)
5 E Ga 3 G3
6 F Ma 1 M1
7 F # (G b) Ma 2 M2
8 G Pa P1
9 G # (A b) Dha 1 D1
10 A Dha 2 (Ni 1) D2 (N1)
11 A # (B b) Dha 3 (Ni 2) D3 (N2)
12 B Ni 3 N3
________________________________________
It is also common to abbreviate the seven notes sa, ri, ga, ma, pa, dha, ni to letters S, R, G, M, P, D and N. The way to use this table is to realize that when you hit the first key of the octave (the C key) you will sing out 'Sa'. When you hit the first black key (C sharp) you will sing out 'Ri'. On the third key, you will sing out 'Ri' or perhaps a 'Ga' depending on the context. More about this 'context' later.
________________________________________
complete names...
(An aside: The complete names of the Indian notation are as follows: Shadjam for Sa, Rishabham for ri, Gandhaaram for ga, Madhyamam for Ma, Panchamam for pa, Dhaivatam for dha and Nishaadham for ni - This information is provided just so that you don't get too zapped when someone uses these full names)
Even in case of Indian music, we can extend our labeling of the keys to other octaves, much like in the Western system. In Indian music, the main octave is called 'Madhya stayi', the octave above it (higher) is called 'tara stayi' and the octave just below the Madhya stayi is called 'Mandra stayi' (based on the way 'mantras' were chanted in low frequencies in the centuries past). In terms of notation, the keys in the higher octave are labeled with a dot on TOP of the notes. The keys in the Mandra (lower) stayi are identified with dots BELOW the solfege notes.
Many good Indian musicians have voices spanning the entire three octaves, although most Indian compositions use up just the complete Madhya stayi scale and the top half of the Mandra stayi (only half an octave below) and the bottom half of the Tara stayi (just half an octave above the Madhya stayi).
We also see that the twelve keys of the octave divide into two halves. The four keys which are designated as ri and ga are called the 'bottom tetrachord' (in Indian terminology, 'Poorvaangam') and similarly the four keys corresponding to dha and ni are called the 'upper tetrachord' or 'Uttaraangam'. There is some kind of a symmetry between the bottom and the top tetrachords and key label assignment.
Just when you thought you had seen enough of the buzzwords, here is one more ! The starting frequency of your personalized octave relative to a 'standard' octave determines the 'pitch' of your voice. Your signature 'pitch' or 'sruti' (here we are using the word 'sruti' to mean 'the starting frequency of 'your' octave') is measured in a weird sounding unit called 'kattai'. Half a 'kattai' is a semitone and a full kattai is a 'whole tone'. If your octave happens to start at 240 Hz then you have a 'four kattai sruti', by definition. If your voice is very low pitched then you can have lower than four kattai as in case of many males. Women and children are high pitched and can have higher than four (even six) kattai srutis and their octave will start at frequencies higher than 240 Hz. An approximate Western equivalent of this is called 'Register'. In Indian classical music, the octaves are 'free floating', varying from person to person. The starting points are not pegged at 240 Hz.
Even in case of Indian music, we can extend our labeling of the keys to other octaves, much like in the Western system. In Indian music, the main octave is called 'Madhya stayi', the octave above it (higher) is called 'tara stayi' and the octave just below the Madhya stayi is called 'Mandra stayi' (based on the way 'mantras' were chanted in low frequencies in the centuries past). In terms of notation, the keys in the higher octave are labeled with a dot on TOP of the notes. The keys in the Mandra (lower) stayi are identified with dots BELOW the solfege notes.
Many good Indian musicians have voices spanning the entire three octaves, although most Indian compositions use up just the complete Madhya stayi scale and the top half of the Mandra stayi (only half an octave below) and the bottom half of the Tara stayi (just half an octave above the Madhya stayi).
We also see that the twelve keys of the octave divide into two halves. The four keys which are designated as ri and ga are called the 'bottom tetrachord' (in Indian terminology, 'Poorvaangam') and similarly the four keys corresponding to dha and ni are called the 'upper tetrachord' or 'Uttaraangam'. There is some kind of a symmetry between the bottom and the top tetrachords and key label assignment.
Just when you thought you had seen enough of the buzzwords, here is one more ! The starting frequency of your personalized octave relative to a 'standard' octave determines the 'pitch' of your voice. Your signature 'pitch' or 'sruti' (here we are using the word 'sruti' to mean 'the starting frequency of 'your' octave') is measured in a weird sounding unit called 'kattai'. Half a 'kattai' is a semitone and a full kattai is a 'whole tone'. If your octave happens to start at 240 Hz then you have a 'four kattai sruti', by definition. If your voice is very low pitched then you can have lower than four kattai as in case of many males. Women and children are high pitched and can have higher than four (even six) kattai srutis and their octave will start at frequencies higher than 240 Hz. An approximate Western equivalent of this is called 'Register'. In Indian classical music, the octaves are 'free floating', varying from person to person. The starting points are not pegged at 240 Hz.
Western keyboard...
We have enunciated again and again that we need many, many microtones to produce Indian music. Still, in this chapter, we are going to use a conventional, Western keyboard to learn about Indian music. It is almost like the Indian music is an analog entity and we are trying to quantize or digitize it into twelve keys, knowing fully well that we will have something akin to truncation (approximation) errors.
But before we begin, let us define one more term - the 'note'. The 'note' is just a primitive element of a musical phrase. An analogy will be the concept of a 'syllable' in a spoken word or a letter in a written word.
