I found a similar question on SE already, but it still didn't adequately explain what I'm trying to figure out, so here goes:
What exactly is a scale, what are they for, and how does practising them make me a better guitarist? I have purchased six "beginning guitar" and "beginner music theory books", and for some reason, they all assume I already know what a scale is.
For example, I'm assuming the chromatic scale is a way of breaking up a single octave (ie: a doubling in frequency) into smaller sub-units. So, assuming for example, if I pluck the open fifth ('A') string, it will generate a sound centered around 110Hz.
String Frequency Scientific pitch notation 1 (E) 329.63 Hz E4 2 (B) 246.94 Hz B4 3 (G) 196.00 Hz G3 4 (D) 146.83 Hz D3 5 (A) 110.00 Hz A3 6 (E) 82.41 Hz E2
By this logic, I'm assuming that if if I pluck the next 'A', (ie: fifth string, 12th fret), the frequency of the sound generated would be 220Hz. Does this make sense? Also, since the distance between frets is not the same, the change in pitch from fret to fret scales non-linearly, and possibly semi-logarithmically: does this sound right?
Finally, what does it mean to play in a certain key or scale? I've seen how the pentatonic scale seems to divide octaves (doubling of frequencies) into 5 units rather than 12 with the chromatic scale, but just about any other scale (jazz, blues) has me thoroughly confused. Is it a mapping to use some sharp/flat notes instead of the note itself? It makes zero sense to me.