Dr. Parthasarathy Sriram
"Nature has endowed this universe with many beautiful life forms, of so many different shapes, sizes and abilities. Most animal forms have the ability to produce sounds and some of them even have the capability to communicate using varied sounds. Man is unique in that he can express his thoughts using sound." This is how Swami Jayendra Saraswathy, the Sankaracharya of Kanchipuram, introduces the Kamalaambaa Navaavarna Kritis of Muthuswamy Dikshithar. The ability to express thoughts through sounds has evolved into an art which we call music. Music can thus be defined as an art form that arranges sounds in a fashion that follows certain natural principles and provides that special inner feeling of happiness and contentment. It is important to note that the basic principles are natural and thus the theory of music is only an attempt by man to rationally explain what is already beautiful. As a fringe benefit, this rationalization helps in understanding the inherent beauty of music and creates increasingly higher levels of appreciation in the listener.
The most basic unit of music is the swara (or note) which simply indicates the position in the audible spectrum occupied by a particular sound or the pitch of the sound. Actually, the spectral position is better described as swara sthana. Inherently, certain sounds 'go together' and certain others do not. This property was realized by man thousands of years ago and is indicated by the term harmony; lack of harmony is called disharmony. Before going any further, let me introduce, as a practical tool, a keyboard, that will help us immensely as we go along deeper into the fundamentals of Carnatic music. Purists may frown at this, but as long as we realize the limitations of the keyboard and why the purists frown, we are committing no sin.
At first glance, a keyboard is simply an assortment of black and white keys of two different lengths, usually the black keys being the short ones. A closer examination shows a pattern of keys repeating a few times to produce the full keyboard. The repeating pattern is shown in the following figure. Many keyboards indicate the location of the 'C' key as shown in the figure. In any case, a C key can be identified as the white (or long) key immediately to the left of a group of two black keys or the first key in the above figure. Evidently, there is more than one C key (perhaps 4 or even more) on the keyboard. The C key is so called due to the notation used in western music for the notes. The successive white keys to the right of C are labeled D, E, F, G, A and B. As a first example of harmony, play a C key and the next C key simultaneously and listen carefully (It is assumed here that the keyboard is polyphonic i.e., has the ability to produce more than one tone at a time. Many inexpensive keyboards lack this ability and are not suitable for this demonstration). The combined sound has an oneness. Playing a C key and the white key next to it (the D key) does not produce a similar effect and the two tones stand out separately. They do not merge as in the case of the two C keys. Total disharmony is difficult to demonstrate using a keyboard due to the discrete nature of the notes that can be played. One would have to produce a sound that is located 'between' two keys in order to hear a set of highly disharmonious (abaswara) notes but the preceding demonstration is a simple example of two levels of harmony.
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Keyboard Layout: Seven white keys and five black keys in between.
Two successive C keys are separated by what is called an octave which corresponds to a ratio of two in frequency. That is, the frequency of a C note is exactly double the frequency of the C immediately below (to the left of) it and exactly half the frequency of the C immediately above it. Two sounds are perceived to be very similar if they are separated by an octave and the only explanation for this is that that is how mother nature has made it!
The concept of harmony is closely related to the notion of harmonics. Consider a string fixed at both ends and vibrating at a fundamental frequency f. From basic physics, the upper harmonics of the string are at integral multiples of f, namely, 2f, 3f, 4f etc. Harmonious tones have common harmonics and this implies that the tones have fundamental frequencies that are related as a ratio of two integers. A high degree of harmony is associated with ratios involving powers of 2 (2:1, 4:1, 8:1 etc.) and small integers (eg. 3:2). The ratio 3:2 signifies that the second harmonic of the higher frequency tone coincides the third harmonic of the lower frequency tone and such a relationship is very easily detected by the human ear. Two tones related through a ratio 91:85 are not perceived as being very harmonious because the common harmonics are the 91st and 85th. Such high harmonics typically have very low intensity and may even be beyond the frequency range of the human ear. The principle of integral ratios is inherent in our perception of sound. A tune is identified by the ratio of frequencies that appear in succession to produce it and only special training develops the ability to perceive the absolute pitch (frequency) of sounds.
Next we observe that there are a total of twelve keys in the repeating pattern (or twelve swara sthanas in an octave). This division of an octave into twelve swara sthanas has evolved over a period of millennia. This is evident from the fact that while some ancient forms of music use fewer swara sthanas, the current forms of many styles of classical music which evolved independently (including Western, Hindustani and Carnatic) use only twelve swara sthanas to an octave. In ancient Vedic chantings, we have only three swara sthanas, denoted as normal, low and high. Interestingly, the pitch steps corresponding to these three swara sthanas can be represented by the F, G and A keys. Vedic chants of later periods use as many as seven swaras and are often described as the precursors of the raga system. The twelve swara sthanas are generally considered to be the maximum number of sthanas that a normal human ear can perceive to be different without too much difficulty.
Western music believes in specifying the absolute pitch of all swaras and thus, the frequencies of all keys are fixed and the same for all keyboards (in fact, all instruments, if one can locate the corresponding notes). Indian music is based on relative positioning and thus, notes are not of fixed pitch. The note Sa is the analog of the note C. The white key marked C is called as one kattai and the successive white keys are assigned values of two kattais, three kattais and so on. The black keys are assigned fractional values (one and a half, two and half and so on). Note that there is no three and a half kattai pitch. The sruthi accompaniment (tampoora or sruthi box) provides the reference pitch and we indicate the reference pitch by saying that somebody sings at one and half kattai pitch, or a veena is tuned to four and half kattais. This simply means that the Sa has been set to that pitch and all other swaras occupy corresponding sthanas. The importance of the Sa is that it provides the fixed foundation note upon which the rest of the music is built. Such a foundation note exists in classical Western music also and is indicated by the scale name eg. F-Major indicates that the tune is built using F as the base note. The base note can be discriminated with a little practice since the music generally returns to dwell on the base note every now and then.