Indian music is known for its complex use of microtones and ornamentation. But for notation and explanation, we divide an octave into 12 semitones. We use a movable scale, which means that your octave can start anywhere you like. Your starting point is the root of your octave, all the other notes are defined in relation to the root. Each of the 12 notes in the octave has a unique identity, given by S, r, R, g, G, m, M, P, d, D, n, N. Keyboard instruments make it very easy to visualize music, so if you have access to one, do make use of it. Pick any key on the keyboard as your root. Then play 12 consecutive keys in ascending order including both blacks and whites. That would give you the chromatic scale, which is not very pleasant to listen to but is a good way to learn all the notes in an octave.
The "Notation ID" column gives you the names of the notes as they are used in musical notation. With the exception of sa and pa, all the other notes (re, ga, ma, dha and ni) have two notation IDs each, one denoted by a small letter and one by a capital letter to distinguish between the two versions. Notice that the final sa in Table 1 is notated S', with an apostrophe after it. Notes in octaves below or above your basic octave are notated with apostrophes before or after them to show which octave they belong to. Here are a couple of ways to notate the keyboard, one using C as the keynote and the other using A♭ as the keynote.
In the video below, Pt. Venkatesh Kumar sings in sargam between 9:10 to 11:15 or so.
Pt. Venkatesh Kumar
The Basic Seven-Note Scale
The chromatic scale comprises twelve notes separated by uniform (or nearly uniform; Indian music is based on natural temperament) intervals, but it is much easier to create pleasing melodies by combining notes separated by non-uniform intervals. Since ragas are so central to Indian classical music, we are always on the lookout for note combinations that offer significant melodic potential. We know of about 500 ragas in the Hindustani tradition now. Sometimes ragas fade out as they lose popularity and people stop singing or learning them, sometimes new ragas are born out of new encounters or mixing existing ragas to come up with surprising new melodies. A number of ragas have been derived from folk tunes sung in various parts of India. So long as a scale is versatile enough to be developed into a full-fledged raga, artists are happy to play with it and see where it takes them, and if the new raga stands the test of time, it may eventually receive a place of honor alongside the other classical ragas.
But one must begin somewhere, and all new students of Hindustani classical music begin by learning the all-natural (all shuddha) seven-note scale comprising S R G m P D N.
Click to hear: All-Natural Seven-Note Scale
(Ascent: S R G m P D N S' / Descent: S' N D P m G R S)