For example, in the nursery rhyme 'Baa baa black sheep' there are four 'notes', namely 'baa', 'baa', 'black' and 'sheep'. By a curious coincidence, this line also has four syllables - and we have managed to make a 'note' for each syllable. The concept of a note is so simple that even if you know nothing about music, you may be able to tell how many notes there are in a (simple) melodic pattern.
On the other hand, consider 'Roop tera mastana, pyaar meraa...' When spoken, the word 'roop' has only one syllable. However, when sung, it is distorted to sound like 'roo - pu' and uses TWO 'notes'. Similarly, when the singer goes 'pyaar meraaaa', he glides the end of the word 'meraaaa' into several 'notes'. The term 'note' and 'tone' are different and make sure you understand it. The word 'tone' is essentially a frequency, whereas the 'note' is the smallest part of a melody and could last one 'tone' plus possible microtones. The Indian word for 'note' is 'Swaram' or 'sur'. Now we are ready to get more technical and tinker with any commercially available keyboard to learn about Indian classical music. A diagram showing a typical keyboard octave is given in Table II, except that now we have labeled the keys with Indian names. Onceagain, eight out of the twelve keys have unique labels, whereas four of the remaining keys - keys 3, 4, 10 and 11 - have ambiguous (two possible) names. Unlike the Western notation, the keys with ambiguous labels are both black and white (two of each).
In the Indian system, we do not use alphabets to label keys. Instead, we use short, meaningless (please don't beat me to death on this - I know there are etymological reasons for choosing these set of syllables) syllables which go - Sa ri ga ma pa dha ni. These seven syllables are actually mnemonics to represent the 'notes' or 'Swarams' in Indian music. They are referred to as the 'Saptha Swarams' or 'Seven Swarams'. So, confusing as it may sound, in Indian music, we use the 'notes' to represent the 'tones'. Upon looking at Table II some more, we see that some THREE keys can be designated as 'ri', (even though they are designated as ri 1, ri 2 etc, they are all 'called' ri) three keys as 'ga', two as 'ma', three as 'dha' and three as 'ni'. However, there is no ambiguity when we want to press the keys corresponding to 'Sa' or 'Pa' - they are unique.
This notation (and this set of seven 'notes') is also called the 'Solfege notation' (in the West). Remember, even in the West, there is a solfege notation which goes do, re, me, soh etc. Basically, the solfege notation is a 'singable' set of syllables which helps us describe a musical melody. It will sound quite ridiculous to sing out words like 'C, C sharp, E flat' - instead of 'do fa la' when we hit the keyboard keys.
But before we begin, let us define one more term - the 'note'. The 'note' is just a primitive element of a musical phrase. An analogy will be the concept of a 'syllable' in a spoken word or a letter in a written word.
For example, in the nursery rhyme 'Baa baa black sheep' there are four 'notes', namely 'baa', 'baa', 'black' and 'sheep'. By a curious coincidence, this line also has four syllables - and we have managed to make a 'note' for each syllable. The concept of a note is so simple that even if you know nothing about music, you may be able to tell how many notes there are in a (simple) melodic pattern.
On the other hand, consider 'Roop tera mastana, pyaar meraa...' When spoken, the word 'roop' has only one syllable. However, when sung, it is distorted to sound like 'roo - pu' and uses TWO 'notes'. Similarly, when the singer goes 'pyaar meraaaa', he glides the end of the word 'meraaaa' into several 'notes'. The term 'note' and 'tone' are different and make sure you understand it. The word 'tone' is essentially a frequency, whereas the 'note' is the smallest part of a melody and could last one 'tone' plus possible microtones. The Indian word for 'note' is 'Swaram' or 'sur'. Now we are ready to get more technical and tinker with any commercially available keyboard to learn about Indian classical music. A diagram showing a typical keyboard octave is given in Table II, except that now we have labeled the keys with Indian names. Onceagain, eight out of the twelve keys have unique labels, whereas four of the remaining keys - keys 3, 4, 10 and 11 - have ambiguous (two possible) names. Unlike the Western notation, the keys with ambiguous labels are both black and white (two of each).
In the Indian system, we do not use alphabets to label keys. Instead, we use short, meaningless (please don't beat me to death on this - I know there are etymological reasons for choosing these set of syllables) syllables which go - Sa ri ga ma pa dha ni. These seven syllables are actually mnemonics to represent the 'notes' or 'Swarams' in Indian music. They are referred to as the 'Saptha Swarams' or 'Seven Swarams'. So, confusing as it may sound, in Indian music, we use the 'notes' to represent the 'tones'. Upon looking at Table II some more, we see that some THREE keys can be designated as 'ri', (even though they are designated as ri 1, ri 2 etc, they are all 'called' ri) three keys as 'ga', two as 'ma', three as 'dha' and three as 'ni'. However, there is no ambiguity when we want to press the keys corresponding to 'Sa' or 'Pa' - they are unique.
This notation (and this set of seven 'notes') is also called the 'Solfege notation' (in the West). Remember, even in the West, there is a solfege notation which goes do, re, me, soh etc. Basically, the solfege notation is a 'singable' set of syllables which helps us describe a musical melody. It will sound quite ridiculous to sing out words like 'C, C sharp, E flat' - instead of 'do fa la' when we hit the keyboard keys.
Having said all this....
