Gripping a sword may sound like the easiest part of fencing; I mean it is just a matter of grabbing a sword and holding on to it. However, as we will briefly examine below, at least with some fencing masters like Hans Talhoffer, things are just a little bit more complicated than that. In fact, the practice of gripping the arming and longsword in different ways may well have been a strong factor in the development of swords with complex hilts.
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 over the cross with the index finger or even the thumb.
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.
And looking at both the 1542 and the 1550 manuscript of Paulus Hector Mair reveals a preference for, in almost any cut and guard, keeping the thumb of the leading hand held forwards, often on the side of the schilt, over the cross, a type of grip where the thumb aids little in the grip itself, but rather reinforces the stability of the blade in the bind.
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" and reversed grips were common and not properly portrayed in many illustrations or more of a personal preference amongst certain swordsmen. But, it is interesting to compare the images to Myamoto Musashi's advice on gripping the sword with the last three 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."
Solothurner Fechtbuch 1423
Codex Wallerstein 1470
Andreas Paurnfeindt - 1516
Hans Medel / Sigmund Shining 1539
Paulus Hector Mair 1550
Joachim Meyer 1560
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Sources: (These will be updated properly shortly)