Hroarr.com - Hema sword grips

Regarding gripping the sword.

These are various images showing variations in grip and wrist angles with different types of sword. The earliest images are from the early 15th century and the last from the late 16th century. The grip variation may be used for various reasons; to gain more strength in the bind by reinforcing against the flat with the thumb, or changing the balance of the sword by gripping the cross with the index finger.

Especially the Talhoffer and Joachim Meyer images are interesting in my opinion, since a few images show both the thumb and index finger held straight in an open grip, which goes very well with Musashi's advise below.

A couple of more things of interest in Talhoffer: One of the images of duelling shields in the 1459 manuscript shows a kick against the shield, where the attacker causes the shield to spin open, thus creating an opening.

It is hard to know if the "open" grips were common and not properly portrayed in many illustrations or more of a personal preference amongst certain swordsmen. But, another thing that came to mind is Myamoto Musashi's advice to grip the sword with two fingers only.

"A sword is to be held in the following manner: the middle, fourth and little fingers should grip the hilt vigorously while the thumb and index finger should be lightly placed on the hilt.

There are two types of swords and hands - live ones and dead ones. If the hands grips the sword too firmly when taking the stance or parrying, then it is too difficult to take the offensive. These are what I call "dead" hands.

On the other hand, if one grips the sword in a relaxed manner, he can continually take the offensive. These are "live" hands. One must not cross one's wrists nor bend one's elbows too much or too little. Muscles on the upper side of the arm should be relaxed, those on the lower taut."

source: Kampai Budokai

And in relation to this, Peter Johnson's (and others) discussion on gripping a viking sword is interesting.