Having said all this, we should also realize that there is nothing inherently scientific or sacred about this 'Equally tempered, twelve key per octave' Western music system, where an arbitrary set point is created at 240 Hz. There are other alternate systems and creative musicians are always experimenting with unconventional systems - in music it is 'cool' to break tradition ! For example, there is no need to have just twelve keys in an octave. In fact, the traditional Indian music system over thousands of years is based on a 22 key per octave system. Even if you chose twelve keys to fill in an octave, there is no reason to tune them in a geometric progression. In other words, you don't have to have an 'Equally tempered scale'. You can locate your frequencies based on some other non-geometric criteria which might 'sound' even better. Such scales in fact, exist and they are called 'Just tempered scales'. In fact, the Indian musical system uses one such scale. And in the final analysis, there is no need to even stick to the concept of octaves when producing music. In short, to produce music, there is no need for a grammar and rules ! If it sounds pleasnt, you are on. However, let us first learn the established grammar and tradition, before we attempt to break them!
Even though Indian musical systems are very different from the traditional Western Music system, we can still get a lot of insight into Indian music using the Equally tempered, twelve keys per octave methodology - essentially because it makes things simple. (Also, the keyboard is probably one of the easiest instruments to play). This has always been a bone of contention between the traditional Indian musicologists and the 'quick and dirty' folks like us. The Indian traditionalist will argue that we are compromising by limiting ourselves to just twelve 'tones' per octave, when tradition, dating back thousands of years, categorically spells out twenty two 'tones' per octave. The twenty two 'sruti' for the middle C octave is given in Table III. By the way, the Indian word for frequency or pitch or 'tone' is 'Sruti. A word of caution though - the term 'Sruti' has several other interpretations and meanings. We will come across some of them later.
Why, some Indian schools of thought even propose that there are infinite frequencies in an octave. The basic reason for such demands for more than twelve 'srutis' per octave is that Indian music, (not just Karnatic music) seems to 'flow' through the frequencies, whereas a Western song seems 'jumpy'. Take for example, 'Baa baa black sheep' and compare it to an Indian song, say, a movie song like 'Roop tera mastaana'. The Indian song seems to involve a lot of vocal acrobatics and nuances and not just go through piano-like jumps. This is the main difference between the Indian and Western music and we will return to this point again and again in this primer.
This is the reason why Indian classical music cannot be played effectively in a twelve key per octave instrument like a piano. Of course, several Western instruments have been 'adapted' with a little modification here and there, to play Indian classical music - violin, mandolin and guitar, for example. Some other instruments have been simply 'used', without modification, such as the harmonium and its latest cousin, the keyboard. Indian purists abhor such blatant use of Western, 'equally tempered' instruments. Expert harmonium player, Rajan Parrikar, points out that 'Just tempered' harmoniums, harmoniums with 22 tones per octave, even over 50 tones per octave etc have been built by various people.
Now let us come back to this basic difference between the Western and the Indian classical music system. We noted that in Indian music it is not enough to produce just twelve or even twenty two 'tones' in an octave. One ought to produce even the intermediate frequencies. These intermediate frequencies, which do not have any keys to produce them, are called 'microtones'. The Indian word for the 'microtone' is 'gamakam'. (of course, 'gamak' in hindi) It is often very difficult to explain this concept clearly and precisely. If the C key produces 240 Hz and the C# key produces 254 Hz what intermediate frequencies are we talking about ? Does Indian music use sounds produced at 247 Hz ? Treatises have been written in India about such microtonal apects of music. Suffice it to say that microtones or gamakams tend to be clustered around the primary key frequency, although this need not always be the case.
Note that if you postulate that an Indian music octave has twenty two or two hundred keys or infinity per octave, then what used to be a 'microtone' in a twelve-key system could now very well be a key. Of course, you can make a piano with such large number of tones per octave. It may be a long piano and you will need a superhuman dexterity to play it. But the positive side of it is that you will be able to play Indian music on it. The bottomline is, the piano produces just twelve frequencies in one octave and that is enough to compose a lot of Western songs. Whereas, to make Indian music, twelve keys are not enough in an octave.
Let us talk some more about microtones or gamakams. The vocal gliding and rolling in Indian music, (Remember Kishore Kumar's yodelling ?) whether it sounds good or not, are again examples of microtone usage. In fact, the microtones add variety to the Indian classical music - an extra dimension. From movie songs to folk music to classical music, the very heart of Indian music is this 'continuous flow' or 'gliding through a continuum of frequencies' or gamakam or microtonal excursions. Thus it is often said that Indian music is 'melody-based'. Since microtones are so important in Karnatic and Hindustani music and very few instruments can produce all the frequencies in an octave, the best enunciation of Indian classical music is in vocal singing. Many instruments like the violin, Gottuvadhyam (called Chitra Veena these days) and even the simple bamboo flute can produce a lot of gamakams, of course.
Just to drag the concept a little farther - some of you who have grown up in India may have developed a taste for Indian music, be it movie songs or highly classical songs. When you were exposed to Western rock and roll music you may have been drawn toward the numbers rich in gamakams (The Beatles, Simon and Garfunkel et al have produced many such pieces) rather than the rhythm oriented heavy metal numbers.
In the same breath, people say that the Western music is 'harmony-based', which brings out yet another difference between the two systems. 'Harmony' is produced when several instruments play different melodies or pieces simultaneously like in an orchestra. Harmony is also produced when more than one tone is produced at the same time. In the Western Music, 'harmony' is an important element.
