While there is nothing wrong with playing with your thumb over (as long as it does not cause strain in your arm or does not limit your playing possibilities)
That being said: there are three exceptions that make playing with your thumb over the fret board not only acceptable, but actually a necessity.
1. Bending Notes
String bending is one of the techniques that make guitar such an expressive instrument. Pushing up a string to bend to another note, takes so much finger strength that your thumb is needed, grabbing over the guitar neck to give your hand leverage. Having a grip on the guitar-neck makes your bends more accurate and more controlled. Whether you want to add bluesy blue note micro bends or more flamboyant larger interval bends like Pink Floyd’s David Gilmour, you always benefit from grabbing over with your thumb when bending. You typically only need to grab over the fret board with your thumb for these note bends and not for the entire solo or song. What this means is that you would change your hand position often in a guitar solo depending on the particular phrase you’re playing. When you intend to bend, grab over, when your next phrase is going to be a scalar run, lower your thumb behind the guitar neck. If however: the whole solo contains constant bends, which would be the case when you play Jimi Hendrix solos, or any blues or blues rock solo for that matter, you would typically keep your thumb behind the guitar-neck throughout the solo. Best advice really is: use common sense and be present and aware of how your arm and wrist feel.
2. Muting the Low E String
Certain chords require the low E bass string to be muted in order for the chord to sound good. For example: it is advised to mute the low E string when playing the regular, open string D chord on the 2nd fret that beginning guitar students learn. The D chord sounds much better without that low E rumble underneath the chord. This is accomplished when the guitarist extends his thumb over to touch that low E string so it can't vibrate. In order to mute the low E sting, grab over the fret board with your fretting hand and slightly touch the E string with the inside of your thumb, just enough to mute it. This muting technique is also commonly used with any rhythm style that requires lots of percussive, muted attacks, like for example Texas blues, funk rhythms played on the top strings, or reggae.
3. Playing Thumbed Bass Notes or E Shape Bar Chords.
Jimi Hendrix often used his thumb to grab over the fret board to play bar chords. Bar chords tend to be straining on the hand muscles. Playing the low E string note with your thumb on E shape bar chords, rather than underneath your index finger as a bar, conforms more ergonomically to how your hand functions. It makes the E shape bar chords less strenuous, no longer turning songs with bar chords into physical endurance exercises. You can also grab over the fret board with your thumb to play moving bass notes on the 6th string while playing chord on top of those bass notes with your fingers. This technique is sometimes used in certain playing styles that are heavily finger picking based, such as flamenco and some bluegrass.
In conclusion: in some cases grabbing over the fret board with your thumb is a necessity. The main reasons why guitar teachers are usually adamant about keeping your thumb behind the guitar-neck, are:
1. To teach you “proper” guitar technique. Even if grabbing over with your thumb is not an issue as long as it does not create tension in your wrist or arm, you still benefit from getting used to holding your thumb behind the guitar neck as well.
2. To avoid tension in your wrists, hands and fingers, which can cause physical hand and arm problems, including tendinitis and in later stages possibly carpel tunnel syndrome.
3. To accommodate the style you want to learn or practice. When learning classical guitar, or work on shred picking technique; thumb is always behind the guitar neck.
Always remember, it is good to stretch before and during playing if you practice for longer periods of time or practice on techniques that are intense on your hand muscles and tendons. Take care of your body and play with good form and technique, and you will preserve your hands and wrists for a life time of guitar playing comfort. Now go grab that guitar neck and rock out!
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