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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.

Thank you.

closed as too broad by Shevliaskovic, Matthew Read Jun 15 '15 at 6:08

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 2
    possible duplicate of Why learn scales? What are they for? – Jacob Swanson Jun 15 '15 at 3:17
  • This is several questions that aren't even all related; please keep it to one per post. As for the duplicate question, you can create a bounty or leave a comment if you want to ask for more clarification rather than reposting the question. – Matthew Read Jun 15 '15 at 6:08
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I'm not going to answer your first or last question because I believe they are answered in the question you linked.

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?

Yes, this is correct. To get from one A to the next A up, you double the frequency, and to get the next A down, you halve the frequency.

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?

" On instruments such as guitars, each fret represents one semitone in the standard western system, in which one octave is divided into twelve semitones. " -Wikipedia

" pitch relates to frequency logarithmically; pitch increase by an octave corresponds to frequency doubling. " -http://acousticslab.org/psychoacoustics/PMFiles/Module05.htm

Yes. It is a logarithmic function.

There is also a figure were this was from that shows the relation of frequency to pitch.

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