Orchestration and 'harmony' are absent in Indian classical music. People have tried out orchestration of Indian classical music time and time again with limited success. (and there have been probably as many Western attempts to compose and play 'Indian style' melody based classical music) There is not much of a market for such 'Fusion' music, except perhaps among the fringe elements of the immigrant Indian community :-) Even if there is a 'Jugal bandhi' - a standard fare in Hindustani classical music where two instruments (or even two vocalists) are featured together, the musicians usually follow the same melodic pattern one after another with minor variation rather than play different melodies simultaneously.
There are a number of other differences as well between the two systems of music. Indian classical music, for example, does not use what are called chords, or pressing more than one key simultaneously. Chords are a major aspect of Western music and producing harmony via chords is a natural consequence of the Equally tempered (geometric series) arrangement of the keys. If keys were arranged in a Just tempered sequence, pressing more than one key at a given time might produce an unpleasant sound pattern resulting in what is called 'Besur' (in Hindustani music) or 'Abaswaram' (in Karnatic music). By the way, one more advantage of Equal temperment of pianos and keyboards is that it makes it easier to 'tune' them, (they go out of tune every once in a while and need to be tuned periodically) since each key is harmonically related to the other keys. In case of Just tempered arrangement, since the key ratio between adjacent keys is not a constant, most keys will have to be tuned individually.
Also absent is 'polyphony' - where several instruments (melodies) come and go asynchronously instead of at periodically predictable times. Also, the Western scales are standardized. The middle C octave ranges from 240 to 480 Hz. There is no reason to stick to these frequencies. In fact, in Indian music, you have the freedom to choose the frequency range of the octave from anywhere to twice anywhere. You can start at 230 Hz, if you wish. Also, in Western classical music, most musicians have music notated on sheets of paper and 'read' it when performing. Indian music is always played by 'ear'.
Just to summarize, the essential differences between Indian classical music system and the Western music are (a) the Western keyboard is 'Equally tempered' whereas the Indian keyboard ideally should be 'Just tempered' (b) Only twelve keys per octave are used in the West, whereas to play Indian music one needs to produce several intermediate microtones, not represented by a conventional keyboard - This is the most major difference (c) Harmony, chords, polyphony etc are absent in Indian classical music (d) In Indian music, there is no need to standardize an octave to begin at 240 Hz.
Even though Indian musical systems are very different from the traditional Western Music system, we can still get a lot of insight into Indian music using the Equally tempered, twelve keys per octave methodology - essentially because it makes things simple. (Also, the keyboard is probably one of the easiest instruments to play). This has always been a bone of contention between the traditional Indian musicologists and the 'quick and dirty' folks like us. The Indian traditionalist will argue that we are compromising by limiting ourselves to just twelve 'tones' per octave, when tradition, dating back thousands of years, categorically spells out twenty two 'tones' per octave. The twenty two 'sruti' for the middle C octave is given in Table III. By the way, the Indian word for frequency or pitch or 'tone' is 'Sruti. A word of caution though - the term 'Sruti' has several other interpretations and meanings. We will come across some of them later.
Why, some Indian schools of thought even propose that there are infinite frequencies in an octave. The basic reason for such demands for more than twelve 'srutis' per octave is that Indian music, (not just Karnatic music) seems to 'flow' through the frequencies, whereas a Western song seems 'jumpy'. Take for example, 'Baa baa black sheep' and compare it to an Indian song, say, a movie song like 'Roop tera mastaana'. The Indian song seems to involve a lot of vocal acrobatics and nuances and not just go through piano-like jumps. This is the main difference between the Indian and Western music and we will return to this point again and again in this primer.
This is the reason why Indian classical music cannot be played effectively in a twelve key per octave instrument like a piano. Of course, several Western instruments have been 'adapted' with a little modification here and there, to play Indian classical music - violin, mandolin and guitar, for example. Some other instruments have been simply 'used', without modification, such as the harmonium and its latest cousin, the keyboard. Indian purists abhor such blatant use of Western, 'equally tempered' instruments. Expert harmonium player, Rajan Parrikar, points out that 'Just tempered' harmoniums, harmoniums with 22 tones per octave, even over 50 tones per octave etc have been built by various people.
Now let us come back to this basic difference between the Western and the Indian classical music system. We noted that in Indian music it is not enough to produce just twelve or even twenty two 'tones' in an octave. One ought to produce even the intermediate frequencies. These intermediate frequencies, which do not have any keys to produce them, are called 'microtones'. The Indian word for the 'microtone' is 'gamakam'. (of course, 'gamak' in hindi) It is often very difficult to explain this concept clearly and precisely. If the C key produces 240 Hz and the C# key produces 254 Hz what intermediate frequencies are we talking about ? Does Indian music use sounds produced at 247 Hz ? Treatises have been written in India about such microtonal apects of music. Suffice it to say that microtones or gamakams tend to be clustered around the primary key frequency, although this need not always be the case.
Note that if you postulate that an Indian music octave has twenty two or two hundred keys or infinity per octave, then what used to be a 'microtone' in a twelve-key system could now very well be a key. Of course, you can make a piano with such large number of tones per octave. It may be a long piano and you will need a superhuman dexterity to play it. But the positive side of it is that you will be able to play Indian music on it. The bottomline is, the piano produces just twelve frequencies in one octave and that is enough to compose a lot of Western songs. Whereas, to make Indian music, twelve keys are not enough in an octave.
