Swaras and Swarasthanas
There are seven swaras in Carnatic music, namely, Shadjam (Sa), Rishabam (Ri), Gandharam (Ga), Madhyamam (Ma), Panchamam (Pa), Dhaivatham (Da) and Nishadam (Ni). There is some theoretical basis for why there is an odd number (seven) of swaras and we will deal with this subsequently. For simplicity, let us fix the Sa at one kattai and place the remaining swaras at the successive white keys. This provides us with a scale or a raga (in this case, containing all the seven swaras). As mentioned previously, ancient Vedic chants have but three swaras and somewhat later forms of music (Indian as well as other forms, eg. Chinese) use five swaras - eg. the Sa, Ri, Ga, Pa and Da of the scale we just created. Our present system is based on seven swaras, and perhaps, a few thousand years from now, the human race will advance to a point of discriminating scales of more swaras (unlikely). The seven swaras are mythologically associated with the sounds produced by certain animals and the names of the swaras are related to the names of these animals. The name Madhyamam appears to be related to the central or madhya location in the seven notes and Panchamam is most probably derived from the number five, denoting the position of the note.
We observed earlier that doubling the pitch of a swara by a factor of two results in going up in pitch by one octave. Thus, doubling the pitch of Sa (say Sa1) results in another Sa (Sa2) which is one octave higher than our original Sa. A further doubling produces Sa3 which is one octave higher than Sa2 and two octaves above Sa1. Three times the original Sa produces the Pa located between Sa2 and Sa3. In other words, the pitch of the swara Pa is one and half times the pitch of the Sa below it (and three fourths the pitch of the Sa above it). Now we come to an important limitation of the keyboard - the way the octave is divided into the twelve swara sthanas. Since it is based on current western music norms, the division is done on a logarithmic basis (which is just a more technical way of saying that the pitch values of the successive swara sthanas form a geometric progression). An octave is a factor of two and there are twelve intervals in it. If we make all the intervals equal to a multiplicative factor x, then the pitch corresponding to any key will be x times the pitch of the key (white or black) immediately to the left of it. Extending the procedure we arrive at what the value of x should be. The thirteenth swara sthana results in an octave, or, stated mathematically, x12=2. Then, we have x to be the twelfth root of two or a factor of approximately 1.06. Using this logarthmic division procedure, Pa (the 8th swara sthana) corresponds not to a ratio of 1.5 but 1.498. Though the discrepancy is very small, a well trained ear (eg. professional musician) can pick out this difference.
Carnatic music is based not on logarithmic division but on rational division. An octave is based on the ratio 1:2; Pa is located through the ratio 2:3; similar definitions exist for all the twelve swara sthanas. A few centuries ago, Western classical music too was based on rational division (the resulting scale was called as the natural scale), but this has given way to the equally tempered (also called chromatic) scale produced by logarithmic division. The difference is subtle, but quite important. The rational division claim is supported by the fact that tuning of instruments (for example, in setting the frets of veena) is performed mostly by the ear and not by reference to standards. Further, the swara sthanas of Carnatic music define only nominal locations for the swaras. Depending on the raga in which the swara is used, it manifests a deviation from the nominal sthana. Actually, the deviation from the nominal sthana depends on the swara phrase in which the swara occurs; thus, a single swara in a given raga can appear at different deviations from its nominal sthana when occuring along with various other swaras of the same raga. In a general sense, this deviation is called gamaka. Gamaka can refer to a constant deviation from the nominal swara sthana or a time dependent deviation or the path taken in reaching the nominal swara etc. Truly, gamaka is the life blood of Carnatic music and the raga system. Ragas are defined more by the gamakas and the way in which certain swara phrases (chain of swaras) are used than by the mere presence or absence of certain swaras. Thus, playing the keys corresponding to the swara sthanas of a certain raga will not reproduce the true character of the raga but only provide a general idea of what it sounds like. This is the reason why purists object to the use of keyboard instruments in Carnatic music - the lack of gamaka, which leads to a mutilation of the raga swaroopa. The use of gamaka also implies that the method used for defining nominal swara sthanas (rational or logarithmic division) is not too critical as long the correct raga swaroopam can be accommodated.
