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Concept of Swara [ Note ] and Saptak [ Octave ]

A note ( Swara ) is just sound waves, caused by some sort of vibration, of a specified wavelength.

The source of the vibration could be as diverse as a string ( piano, sitar, violin ), or a blow ( flute, vocal )

The number of those vibrating waves that hit your eardrum each second is called the "frequency" and each music note has fixed Fequency.

Below are the examples of notes,  ( Click on note in any table to hear sound, enter tempo 300 to increase response time )
[melody start]
[S1][notations]
[G1][notations]
[P1][notations]
[melody end]
There are seven pure ( Shudha ) notes in music, as shown below
[melody start]
[1|2|3|4|5|6|7][lyrics]
[S1|R1|G1|m1|P1|D1|N1][notations]
[melody end]
Out of these seven notes following five notes have sub-notes called as Komal ( Flat ) and  Tivra ( Sharp )

In below table, first row shows pure notes and second row shows its sub-notes [ denoted by underline ].

Re, Ga, Dha, Ni have Komal sub-notes because they appear before pure notes means their frequencies are less than its pure notes

Ma have Tivra sub-note because its frequency is greater than its pure note
[melody start]
[1|2|3|4|5][lyrics]
[Shudh|Shudh|Shudh|Shudh|Shudh][lyrics]
[R1|G1|m1|D1|N1][notations]
[Komal|Komal|Tivra|Komal|Komal][lyrics]
[r1|g1|M1|d1|n1][notations]
[melody end]
Sa and Pa are constant and they do not have any sub-notes

So total there are 12 notes 
7 ( pure ) + 5 ( sub-notes ) = 12

All these notes have fixed frequencies.
[melody start]
[1|2|3|4|5|6|7|8|9|10|11|12][lyrics]
[Shudh|Komal|Shudh|Komal|Shudh|Shudh|Tivra|Shudh|Komal|Shudh|Komal|Shudh][lyrics]
[S1|r1|R1|g1|G1|m1|M1|P1|d1|D1|n1|N1][notations]
[melody end]
After Ni, there is again Sa which has exactly double frequency compared to previous Sa. And same with Re, Ga and so on.

For example if previous Sa has 100 frequency then next Sa will have 200 frequency and same rule is applicable to other notes
( * in case of Equitempered scale )

These thirteen notes are called as Octave ( Spatak )
[melody start]
[1|2|3|4|5|6|7|8|9|10|11|12|13][lyrics]
[Shudh|Komal|Shudh|Komal|Shudh|Shudh|Tivra|Shudh|Komal|Shudh|Komal|Shudh|Shudh][lyrics]
[S1|r1|R1|g1|G1|m1|M1|P1|d1|D1|n1|N1|S2][notations]
[melody end]
Normally three octaves ( Spatak ) are used in Indian classical music.

1. Kharja Saptak : Denoted by dot below every note. Notes have lower frequencies
2. Mandra Saptak
3. Taar Saptak : Denoted by dot above every note. Notes have higher frequencies

[melody start]
[1|2|3|4|5|6|7|8|9|10|11|12][lyrics]
[Shudh|Komal|Shudh|Komal|Shudh|Shudh|Tivra|Shudh|Komal|Shudh|Komal|Shudh][lyrics]
[S0|r0|R0|g0|G0|m0|M0|P0|d0|D0|n0|N0][notations]
[S1|r1|R1|g1|G1|m1|M1|P1|d1|D1|n1|N1][notations]
[S2|r2|R2|g2|G2|m2|M2|P2|d2|D2|n2|N2][notations]
[melody end]

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Concept of Swara [ Note ] and Saptak [ Octave ]