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Fretboard layout of C notes - CAGED System

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Let us have a look at this post on Middle C on Guitar - F above and G above middle C on a Guitar. Note the positions of the C4 note. Similarly, if we include all the C notes on the guitar (here open string i.e. 0 to 15th fret), we get a picture like this:
The red dots show the position of the C note on the neck of the guitar. As is obvious, the locations of C on the fret board are as follows -

6th string - 8th fret, 5th string - 3rd and 15th fret, 4th string - 10th fret, 3rd string - 5th fret, 2nd string - 1st and 13th fret, 1st string - 8th fret.

Here we see something interesting - straight out of the anatomy of the guitar - The strings where the C note repeats itself, it does so only after 12 frets. This is because, when we traverse 12 frets from any position on the guitar, we arrive at the harmonic of the note that we started off from, making it the same note (same pitch class). The same principle applies to chords - only thing is that we do not have "harmonics" of chords. As we move a chord down 12 frets, we effectively arrive at the harmonic of every note we started from, thus preserving the chord.

The point of this discussion being, that the shape of a chord at a position is basically the same as that within the first 12 frets of the guitar. Only a "bar" is a added using the index finger at the beginning of such a chord. For example, the E major in 1st position chord is 022100. The same chord is also playable using the same shape at the (0+12 = 12) 12th fret as (adding 12 to all the notes) 12-14-14-13-12-12.

Using the example of C major chord, we see that C major in root position is played as x32010. It is also playable at 12 position as x-15-14-12-13-12 (adding 12 to each note). Now have a look at the diagram above, The bar is placed at the 12th fret; the pattern of C notes begins to repeat after the 12 fret (bar shown). Again, verifying the chord, we see that both these chord forms are made of the notes x-C-E-G-C-E (also in the same order, from 5th to 1st string). Thus, both of these are indeed C major chords and each of the notes of the 12th position are harmonics of their same string counterparts in the 1st position.

A similar simple calculation proves the same thing for the E major chord described earlier. The notes played are E-B-E-G#-B-E in both cases.

Thus we have effectively entered into the heart of the matter of the CAGED system and already discussed and equated two positions of the C major and E major chords (to be elaborated later on).

This brings us to the point of the "bar" and bar chords. Continue...

The CAGED System on a Guitar:

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Fretboard layout of C notes - CAGED System

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