In the past, Hindustani music also had complex gamaka schemes, but the acceptance of the Harmonium has caused their virtual disappearance and only a few of the gamakas remain in use. The result is that the current form of Hindustani music has lost some of its traditional character - perhaps forever. Carnatic music is one of the very few musical forms in the world that have not lost their traditional character due to the influence of western culture. On the contrary, Carnatic music has enhanced its traditional character by borrowing good things from other systems of music. The introduction of the violin is a very good example of a positive influence. The instrument and its playing techniques have been successfully adapted to fit in with the rest of the system. This adaptation is so complete that the present day listener can hardly imagine a concert without a violin accompanying the singer.
The seven basic swaras occupy various swara sthanas and produce a total of sixteen swaras that form the basis of the raga scheme. It should be emphasized that the swara sthanas are nominal and in actual usage, depending on the raga, the swara is not fixed at any one sthana but appears at various locations around a nominal swara sthana in different swara phrases. The Shadja and Panchama swaras are like the foundations upon which the rest of the melody is constructed. So, these occupy fixed sthanas. This is denoted by naming these swaras as Prakruthi swaras (all the other swaras are grouped under Vikruthi swaras). Further, these two swaras are usually employed without any gamakas. In order to identify the sthanas of the various swaras, let us number the twelve sthanas. The names of the swaras and the swara sthanas they occupy are given in the following table.
The numbering used above allows one to easily locate the swaras on fretted string instruments (veena, mandolin etc.). One simply counts up the frets till the desired swara is reached. For example, if a Sa is played on a particular fret, to get a Prati Madhyamam, one simply moves up 6 frets on the same string (moving six steps from 1 results in 7, the number denoting the Prati Madhyamam). The Ra-Ri-Ru notation exists chiefly for convenience and is not used very widely. In conformance with that practice, this document will point out when the notation is being used. In the absence of such an indication, Ra should be taken to imply not Suddha Rishabam but a generic Rishabam. The following keyboard diagrams show the locations of the swaras for one kattai and four and a half kattai reference pitch using the ra-ri-ru notation. A similar indication can be easily made up for fretted string instruments simply by using the swara sthana table and counting up the frets starting from Sa.
The use of sixteen swara names has led to some people describing an octave as being divided into more than twelve swara sthanas (as many as twenty two). But, as the table and keyboard diagrams show, there are only twelve sthanas and certain pairs of swaras occupy the same nominal swara sthana (eg. Chatusruthi Rishabam and Suddha Gandharam). In an earlier era (or for that matter, in contemporary Hindustani music), the duplicate name swaras were not used i.e. each swara sthanam was associated with one and only one swaram. The swaras of the octave then read (in Ra-Ri-Ru notation) Sa - Ra - Ri - Gi - Gu - Ma - Mi - Pa - Da - Di - Ni - Nu - Sa. The remaining swaras, Ru, Ga, Du and Na, were considered to be tainted ('Dhosham') and their use was to be avoided. These four swaras are called as Vivadi swaras and their use is now generally accepted. The occurrence of combinations of swaras gives rise to melodies which can then be classified on the basis of the swaras that are used. This leads to the scheme of ragas which is our next topic of discussion.
==================================== ## ## ## ## ## ## ## ## ## ## Ra Ru Mi Da Du ## Gi ## ## Ni __ __ __ __ __ Sa Ri Gu Ma Pa Di Nu Ga Na ____________________________Swaras for one kattai reference pitch
========================================================= ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## Ri ## ## Di ## ## ## Sa Ga Gu Pa Na ## __ __ __ __ __ __ __ __ Ru Du Ra Gi Ma Mi Da Ni Nu ____________________________________________Swaras for four and half kattai reference pitch