GRAVITY AND CENTER OF GRAVITY. HOW DOES THE BOW FEEL ABOUT STRING CROSSINGS?
Even though the bow is an inanimate object it does however have its definite preferences when it comes to string crossings. Going against the bow’s wishes is definitely possible – and very often unavoidable – but we can make life much easier for ourselves if we apply a little intelligence to the understanding and respecting of its wishes (natural tendencies). Of course the bow has no real “wishes” or “natural tendencies”. These are simply the effects of gravity and motion, which produce forces that we can either use to help us, or that we must work against.
To use a sporting analogy, using the bows momentum, weight and centre of gravity to help us, is the equivalent of swimming with the current, sailing with the wind (downwind), running downhill, or of a judo fighter using his opponent’s weight and momentum to make him fall etc. What then are these “natural tendencies” derived from gravity (bow weight), centre of gravity (balance), and momentum and what is their effect on string crossings? Before we look at this question however, it is important to take into account the fact that the more horizontal the cello’s position is, the greater the effect gravity will have on the bow’s string crossings. And, for the same reason, the more vertically we have the cello, the less effect gravity will have on these same string crossings.
Let’s start by finding the centre of gravity of the bow. When the bow is perfectly balanced on a finger inserted between the hair and the stick, that finger is at the bow’s “balance point”, or in other words, at its centre of gravity. Because the frog is the heaviest part of the bow, the bow’s centre of gravity is much closer to the frog than to the middle of the bow.
When the bow is resting on the string at its centre of gravity, it doesn’t want to “tip” either “up” to the left (towards the higher strings) or “down” to the right (towards the lower strings). However, as we draw the bow’s point of contact (with the string) gradually further away from this centre of gravity, the bow has an increasing “desire” to “tip”, one way or the other depending on which side of its balance point it is touching the string. If this point of contact with the string is closer to the frog than the balance point, the bow will want to tip (fall) towards the higher strings. If, on the contrary, the point of contact with the string is more towards the tip than its centre of gravity, the bow will want to fall towards the lower strings. The further the point of contact is away from the centre of gravity, the greater is this desire to tip (fall).
Because the centre of gravity is closer to the frog than to the middle of the bow, in the greater part of the bow (from the center of gravity to the tip), its natural tendency is to want to fall towards the lower strings. The weight of the bow-arm also follows this same tendency in the sense that the further out we are towards the tip, the greater the natural desire is for the arm to fall down towards the lower strings. But this occurs only when we get out past the centre of gravity. On the frog side of that balance point the tendency is the opposite and the bow will want to tip towards the higher strings.
The effect of “momentum” is identical. A downbow is going in a direction in which the gravitational forces pulling the bow down to the lower strings are always increasing and vice-versa for the upbow. Let’s look now at the detailed practical implications of this for both the downbow and the upbow.
As we draw the bow out to the right past its centre of gravity, the bow starts to want to “fall” to the right of the string (i.e towards the lower strings). The further out our bow is past this centre of gravity (in other words the further out the bow goes towards the tip) the greater the mass (weight) of bow that is to the right of the point of contact (between bow and string) thus the more it wants to “fall”. For the upbow, the situation is perfectly inverted: now, as we come towards the frog from the tip, the tendency of the bow (and arm) to want to “fall” towards the lower strings is progressively reduced. At the centre of gravity the tendency is zero, but as we pass that point and go towards the frog the tendency is now to want to fall toward the higher strings and this tendency increases exponentially as we go towards the frog thanks to the leverage effect.
Thus, in conclusion, due to the influences of gravity, centre of gravity, and momentum, a downbow naturally wants to “fall” in the direction of (towards) the lower strings and an upbow naturally wants to “fall” in the direction of the higher strings.
THE ELBOW IN STRING CROSSINGS
For a smooth string crossing it is the elbow that leads, actually anticipating the bow-level change and thus leading the hand and forearm to the new string in a flowing, rounded movement. To experiment with (and illustrate) this phenomenon, try playing some spread, 4-string chords. The first chord of the soloist’s entry in Haydn’s C major Cello Concerto is an excellent example. While crossings to adjacent strings can usually be done quite economically (with little movement) with the hand and wrist, the addition of the elbow movement – even though not strictly necessary – adds flow, energy and looseness to the bow movement and thus makes the playing gesture more attractive (more dance-like). In leaps across several strings however, the elbow’s contribution is not just cosmetic but becomes really vital.
When our string-crossing direction is “with the flow” our elbow has less requirement to move than when we bow “against the flow”. The “good” direction is simply much more ergonomically efficient than the “bad” direction. This can be easily observed when we play the above example with the two opposite bowings. Here below is another repertoire example, from the Prelude of Bach’s Sixth Suite. Try this one also with the two opposite bowings:
THE WRIST IN STRING CROSSINGS
We saw in Spiccato that the wrist has a definite preference for clockwise circles. This is not only relevant for spiccato but can be seen also in string crossings. This means that it is not only the bow (for the mechanical reasons explained above) but also the wrist (for anatomical reasons) that have a natural preference for going down towards the lower strings after a downbow.
The only part of the bow where its natural tendency is to fall “up”, is at the frog. However at the frog, we use mainly wrist movement. Thus a short downbow at the frog, even though it is in a zone where the centre of gravity would want the bow to go up, the wrist factor counteracts and makes it want to go down.
BOW FOR THE BEAT OR FOR THE STRING CROSSING?
The natural tendency for the bow is to want to fall down towards the lower strings on (and after) the down bow, while it wants to do the exact opposite on (and after) the up bow. When we manage to choose the bowings in such a way that the natural physical tendencies of the bow are perfectly matched to the music’s rhythmic impulse, then we are swimming downstream (with the current) and making life easy for ourselves. Here is perfect example of this situation, taken from the accompaniment to “Summer” from Vivaldi’s “Four Seasons”:
In the above example the natural tendency of the bow with respect to both the string-crossings and the bounce coincides with its tendency to prefer a downbow on the beat. Often however, especially in faster string crossing passages, the natural desire for the down bow on strong beats contradicts the bow’s natural string crossing (and bouncing) tendencies. This creates situations in which we may want (or need) to use “reverse” (or “upside-down”) bowings with respect to the beat (i.e we need to put upbows on the beat). Here, while the bowings are “upside-down” with respect to the beat, they are however “correct” according to the bows natural string crossing (and bouncing) tendencies.
In the following variation of the first example above, the displacement of the beat to the lower string means it will now feel much more comfortable to play with an upbow on the beat:
Here are some more repertoire examples of this situation. Try all these passages now with the opposite bowing, to see which is easier: bowing for the beat or bowing for the string crossings ?
All the above passages are fast. But the ergonomic advantages of bowing “with/for the crossing” can also be felt in passages at slower and moderate speeds:
In many circumstances however, our choice of “bowing for the crossing” or “bowing for the beat” may be less easy to make because there are a lot more complications happening in the passage than in the preceding examples. Even though the bow prefers to cross down on (or after) a down bow and up on (or after) an up bow, often, because of other non-string-crossing factors, it will not really be clear which is the “best” bowing. And even if we have a very clear idea of which we prefer, very often we are unable, for various different reasons, to choose the bowing that we would really like to do in a certain passage. So we will always need to be able to play bowings that are “upside-down” to the beat, as well as bowings that are “upside-down” to the crossings.