In my description of how to hold the bow, the basic or neutral hold will be presented first. However, it must be understood that in the actual playing of the violin, the bow hand is not fixed or rigid.
Due to the nature of the bow, the bow hold will experience slight changes at the frog and at the tip (a down-bow position and an up-bow position), when the hand is allowed to naturally pivot throughout the course of the bow stroke. This concept is beyond the scope of this text and will be discussed in a later work.
When placing the fingers on the bow, it must be kept in mind at all times that the ideal / natural bow hold should look nearly identical to that of the hand when it is holding nothing at all. If you reach out with your right hand, make a fist, turn it slightly to the left (pronate), and then release it, you will see the correct form of the bow hold. If you then go and place a pencil in your right hand without changing the position, you will have achieved a proper bow hold on the pencil. All that being said, it is still important to understand the proper placements of each finger on the bow itself.
To set the basic position of the bow hold, take the bow in the left hand, pointing it vertically upward. Place the tip of the thumb on the bow stick in the space between the leather grip and the frog. [1] The thumb should be in its natural, semi-bent, slightly-curved position, i.e., not super straight as if giving a “thumbs up,” and not fully bent at a 90 degree angle. [2] The thumb should be the loosest out of all the fingers. The thumb joint must always remain flexible. The middle finger should be placed directly opposite of the thumb and should contact the stick at the first joint, nearest to the nail. The ring finger should then be allowed to fall into its natural position, primarily touching the stick, but slightly reaching over the frog.
Similarly, the index finger should then be allowed to fall into its natural position, also contacting the stick (or grip) at the first joint, nearest to the nail. The pinky, due to its short length, is placed on top of the stick. Most bow sticks are of an octagonal shape near the frog, even when the stick itself is round. The optimal position for the pinky is not directly on top of the stick, but on the first face of the octagon from the top (on the same side as the other fingers). Additionally, the pinky should retain its natural curve and never be extended straight; otherwise it will lock and create tension.
The four fingers on top of the bow stick should rest there with the same distance between them that is natural when the hand is at rest. The bow hold itself must be comfortable and balanced. Mechanically, the central feeling of balance in the bow hold must be between the thumb and the middle finger. The two weaker fingers (the ring finger and pinky) balance out the strong index finger on the opposite side. The lack of a balanced bow hold is the cause of many bow problems. If there is an uneven distribution of weight in the hand, it is very easy for the muscles to become rigid.
The bow hold, even in its neutral position, is always slightly pronated (the hand slanted to the left). This is an important aspect of the bow hold and bow technique. The bow hold becomes more pronated as the bow moves towards the tip, and less pronated as it approaches the frog. Some teachers say that the hand pronates towards the tip and supinates towards the frog. At first glance, this is correct; however the physiological reality is that the hand simply un-pronates.
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[1] The thumb should never be placed on the frog, on the bottom of the frog, or into the cut-out of the frog. It should also not protrude on the opposite side of the stick.
[2] There are some schools of thought that advocate a fully bent thumb all of the time. The main issue with this is that it may cause the thumb to lock and become tense. It also prevents the natural pivot of the hand from taking place during the bow stroke. That being said, a fully bent thumb may work for some people. If working with a teacher that advocates it, follow their judgment on that matter. It is worth saying, however, that many world-class soloists can be seen not keeping their thumbs at a fixed / bent position.