This grip is called traditional because it originates from military marching drummers who carried a snare drum on a sling hung from the neck or one shoulder, with the drum riding closer to one hip than the other and tilted slightly for easier reach.
Many drummers use traditional grip on drums that are perfectly horizontal, especially in marching percussion.
With the underhand grip, there are several different techniques employed which involve slight variations in finger positioning and usage.
[2] Some Scottish pipe band players have a variation on the traditional left hand grip in which the underhand grip is played entirely with the thumb[3] on top of the stick,[4] utilizing no other fingers for downward pressure.
[6] Matched grip is therefore technically easier to play, though for reasons stated above, it is not always the superior choice for every application.
This allows the stick to move freely and bounce after striking a percussion instrument.
This allows a greater degree of finesse and the addition of forearm rotation to the stroke, which is why many timpanists prefer French grip.
It also comes in handy for playing fast tempos, including for swing or jazz on the ride cymbal.
In German grip, the palms of the hands are parallel to the drumhead or other playing surface, and the stick is moved primarily with the wrist.
German grip provides a wide dynamic range, achieving the control necessary for pianissimo passages without the need for much rebound from the drum and also allowing for very loud fortissimo strokes from the arm.
The palms of the hands typically are at about a 45-degree angle to the drum and both the fingers and wrist are used to move the stick.