With the palms held completely parallel with the drumhead, the sticks lay in a broad “pie-slice” arrangement over the drum. The combined use of wrist, finger, and inner forearm muscles gives this grip a significant advantage in terms of power.
With the palms turned perpendicular to the drumhead and the thumbs placed on top of the stick, the French, or timpani grip, brings the elbows in closer to the body and brings more of the fingers in contact with the stick, allowing for a more controlled, finesse-driven stroke.
An obscure technique good for volume and little else, this grip hasn't been seen much since the war — Civil War, that is. With the thumb wrapped under the stick, the pinkie acts as the “fulcrum” and the resulting stroke relies almost entirely on wrist action, with things like rebound and dynamics relegated to distant afterthoughts.
Opposite traditional grip you’ll find any of the overhand grips for the dominant hand which, when employed with both hands, are known as “matched.” These have less to say visually (other than the fact that you were probably not reared on Buddy Rich/Gene Krupa drum battles), and are perhaps more invested in the ergonomics of drumming. The advantages are obvious. For one, you don’t have to learn how to hold the stick twice; both hands perform the same exact operation. Because of this, you have a better shot at achieving a consistently uniform sound between the hands.
For an overhand grip, simply open your palm face up, place the stick in it with the bead pointing away from you, and close your hand as you naturally would, planting the pad of your thumb (the finger fulcrum in any style of overhand grip) firmly on the stick opposite your index or middle finger. The motion of the active stick now depends on the style of overhand grip you choose to employ. The vast majority of players use some variation of “German,” “French,” or the hybrid combination of the two known as “American.”
With German grip, the palms are held parallel to the drumhead so as to position the thumb on the side of the stick and keep the top of the hand flat. The principle motion of the stroke combines equal parts finger action with the flexing of the wrist up and down. Because of the strong presence of inner forearm muscles used to snap the wrist in this technique (and to respectfully contradict Stewart Copeland) it is often believed to provide a more powerful stroke.
In contrast, French grip sees the palms facing inward, with the thumb positioned directly on top of the stick. This removes some of the responsibility of the wrist, resulting in a stroke that relies more heavily on finger action for its principle motion. It becomes the role of the smaller muscles of the palm and fingers that is believed to provide more control, finesse, and speed within a greater dynamic range. Famous practitioners of French grip include John Bonham, Billy Cobham, and Bill Bruford. Likewise, if you’ve ever witnessed a “World’s Fastest Drummer” competition, you’ll note the winners invariably use a fixed-wrist version of this technique that relies entirely on finger action, which here we call the “speed stroke.”
In reality, a large percentage of drummers don’t adhere strictly to either of the aforementioned grips. Among these will always be the beginners and self-taught players who simply pick up a pair of sticks and begin to play, holding them in a manner that comes most natural to them. These folks employ what is generally referred to as “American” grip. With the palms neither facing exactly down or inward, American grip can be thought of either as a deliberate hybrid of German and French grips, seeking the distinct benefits of each, or as a rejection (or ignorance) of the others’ strict ergonomic requirements. Ultimately, American grip has one main feature going for it: It is instinctual, and therefore requires the least attention and muscle training of any grip.