The exciting moment you've all been waiting for - yes, the 2nd part of Thinking Tonally...! (Start here if you missed part 1)
Now, let's get right to the exercises: Play your low E string and let it ring, then play an E major scale starting on the D string. What this exercise is doing is it's beginning to train your ear to become familiar with the essence of the major tonality. Then do the same with the other three tonalities. (E minor, major blues and minor blues)
The next exercise is very similar but instead of the open E note as the comparison to the scales you will play chords to compare to the scales: An E major chord against the E major scale, E minor chord against the E minor scale, E7 chord against the E major blues and the E minor blues. This will train your ear to hear the reflections of the scales in the chords and vice versa.
In the last exercise, we'll use the high E and B strings to create double stops ( two notes at once ) that define the four tonalities. We're going to harmonize the four scales in 3rds, that means you'll play the root and 3rd (or flat 3rd for a minor chord ) together. Begin with the E on the B string, fret 5 and the G# on the E string, fret 4. ( E to G# is a 3rd ) Then you simply ascend within the E major scale one step at a time on both strings simultaneously, then repeat the same process with the other three scales.
Once you do this exercise you'll have a much better understanding of the defining characteristics of the tonalities.