When soloing in a key, the quickest way to modulate to III minor, is via the Dorian mode. Raising its root creates the mode Alt bb37, mode VII of the Neapolitan minor scale. In C Major, this is the modal equivalent of using a secondary dominant chord of B7 to emphasize the change to E minor. This can then be thought of a new key in its own right, if the musician chooses, or can continue functioning as chord III in C Major. When the D# is played over the C Major chord the modal sound is C Ionian #2, creating a really nice effect.
A simple exercise to hear the benefits of utilizing the Neapolitan minor scale in your playing is to play a basic chord change, C Major to E minor, and give yourself space after the initial C Major chord to put in a phrase from E Neapolitan minor before resolving to the E minor. A scalar example is shown below in Ex. 2 in both notation and tab. Try it and see how it sounds.
Now, we are only raising the D to D# when we play E Neapolitan minor, but it creates a whole world of possibilities. The arpeggios from E Neapolitan minor are:
E minMaj7
F7 (D# acting as an enharmonic equivalent of Eb)
G7+
Amin7b5 (D# acting as Eb again)
B7b5
CminMaj7 (D# acting as Eb)
Eb+ (Eb G B plus I to add the C in an arpeggio which is an inversion of the CminMaj7)
Playing any one or more of these arpeggios over the C chord sounds great. I have shown F7 leading into E minor in Ex.1 in the score.
The same approach can be used for the other chords in C Major when the next chord is E minor, but care must be taken if the D# is played over a chord that has D in so no lingering on D# and best play it only on weak beats or part of the beat. Example 3 shows the same scalar lick played over A minor to E minor. Over A minor, the modal sound is Aeolian #4 which sounds rather sophisticated. Hope you have fun with it.
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