Let us talk some more about microtones or gamakams. The vocal gliding and rolling in Indian music, (Remember Kishore Kumar's yodelling ?) whether it sounds good or not, are again examples of microtone usage. In fact, the microtones add variety to the Indian classical music - an extra dimension. From movie songs to folk music to classical music, the very heart of Indian music is this 'continuous flow' or 'gliding through a continuum of frequencies' or gamakam or microtonal excursions. Thus it is often said that Indian music is 'melody-based'. Since microtones are so important in Karnatic and Hindustani music and very few instruments can produce all the frequencies in an octave, the best enunciation of Indian classical music is in vocal singing. Many instruments like the violin, Gottuvadhyam (called Chitra Veena these days) and even the simple bamboo flute can produce a lot of gamakams, of course.
Just to drag the concept a little farther - some of you who have grown up in India may have developed a taste for Indian music, be it movie songs or highly classical songs. When you were exposed to Western rock and roll music you may have been drawn toward the numbers rich in gamakams (The Beatles, Simon and Garfunkel et al have produced many such pieces) rather than the rhythm oriented heavy metal numbers.
In the same breath, people say that the Western music is 'harmony-based', which brings out yet another difference between the two systems. 'Harmony' is produced when several instruments play different melodies or pieces simultaneously like in an orchestra. Harmony is also produced when more than one tone is produced at the same time. In the Western Music, 'harmony' is an important element.
Orchestration and 'harmony' are absent in Indian classical music. People have tried out orchestration of Indian classical music time and time again with limited success. (and there have been probably as many Western attempts to compose and play 'Indian style' melody based classical music) There is not much of a market for such 'Fusion' music, except perhaps among the fringe elements of the immigrant Indian community :-) Even if there is a 'Jugal bandhi' - a standard fare in Hindustani classical music where two instruments (or even two vocalists) are featured together, the musicians usually follow the same melodic pattern one after another with minor variation rather than play different melodies simultaneously.
There are a number of other differences as well between the two systems of music. Indian classical music, for example, does not use what are called chords, or pressing more than one key simultaneously. Chords are a major aspect of Western music and producing harmony via chords is a natural consequence of the Equally tempered (geometric series) arrangement of the keys. If keys were arranged in a Just tempered sequence, pressing more than one key at a given time might produce an unpleasant sound pattern resulting in what is called 'Besur' (in Hindustani music) or 'Abaswaram' (in Karnatic music). By the way, one more advantage of Equal temperment of pianos and keyboards is that it makes it easier to 'tune' them, (they go out of tune every once in a while and need to be tuned periodically) since each key is harmonically related to the other keys. In case of Just tempered arrangement, since the key ratio between adjacent keys is not a constant, most keys will have to be tuned individually.
Also absent is 'polyphony' - where several instruments (melodies) come and go asynchronously instead of at periodically predictable times. Also, the Western scales are standardized. The middle C octave ranges from 240 to 480 Hz. There is no reason to stick to these frequencies. In fact, in Indian music, you have the freedom to choose the frequency range of the octave from anywhere to twice anywhere. You can start at 230 Hz, if you wish. Also, in Western classical music, most musicians have music notated on sheets of paper and 'read' it when performing. Indian music is always played by 'ear'.
Just to summarize, the essential differences between Indian classical music system and the Western music are (a) the Western keyboard is 'Equally tempered' whereas the Indian keyboard ideally should be 'Just tempered' (b) Only twelve keys per octave are used in the West, whereas to play Indian music one needs to produce several intermediate microtones, not represented by a conventional keyboard - This is the most major difference (c) Harmony, chords, polyphony etc are absent in Indian classical music (d) In Indian music, there is no need to standardize an octave to begin at 240 Hz.
bizarre technical terms
Now here is a set of bizarre technical terms - by definition, each key is supposed to be a 'semitone' or 'half tone' apart from its adjacent key. Thus, keys which are second nearest neighbors are considered a 'whole tone' apart. (Note that the sense in which we use the word 'tone' here is quite different from our earlier usage of it to mean frequency). For example, the first white key ('C' key) and the first black key ('C sharp') are a 'semitone' apart, whereas the first white key ('C key') and the second white key ('D key') are a full tone (whole tone) apart. And the 'C sharp' and 'D' keys are a semitone apart, as well.
Yet another aside: All keyboards are not necessarily tuned to the middle C key (which is set to 240 Hz). You can build keyboards which have a different reference point. Fixing the middle A key to a particular frequency (440 Hz) is a common alternative.
You can play with the keys and produce music. The keys and the 'tones' they produce are the basic building blocks of music. You can even press the same key twice or stay on one key for an extended period of time. You will also notice that although some 'melodies' are pleasant to the senses, some other sequences are not. If it is the very first time you are tinkering with a keyboard, the odds are that whatever melody you produce sounds 'musical' to you and of course, extremely unpleasant to the others around you. If you increase the volume on the electric keyboard, you are changing the intensity. If you choose different 'instruments' the modern day keyboards simulate, you are then changing the 'quality'. Basically, you now know how to manipulate the essentials of music, namely the pitch, intensity, duration and quality.
Yet another aside: All keyboards are not necessarily tuned to the middle C key (which is set to 240 Hz). You can build keyboards which have a different reference point. Fixing the middle A key to a particular frequency (440 Hz) is a common alternative.
