What I'm going to be covering here is a brief look at two-handed tapping, just a little further beyond the trills and arpeggios played on only one string. To begin, you should already have basic tapping skills down (you probably do, anyways) and should have fairly good right and left hand coordination when it comes to muting the strings; this will be very important as you try to learn and execute the material in this article.
Also, I'd like to say that while this kind of technique looks and sounds cool, and is one of the more fun ways to play the electric guitar, keep in mind that it's not the type of technique to be overdone. In most cases, one should try to refrain from abandoning the pick unless the circumstances call for the two-handed tapping technique.
The technique I use is based on that of guitarists Greg Howe, Michael Romeo and Don Lappin (a Berklee professor who actually plays 90% of the time with two-handed tapping, in a more horizontally oriented fashion), adopted for use with a pick in hand and for all fingers on the left hand and one or two fingers on the right hand. To start, hold your pick with your thumb and index fingers; keep your right hand middle and ring fingers oriented parallel to the strings (and perpendicular to your left hand). If you aren't too accustomed to the two-handed tapping style, try this exercise that I like to warm up with, useful for both alternate picking and tapping:
Note that to continue to the dorian modal run, one must slide the tapping finger (which can be the middle finger throughout this exercise) from the 13th fret to the 15th fret.
If you are having trouble achieving strength in the right hand fingers, try this exercise: just tap a note with the weak finger and watch the finger and string as you release. Try to remove your finger in a downward motion (that is, away from you and towards the floor). Don Lappin uses this technique to compensate for the lack of percussive force that leaves with the temporary abandoning of the pick.
Now let's try something that involves string skipping, and which sounds much more interesting. Fans of Michael Romeo may be familiar with this Emadd9 pattern:
This is where muting really starts to become significant. For the most part, I make use of the wrist of my right hand to mute the thicker strings, much like another form of palm muting. I've also heard Greg Howe swear by a sort of large hair tie/scrunchy thing placed at the top of the neck, but I've never been able to find one (supposedly they can be found at CVS or Walgreen's). One can still make use of a tissue or piece of foam to give that extra muting insurance to prevent unnecessary vibrations.
Also note here that I'm using both my middle (M) and ring/annular (A) fingers. Although most basic tapping licks can be executed with just the middle, it's often more convenient and will over time become more comfortable for some to use the ring finger as well.
Continuing on, here is an example of two different arpeggios being played in the same run:
Here I've combined the Emadd9 pattern with a similar sounding arpeggio: a Gmaj7. These arpeggios differ only by one note (the E becomes a D), and so the pattern sounds rather consonant and forms almost naturally. Again, I'm using two right hand fingers. You might wonder why I don't use my fourth finger on my right hand two tap the high G on the E string, my ring finger for the G string, and my middle finger for the A string. Put simply, I don't have the necessary finger strength in my fourth finger right now, and it's not imperative that I use it.
Next, these examples demonstrate triads broken into groups of three and four notes:
Notice that EX 4 is comprised of the left hand playing one inversion of a five-string Bm arpeggio, while the right hand pattern reminds us of the following inversion. Greg Howe uses this combination of patterns often in his legato passages. Shredders might notice the emergence of three-note-per-string patterns. Typically, I will sequence arpeggios by threes using a picking pattern more closely related to that of Al Di Meola. However, I've presented the pattern as a two-handed tapping example to demonstrate it as such, should the situation call for this variation.
In EX 5, the two hands are merely sequencing a first inversion CM triad played across three strings. The right hand actually only sounds different octaves of the C note. In this example, however the difficulty lies with the left hand, both in producing clean, constant-tempo notes and in crossing the string gap between the E and G of the A and G strings and the E and G of the G and E strings.
These last examples will combine all patterns and sequencing of arpeggios thus far, as well as a scale run or two.
EX 6 was written to fit over a chorus that uses the same progression as the arpeggios. The advantage of being able to use two-handed tapping is in having the ability to execute otherwise difficult passages. The technique itself is also useful for reaching out of the triad box and incorporating more unique and flavourful arpeggios, and works well when incorporated in improvisation and finds use in styles such as jazz fusion, rock, and metal.
A word on the harmonization of runs such as EX 6: for arpeggios other than triads, I find harmonization in 3rds or by inversions effective. Even both used together can yield some interesting results (when dealing with many of these arpeggios, you'll find that harmonizing by thirds or by inversions tend to produce similar products), so try whatever you find works the best in the circumstances you come across. As for triads, I always continue to harmonize them by inversions.
I just covered some basic shapes in this lesson, but a great way to better one's understanding of the fret board is to explore triads, 7th chords, and others using as many root notes and inversions as one can, as well as on different sets of strings.
Finally, I want to stress the importance of muting and cleanliness; the absence of a pick makes articulation difficult, so be sure that each note can be heard on its own and that your fingers are strong enough to really hammer each one. Happy tapping!