Carnatic Music Primer

Dr. Parthasarathy Sriram

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The topics of this section are of fairly advanced nature and somewhat abstract and mathematical. Readers who are not mathematically oriented may skip this section. The basic principles behind Grahabedam and symmetry are rooted in mathematics. Thus, a certain amount of mathematical notation is almost unavoidable in any explanation of these concepts. Grahabedam is the process of modifying ragas by shifting the base note Sa or the sruthi to various swara sthanas. Symmetry indicates certain types of similarities in the structure of the swaras used in a ragam. Grahabedam is defined for melakartas as well as janya ragas. Consider Dheerasankaraabharanam (Bana - Ma), the 29th melakarta ragam. The swara sthanas for it in one kattai sruthi are as shown in the following keyboard diagram.

Swaras in Dheerasankaraabharanam

Suppose we continue to use the same swara sthanas but shift the sruthi to two kattais, what was Sankaraabharanam takes on a different appearance. The swara locations for two kattai sruthi are given in the following figure.

Swaras for two kattai sruthi

Using this figure, we see that what used to be Chatusruthi Rishabam now becomes Sa and Anthara Gandharam becomes Chatusruthi Rishabam. Continuing along, the Suddha Madhyamam becomes Sadharana Gandharam, Pa becomes Suddha Madhyamam, Chatusruthi Dhaivatham becomes Pa, Kakali Nishadam becomes Chatusruthi Dhaivatham, Sa becomes Kaisika Nishadam. Consulting the melakarta tables, we see that the new swaras correspond to the 22nd melakarta Kharaharapriya (Veda - Bhu). Thus, moving the sruthi to the swara Ri of Sankaraabharanam results in Kharaharapriya. It should be remembered that the absolute pitch of the swaras continue to be the same; it is only because of the shifting of the origin of the scale (the Sa) that a different raga is produced. Evidently, one can carry out the process for janya ragas also.

Consider a notation system for the swara and swara sthanas as follows. Let us represent the swara sthanas by a string of 12 digits, each one corresponding to the twelve swara sthanas into which an octave is divided. The presence of a swara sthana is denoted by a one in the corresponding digit and the absence by a zero. Thus, in the above example of Sankaraabharanam, the representation would be [101011010101]. The first 1 corresponds to Sa; the next swara sthana corresponds to Suddha Rishabam which does not occur in Sankaraabharanam and thus the corresponding digit is 0. The third digit is for Chatusruthi Rishabam and Suddha Gandharam. Since Chatusruthi Rishabam occurs in our example, the third digit is set to 1. The same process can be continued to obtain all the twelve digits. Note that the first digit is always 1 to indicate the use of Sa. In the case of melakartas, Pa is always used and thus, the eighth digit is always 1. Further, all melakartas use seven and only seven swaras and thus the notation always contains seven ones and five zeros. In general, the number of ones in the notation denotes the number of swaras used in that raga. The following list gives the number strings corresponding to the twelve chakrams and the Pa-Sri.. designations. Note that the Purvangam is represented by seven digits and the uttarangam by five digits. The purvangam notations carry a 1 in parenthesis to indicate that the next swara is Sa, which is always present.

Using this notation, Grahabeda is very easy to handle. One simply moves digits from one end of the number to the other. In the example just considered, Sankaraabharanam is represented by [101011010101]. To move the sruthi to Ri, we make the digit corresponding to Ri as the first digit to get [1011010101]. The two digits which were removed are moved over to the right end to obtain [101101010110]. This can be easily verified to represent Kharaharapriya. This ability of a raga to generate other ragas through Grahabedam is denoted by the term Murchanaakara. The absence of this characteristic is termed Amurchanaakara. In light of the above example, Dheeraankaraabharanam and Kharaharapriya are Murchanaakara ragas. Sometimes, the process of grahabedam on a ragam leads to non-existent scales. For example, if we take the Ni of Sankarabharanam as the base swara, we get [110101101010]. This scale has two Madhyamas and no Panchamam and such a scale is not allowable under the current melakarta scheme. Evidently, for a raga to be Amurchanaakara, all the grahabeda derived scales of it should be somewhat like this. Jhaalavaraali (39) is an example of a melakarta which is an Amurchanaakara ragam.

