Music as we had mentioned before is a collection of sounds and silences. But it is not as random as it seems. Sound is, as our friend wikipedia says, a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard. So basically, sound is a frequency. Hence music is directly a collection of frequencies.

In western music, people assigned names to particular frequencies. The frequency of 440Hz was chosen and named A. Only 12 fixed frequencies (notes) were assigned names and they are
A, A#, B, C, C#, D, D#, E, F, F#, G, G#.

A# is pronounced Yay-Sharp and likewise the others and they are called semitones. The mathematical relation between the notes and the frequencies and music is given in this page. These 12 notes repeat in both directions i.e lower and upper and are called octaves. It is like as mentioned below :
…..D . D# . E . F . F# . G . G# . A . A# . B . C . C# . D . D# . E . F . F# . G . G# .A . A# . B . C ……
If the A is the 440Hz frequency, then the notes below are the lower octave notes while those beyond G# are the higher octaves.

Well, we will start with how notes are described in Indian music. Here too, we have the same 12 basic notes. You may think, “Hey, but we have always heard of the saptaswara!!!” OK! There are seven notes called swaras. They are

S  – pronounced as Sa
R  – pronounced as Ri
G  – pronounced as Ga
M – pronounced as Ma
P  – pronounced as Pa
D  – pronounced as Da
N  – pronounced as Ni

Just like the A, B, C, D, E, F, G!! Got it?? yup!! The rest five are the semitones.

But unlike the western music structure, the Indian music notes are floating!! Yea, music does makes you fly sometimes but this is not that floating!!
Anyway, in Indian Music, this origin has to be defined. Take one of the western music frequencies and assign it as origin and all the notes then get fixed according to that. So let us say we assign A to be Sa then we have

A – Sa
B – Ri
C – Ga
D – Ma
E – Pa
F – Da
G – Ni

Similar to the western notes, the Indian Music notes also have the higher and lower octaves. The thing to be noted is that the frequency assigned to Sa is not fixed to 440Hz. If C was assigned as Sa then the same table would look only a little different.

C – Sa
D – Ri
E – Ga
F – Ma
G – Pa
A – Da
B – Ni

Ok but what about the semitones?? Here the beauty of Indian Music starts. When Sa has been fixed, we had mentioned all the other notes are fixed. Well, always in Indian Music, for starters, we can have only 7 Swaras defined. So somehow the semitones also have to be assigned with the same swaras. So how to do this?? It’s done as follows. We assume that A is Sa.

A    A#     B       C      C#     D     D#     E    F      F#     G     G#
Ri3                                                          Da3
Sa  Ri1   Ri2   Ga2   Ga3  Ma1 Ma2  Pa  Da1  Da2   Ni2    Ni3
Ga1                                                          Ni1

So we see that there are more than one Ri, Ga, Ma, Da, Ni but Sa and Pa  are only one in number. The names of the different Ri Ga and so on, I feel are not essential for appreciating Indian Music. And so, we will have the same notation hence forth in all our discussions i.e with numbers as Ri1, Ga2 etc.

We also can see that Ri2 = Ga1; Ga2 = Ri3; Da2 = Ni1 and Ni2 = Da3. And these are not some mathematical equations.

A raga is a combination of the aforementioned swaras.

A look above and one can see the huge number of possible combinations. Generally a raga is supposed to have at least 5 swaras.

A raga has ascending and descending scales (called Arohanam and Avarohanam). Each direction can be comprised of at least 5 or more swaras. For example, the raga Mohanam is

S R2 G3 P D2 S’ in the ascending scale or arohanam
S’ D2 P G3 R2 S in the descending scale or avarohanam

Tala is the basic rhythm period. We will not go too much into the intricacies of Tala as it has a direct relation to Mathematics and we do not want you guys running away once such a discussion starts. So the thing to remember about tala is that it is a rhythmic pattern on which a song is based. One can have a period of 3,4,5,7…beats. (6 beats is similar to 3, and 8 to 4 and likewise). The periodicity generally is maintained throughout in a song.