You can play with the keys and produce music. The keys and the 'tones' they produce are the basic building blocks of music. You can even press the same key twice or stay on one key for an extended period of time. You will also notice that although some 'melodies' are pleasant to the senses, some other sequences are not. If it is the very first time you are tinkering with a keyboard, the odds are that whatever melody you produce sounds 'musical' to you and of course, extremely unpleasant to the others around you. If you increase the volume on the electric keyboard, you are changing the intensity. If you choose different 'instruments' the modern day keyboards simulate, you are then changing the 'quality'. Basically, you now know how to manipulate the essentials of music, namely the pitch, intensity, duration and quality.
Table I - Arrangement...
Key # Key color Frequency (Hz) Name
1 White 240 C
2 Black 254 C # (D b)
3 White 269 D
4 Black 285 D # (E b)
5 White 302 E
6 White 320 F
7 Black 338.5 F # (G b)
8 White 358.5 G
9 Black 380 G # (A b)
10 White 402 A
11 Black 426 A # (B b)
12 White 451 B
1 White 240 C
2 Black 254 C # (D b)
3 White 269 D
4 Black 285 D # (E b)
5 White 302 E
6 White 320 F
7 Black 338.5 F # (G b)
8 White 358.5 G
9 Black 380 G # (A b)
10 White 402 A
11 Black 426 A # (B b)
12 White 451 B
WESTERN MUSIC...
Let us examine the frequency aspect of music first. This is perhaps the most studied aspect as well. We mentioned that all music is produced in the audible frequency range, a range which varies from person to person. Although human ears cannot tell very high 'tones', musical instruments can produce frequencies (overtones) even beyond the threshold of human hearing. Music is sometimes described technically as 'tonal' or 'chromatic', both terms simply mean that we use a whole spectrum of frequencies to produce music.
The audible range is divided into 'octaves'. An octave is really a frequency range from a frequency f1 to f2 such that f2 is twice that of f1 in terms of cycles or hertz. For some physiological reason, the human ear is logarithmic and is sensitive to frequency octaves. The audible frequency is then comprised of many, many octaves. We can choose any number to be our f1 (and f2 of course is 2 times f1) - we can define an octave from 10 Hz to 20 Hz or equally well another one, say from 15 Hz to 30 Hz.
In terms of sound production, a typical human voice can produce several frequencies, although it is usually limited to about three or four octaves - even if we have a drum-like, groggy 'morning voice' at the low end of the range and a shrill, ear-piercing shriek at the high end. Only the exceptionally gifted people can produce a wide spectrum of vocal sounds spanning several octaves. (Of course, there are those female Indian movie playback singers who can produce ultra high frequencies which only dogs can hear clearly !) By the way, here we are only talking about 'primary' frequencies and not overtones associated with the 'quality' of our voices - remember, overtones are higher frequency components, but produced in much lower intensities.
A piano or a keyboard is a typical Western musical instrument. All we see is a bunch of keys, some in black and some in white. However, upon a closer look, we see that there is a periodicity. As we go from the left of the keyboard to the right (and here I am assuming you know how to sit in front of a keyboard) the keys produce higher and higher frequencies. In fact, the key frequencies are arranged in such a manner that they are in a geometric series. That is, the frequency between any key and the key immediately to its left (irrespective of the color of the key) is a constant, the constant being equal to the twelfth root of two or 1.059. For example, typically, there is a white key in the keyboard set to 240 Hz. Then the adjacent key on the right, a black one as a matter of fact, is set to 240 X 1.059 = 254 Hertz.
By the specific choice of this ratio (twelfth root of two) we see that by the time we reached the thirteenth key, we have doubled our frequency and thus spanned a whole octave. In fact, if you look at the keyboard you see that the key pattern repeats every twelve keys. If you chose the white key at 240 Hz, then the thirteenth key will be at 480 Hz and your octave ranged from 240 to 480 Hz. Equally well, you could have started counting from the black key at 254 Hz and twelve keys later you would have still spanned an octave, except that this time your octave ranged from 254 to 508 Hz.
This division of the octave into twelve 'tones' which have specific ratio between adjacent keys (the ratio equalling 1.059) is peculiar to Western music. This geometric arrangement of frequencies of the keys in an octave is called an 'Equally tempered' arrangement. And besides the keyboard, most Western musical instruments are also tuned to such an arrangement.
Even though there is a degree of freedom about what you want to be the range of an octave (whether it is from 240 to 480 Hz or 254 to 508 Hz etc.) the Western music defines a standard octave called the 'Middle C octave' (also called the Middle C scale etc) starting from the white key set to 240 Hz. The entire octave (the twelve key pattern, that is) is shown in Fig. 1. On your keyboard, this octave is located somewhere near the middle. Once you figured out where this octave is, you can quickly identify the first key of this octave (set to 240 Hz). And because we know the ratio of the key frequencies now we can pretty much compute the frequency generated by ANY key. You will also notice that the keyboard has about three to four octaves (between 36 to 48 keys, depending on how much you paid for it) The upper octave, starting from 480 Hz is the Upper C octave and the lower octave starting at 120 Hz is the Lower C octave etc.
The audible range is divided into 'octaves'. An octave is really a frequency range from a frequency f1 to f2 such that f2 is twice that of f1 in terms of cycles or hertz. For some physiological reason, the human ear is logarithmic and is sensitive to frequency octaves. The audible frequency is then comprised of many, many octaves. We can choose any number to be our f1 (and f2 of course is 2 times f1) - we can define an octave from 10 Hz to 20 Hz or equally well another one, say from 15 Hz to 30 Hz.
