Preliminaries
There are 12 notes in the musical system:
| C | * | D | * | E | F | * | G | * | A | * | B | C |
| 0` | 1` | 2` | 3` | 4` | 5` | 6` | 7` | 8` | 9` | 10` | 11` | 0` |
Standard
In the standard tuning of the guitar the notes of the nut are given by
If we consider our root tone to be C, we can measure what the intervals are (measured in semitones) which gives us
by going from left to right we can extract the pattern 5 5 5 4 5 in terms of semitones you add to go from one to the other.
Going in the reverse direction would just yield the same pattern but with negatives.
From this we can derive all the different lines, where a zero represents some position you're currently at (anywhere on the fretboard). NOTE: The numbers in the following tables are not notes (which would have been denoted with a `), these are intervals.
| 0 | 5 | 10 | 3 | 7 | 0 |
| 7 | 0 | 5 | 10 | 2 | 7 |
| 2 | 7 | 0 | 5 | 9 | 2 |
| 9 | 2 | 7 | 0 | 4 | 9 |
| 5 | 10 | 3 | 7 | 0 | 5 |
Normalized
| 0 | 5 | -2 | 3 | -5 | 0 |
| -5 | 0 | 5 | -2 | 2 | -5 |
| 2 | -5 | 0 | 5 | -3 | 2 |
| -3 | 2 | -5 | 0 | 4 | -3 |
| 5 | -2 | 3 | -5 | 0 | 5 |
Example
suppose we are interested in finding what interval I is, let's consider 6 as our root, if we're doing that then
we can consider the last row of the noramlized table to see that we need to subtract 2 from 6 to get our answer,
namely 4
Take Aways
We will define close, to be within 0 to 3 semitones of where you are now, far will be anything greater than that.
~> f c c f s
s f c c f <~
Where f, c represent far and close respectively s represents the same
Application
The most difficult part of the guitar is horizontal movement across the fretboard, most people can figure out vertical movement quite quickly,
but for many people horizontal movement is blind. If you want to become better, improve your horizontal movement you can train it here
Modifying the tuning
If your goal is to be able to understand and construct musical objects on the fretboard, then a slight modification to the base tuning can give you some benfits. Only do this if you are comfortable constructing all your chords from scratch and not if you memorize chords from books. Our modification is simple, instead of a pattern of 5 5 5 4 5 with the standard setup, we just use 5 5 5 5 5.
This modification results in a nut:
Here is the result:
| 0 | 5 | 10 | 3 | 8 | 1 |
| 7 | 0 | 5 | 10 | 3 | 8 |
| 2 | 7 | 0 | 5 | 10 | 3 |
| 9 | 2 | 7 | 0 | 5 | 10 |
| 5 | 10 | 3 | 7 | 0 | 5 |
| 11 | 4 | 9 | 2 | 7 | 0 |
Normalized
| 0 | 5 | -2 | 3 | -4 | 1 |
| -5 | 0 | 5 | -2 | 3 | -4 |
| 2 | -5 | 0 | 5 | -2 | 3 |
| -3 | 2 | -5 | 0 | 5 | -2 |
| 4 | -3 | 2 | -5 | 0 | 5 |
| -1 | 4 | -3 | 2 | -5 | 0 |
Notice that there is a lot more symmetry in these normalized lines.
Generalized
| -1 | 4 | -3 | 2 | -5 | 0 | 5 | -2 | 3 | -4 | 1 |
Patterns
Note that in the above if you move in the positive direction (right) odds are positive and evens are negative, moving ot the left makes odds negative and events positive.