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Watch the Open Strings Functioning online guitar lesson by Brad Carlton from Guitar Lab: Open String Universe

This lesson explains the relationship between the 1st, 2nd and 3rd strings (when played open) and the root of a chord occuring on the 5th string. The chart which is included in this lesson clearly shows that as you climb up chromatically on the 5th string, you will descend chromatically in the analysis of each of the top three open strings. Obviously if you are lightning fast with your music theory, you'll instantly know how any note is functioning against the prevailing bass note. If you memorize a particular fret on the 5th string and how the 1st, 2nd and 3rd strings function against it, this might help speed up the process of analyzing any chord rooted off the 5th string and how those open strings affect the harmony.