In terms of sound production, a typical human voice can produce several frequencies, although it is usually limited to about three or four octaves - even if we have a drum-like, groggy 'morning voice' at the low end of the range and a shrill, ear-piercing shriek at the high end. Only the exceptionally gifted people can produce a wide spectrum of vocal sounds spanning several octaves. (Of course, there are those female Indian movie playback singers who can produce ultra high frequencies which only dogs can hear clearly !) By the way, here we are only talking about 'primary' frequencies and not overtones associated with the 'quality' of our voices - remember, overtones are higher frequency components, but produced in much lower intensities.
A piano or a keyboard is a typical Western musical instrument. All we see is a bunch of keys, some in black and some in white. However, upon a closer look, we see that there is a periodicity. As we go from the left of the keyboard to the right (and here I am assuming you know how to sit in front of a keyboard) the keys produce higher and higher frequencies. In fact, the key frequencies are arranged in such a manner that they are in a geometric series. That is, the frequency between any key and the key immediately to its left (irrespective of the color of the key) is a constant, the constant being equal to the twelfth root of two or 1.059. For example, typically, there is a white key in the keyboard set to 240 Hz. Then the adjacent key on the right, a black one as a matter of fact, is set to 240 X 1.059 = 254 Hertz.
By the specific choice of this ratio (twelfth root of two) we see that by the time we reached the thirteenth key, we have doubled our frequency and thus spanned a whole octave. In fact, if you look at the keyboard you see that the key pattern repeats every twelve keys. If you chose the white key at 240 Hz, then the thirteenth key will be at 480 Hz and your octave ranged from 240 to 480 Hz. Equally well, you could have started counting from the black key at 254 Hz and twelve keys later you would have still spanned an octave, except that this time your octave ranged from 254 to 508 Hz.
This division of the octave into twelve 'tones' which have specific ratio between adjacent keys (the ratio equalling 1.059) is peculiar to Western music. This geometric arrangement of frequencies of the keys in an octave is called an 'Equally tempered' arrangement. And besides the keyboard, most Western musical instruments are also tuned to such an arrangement.
Even though there is a degree of freedom about what you want to be the range of an octave (whether it is from 240 to 480 Hz or 254 to 508 Hz etc.) the Western music defines a standard octave called the 'Middle C octave' (also called the Middle C scale etc) starting from the white key set to 240 Hz. The entire octave (the twelve key pattern, that is) is shown in Fig. 1. On your keyboard, this octave is located somewhere near the middle. Once you figured out where this octave is, you can quickly identify the first key of this octave (set to 240 Hz). And because we know the ratio of the key frequencies now we can pretty much compute the frequency generated by ANY key. You will also notice that the keyboard has about three to four octaves (between 36 to 48 keys, depending on how much you paid for it) The upper octave, starting from 480 Hz is the Upper C octave and the lower octave starting at 120 Hz is the Lower C octave etc.
SOUND AND MUSIC
SOUTH INDIAN CLASSICAL (KARNATIC) MUSIC
BY MAHADEVAN RAMESH
Music is an extremely subjective, aural experience. Some sounds are perceived by us as pleasant and some others as unpleasant. What is considered pleasant or unpleasant can be quite personal, based on our specific culture, exposure to particular kinds of music and perhaps even on what our parents told us. A song could be a major hit in one country and could be completely disliked and ignored in some other country. Our musical tastes are indeed developed. As we grow up, and discover music from other cultures or newer musical styles, our tastes too change. Sometimes, we even discover a pleasant piece of music purely by accident - because it simply happened to resonate with our inner sensibilities. Oh, nothing like self discovery !
So how do we make sense of sound and music ? Let us try to answer this by examining some simple concepts first. Our high school physics tells us that sound has several features - such as pitch, intensity, quality and duration. The pitch is just the frequency of the sound vibration - given in hertz or cycles. The musical term for frequency is 'tone'. The audible frequency range extends from about 25 Hz to around eight or ten thousand hertz, although it depends entirely on the individual. Children can hear much higher frequencies. At the lower end of the range, even if we may not 'hear' ultralow frequencies, we may 'feel' the vibrations as a tactile sensation.
The intensity is the same as loudness and it is related to the amplitude of the sound wave. One should learn to not confuse the intensity with the frequency. For example, try to recite the nursery rhyme 'Baa baa black sheep, Have you any wool ?' When you come to the syllable 'bl' in the phrase 'black sheep' (or 'woo' in the word 'wool') you are hitting a higher 'tone' compared to 'Baa baa'. This is the effect of frequency. Now, you can either whisper this nursery rhyme or shout your guts out. In each case, you are simply changing the intensity.
The other attribute of sound - duration - is self-explanatory. It is simply the time during which the specific frequency or 'tone' lasts. The term 'quality' is more difficult to understand. It is simply a signature of the source of the sound. It is a term which explains why a violin sounds like a violin and a drum sounds like a drum. This attribute is precisely the reason you can make out your mother's voice over the phone even if she has a horrible cold. The bottomline is, when you or an instrument produce sound, you not only produce one frequency, but also produce a spectrum consisting of several 'overtones'. This is variously referred to as 'timbre' or 'tone color'. This constitutes the 'Quality' of that sound.
Just to explain this concept some more, let us say you try to produce a single frequency with your voice - one way to 'produce' a single frequency is to get a keyboard and keep pressing one of its keys and you hum along till you resonate. If you actually analyzed the waveform you produced, you will see not only a significant amount of the frequency you were trying to produce but also see small amounts of other frequencies - which are the overtones. The exact composition of overtones you produced is in some sense the signature of your voice and constitutes its quality.
