It is not that difficult and even though I am a musician you don't really need to be one just to determine the frequency of each musical note.
First, c,d,e,f,g,a,b are not all the musical notes that exist in the eastern music system, in fact there are twelve different notes (see those black keys in a piano keyboard?) and they are:
a, a#, b, c, c#, d, d#, e, f, f#, g, g#
Second, the american standard pitch states that the note A has a frequency of 440, and this is the point of reference to determine every other note.
The third part is just mathematics, and it is a simple formula: The frequency of the subsequent note equals the current note multiplied by the 12th root of 2 (the 12th root of 2 can also be expresed as 2 elevated at 1/12, or 2^(1/12)). So with this formula let's make an example: suppose you already have the note A which is 440 and you want to determine the next note which is A#, the mathematical notation is:
A# = A * (2^(1/12))
which is 440 * (2^(1/12)) and equals 466.1637...
following this sequence:
B = A# * (2^(1/12))
C = B * (2^(1/12))
C# = C * (2^(1/12))
and so on.....
You'll get a lot of decimal numbers in all of the notes (except of all A's) and the good news is that you can round to the nearest integer as this difference is imperceptible to the human ear.
Now, what happens to all the notes below A 440???? It is very easy, you just need to use the same formula, except that instead of multiplying you need to divide, for example, to get the note before A:
G# = A / (2^(1/12))
Now you can get any range of notes you want in any scale. Note that this approach requires you to obtain all the notes in a sequential mode. If you want to get a note directly from A 440 you tweak the formula a little bit. Let's say you want to obtain the next F after A 440, F would be the 8th note after A, so you multiply by the 12th root of 2 elevated at the number of steps after the current note, in this case eight. So:
F = A * (2^(1/12))^8
I hope this helps, and sorry if my english is not that good since I'm from Mexico.