It is important to note that Grahabedam is necessarily a two way process. Instead of generating Kharaharapriya from Sankaraabharanam, we can start with Kharaharapriya and move the sruthi to the Ni to get Sankaraabharanam. Hence, it is appropriate to group together ragas which can be derived from each other and state, for example, that Kharaharapriya and Sankaraabharanam are Grahabeda pairs instead of inappropriately stating that Kharaharapriya can be derived from Sankaraabharanam through Grahabedam. The example just considered leads to the most famous Grahabedam group of melakartas consisting of Mechakalyaani (65), Dheerasankaraabharanam (29), Harikaambhoji (28), Kharaharapriya (22), Natabhairavi (20) and Hanumathodi (8). This group possesses another interesting property. Mechakalyaani uses the 'big' variety of all the swaras (big Ri, big Ga etc.) and proceeding down the group as it is written above, the 'big' swaras are progressively replaced by corresponding 'small' swaras. Thus Dheerasankaraabharanam uses 'small' Ma ( and the rest, 'big'), Harikaambhoji uses 'small' Ma and Ni and so on until we reach Hanumathodi, which uses the 'small' variety of all the swaras.

The Grahabedam process as above can be used on janya ragas also. The notation can handle only janya ragas with symmetric arohanam and avarohanam (meaning the arohanam and avarohanam should have the same swaras) and janya ragas with vivadi swaras cannot be distinguished correctly. The most famous Grahabedam group of janya ragas includes Mohanam, Hindolam, Suddha Dhanyaasi, Suddha Saaveri and Madhyamaavathy. Some other groups are listed in the Appendix.

The next logical question that arises is whether it is possible for a raga (assumed to have symmetric arohanam and avarohanam) to be Grahabedam derivable from itself. If the raga has five or seven swaras (including the fixed Sa), then it turns out that it cannot be Grahabedam derived from itself. Thus, melakartas are not self Grahabedam derivable since they all have seven swaras. If a ragam is self Grahabedam derivable, it can be confusing to the listener since the same tune can belong to a single ragam at two different sruthis! Perhaps, it is no coincidence that we see ancient systems of music with five note scales and the current system with seven note scales, but no significant six note scales. The seven swara scale is most probably here to stay since setting more than seven swaras into twelve swara sthanas would allow very little room for the creation of distinct base ragas especially if the Panchama sthana is reserved and always present.

Consider the 1st melakarta, Kanakaangi (Indu - Pa). It is represented by the sequence [111001011100(1)]. Note the symmetry between the lower and upper portions of the structure due to the repeating sequence 111001. This is an example of a class of symmetry, where the lower and upper portions (not exactly the purvangam and uttarangam, but close) of a raga have a similar structure. This characteristic is possessed by the following melakartas: Hanumathodi (Netra - Sri), Maayaamaalavagowla (Agni - Go), Kharaharapriya (Veda - Bhu), Dheerasankaraabharanam (Bana - Ma) and Chalanaata (Ruthu - Sha). The sixth melakarta Thaanaroopi (Indu - Sha) is denoted by the string [111001010011(1)]. The lower portion of this 111001 is the same as the upper portion 100111 written backwards. This means that the swara steps in the lower portion of the raga in the arohanam are similar to the swara steps in the upper portion in the avarohanam, or these ragas employ a similar swara step structure in the arohanam and avarohanam. This is another type of symmetry and the melakartas which possess this property are Thaanaroopi (Indu - Sha), Kokilapriya (Netra - Ma), Maayaamaalavagowla (Agni - Go), Kharaharapriya (Veda - Bhu), Chaarukesi (Bana - Sri) and Yaagapriya (Ruthu - Pa).

Note that Maayaamaalavagowla possesses both types of symmetries we have looked at. Further, it has no isolated swaras (denoted by the ones all appearing in pairs). This characteristic makes a raga easier to sing (or play on an instrument) since pairs of swaras occur together. It is probably for this reason that this ragam is almost invariably the first that a student is taught. In fact many of the initial lessons are set to this ragam. (This practice is generally attributed to Purandara Dasa, who is often called the father of modern Carnatic music). When an advanced stage is reached and students begin to render Kalpanaaswaras, many find it convenient to sing first in Maayaamaalavagowla or its Prati Madhyama pair Kaamavardhani. A systematic examination of the compositions of Muthuswamy Dikshithar reveals a good degree of specialization in Maayaamaalavagowla and its janya ragas. (In fact, there is an interesting story in folklore about how Dikshithar started composing songs. From a very young age, Dikshithar was a religious person and used to travel to many temples. On one such tour, he was at the temple of Lord Subramanya in Thirutthani when an old man suddenly came up to him, dropped a piece of sugar in his mouth and after blessing him, disappeared mysteriously. Dikshithar was inspired by this incident and almost immediately composed the some say his first song 'Sri Naathaathi Guruguho' in Maayaamaalavagowla. Saint Thyagaraja's compositions exhibit a similar lean towards Kharaharapriya and its janya ragas. Perhaps, these facts are related to the high degree of symmetry possessed by these two ragas.

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