This should also set you thinking. Just how in the world do you perceive sounds ? How do you identify your friend's voice ? Clearly you are not decomposing it into frequency components (Fourier analysis). How do you sometimes make out which song it is simply by listening to a few notes ? How is it that you can mentally 'visualize' (!) someone's voice, laughter, sounds, some past conversations, songs ? Basically, when you hear sounds and music, you are simply doing a 'pattern recognition' against what you already know. Over the years, your brain has stored a certain number of 'primitives' - this list is a dynamic one and primitives are added or lost as you grow older - and you have an intrinsic capability to match a freshly heard sound impulse to the basic database. If you hear a strange sound that does not produce a match, sometimes you load it up as a primitive.
An equally interesting exercise - think of five songs you really like. Can you explain why you like them or what is in common with all of them ? Can you 'explain' and define your musical taste ? Unfortunately, however much analysis one does, in terms of frequencies and so forth, it finally boils down to psychological factors when it comes to music and taste. Analysis is merely a tool to understand some of its structure. It can never explain why some musical sounds are deemed 'romantic' or 'harsh' or why some Ragam is an evening Ragam (if you believe in such things). Such mystique about music will come back to haunt us and will forever prevent us from understanding its totality in an objective manner.
This is just a simple stab at the psychology of sound perception. Let us get back to the business on hand!
BY MAHADEVAN RAMESH
Music is an extremely subjective, aural experience. Some sounds are perceived by us as pleasant and some others as unpleasant. What is considered pleasant or unpleasant can be quite personal, based on our specific culture, exposure to particular kinds of music and perhaps even on what our parents told us. A song could be a major hit in one country and could be completely disliked and ignored in some other country. Our musical tastes are indeed developed. As we grow up, and discover music from other cultures or newer musical styles, our tastes too change. Sometimes, we even discover a pleasant piece of music purely by accident - because it simply happened to resonate with our inner sensibilities. Oh, nothing like self discovery !
So how do we make sense of sound and music ? Let us try to answer this by examining some simple concepts first. Our high school physics tells us that sound has several features - such as pitch, intensity, quality and duration. The pitch is just the frequency of the sound vibration - given in hertz or cycles. The musical term for frequency is 'tone'. The audible frequency range extends from about 25 Hz to around eight or ten thousand hertz, although it depends entirely on the individual. Children can hear much higher frequencies. At the lower end of the range, even if we may not 'hear' ultralow frequencies, we may 'feel' the vibrations as a tactile sensation.
The intensity is the same as loudness and it is related to the amplitude of the sound wave. One should learn to not confuse the intensity with the frequency. For example, try to recite the nursery rhyme 'Baa baa black sheep, Have you any wool ?' When you come to the syllable 'bl' in the phrase 'black sheep' (or 'woo' in the word 'wool') you are hitting a higher 'tone' compared to 'Baa baa'. This is the effect of frequency. Now, you can either whisper this nursery rhyme or shout your guts out. In each case, you are simply changing the intensity.
The other attribute of sound - duration - is self-explanatory. It is simply the time during which the specific frequency or 'tone' lasts. The term 'quality' is more difficult to understand. It is simply a signature of the source of the sound. It is a term which explains why a violin sounds like a violin and a drum sounds like a drum. This attribute is precisely the reason you can make out your mother's voice over the phone even if she has a horrible cold. The bottomline is, when you or an instrument produce sound, you not only produce one frequency, but also produce a spectrum consisting of several 'overtones'. This is variously referred to as 'timbre' or 'tone color'. This constitutes the 'Quality' of that sound.
Just to explain this concept some more, let us say you try to produce a single frequency with your voice - one way to 'produce' a single frequency is to get a keyboard and keep pressing one of its keys and you hum along till you resonate. If you actually analyzed the waveform you produced, you will see not only a significant amount of the frequency you were trying to produce but also see small amounts of other frequencies - which are the overtones. The exact composition of overtones you produced is in some sense the signature of your voice and constitutes its quality.
This should also set you thinking. Just how in the world do you perceive sounds ? How do you identify your friend's voice ? Clearly you are not decomposing it into frequency components (Fourier analysis). How do you sometimes make out which song it is simply by listening to a few notes ? How is it that you can mentally 'visualize' (!) someone's voice, laughter, sounds, some past conversations, songs ? Basically, when you hear sounds and music, you are simply doing a 'pattern recognition' against what you already know. Over the years, your brain has stored a certain number of 'primitives' - this list is a dynamic one and primitives are added or lost as you grow older - and you have an intrinsic capability to match a freshly heard sound impulse to the basic database. If you hear a strange sound that does not produce a match, sometimes you load it up as a primitive.
An equally interesting exercise - think of five songs you really like. Can you explain why you like them or what is in common with all of them ? Can you 'explain' and define your musical taste ? Unfortunately, however much analysis one does, in terms of frequencies and so forth, it finally boils down to psychological factors when it comes to music and taste. Analysis is merely a tool to understand some of its structure. It can never explain why some musical sounds are deemed 'romantic' or 'harsh' or why some Ragam is an evening Ragam (if you believe in such things). Such mystique about music will come back to haunt us and will forever prevent us from understanding its totality in an objective manner.
This is just a simple stab at the psychology of sound perception. Let us get back to the business on hand!
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