By Paul Stein: A popular discussion about vibratos direction has always confused me. Its the debate as to whether you vibrate up to the pitch from below, or starting at the pitch and vibrating below it. I heard this first in college, and I bought into it because it had an air of logic and erudition around it. (I dont remember which direction was "correct," but its not important.) Many years later I found a more logical way of understanding vibrato, without worrying about which direction I was using.
Vibrato in Its Purist Form
The explanation that makes sense to me is that its an even oscillation around the pitch, not below it or above it. In essence, make sure the note is in tune, then vibrate around it. The center of the oscillation will ring with pure intonation. Parsing a pendulum, and over-analyzing which direction youre going in, will dig a deep hole thats hard to get out of.
In the scenario of vibrating around the pitch, the purity of the intonation is always heard, helped along by the fact that the distance from the pitch is consistent. In other words, the center of the movement is always the dead center of the pitch. However, if I split hairs and let things get too complicated, while concentrating on vibrating up to the pitch, Im more likely to play out of tune.
If you alter the basic area or equilibrium in which vibrato resides, the pitch will start migrating. If you change the principle of vibrato having an evenly spaced area above and below the pitch, youre complicating a simple process.
The Hummingbird Principle
Vibrato presents an interesting paradox: the pitch changes, but the underlying, dominant pitch doesnt. A hummingbirds speed of flapping its wings shows how vibrato can be mirrored in nature: though the wings are in constant motion, the hummingbird can hover in one place.
The success of vibrato depends on:

- A propulsive pendulum being activated instantaneously.
- The inner workings being free of encumbrance - with the change of direction happening freely in the finger, with joints of the elbow and wrist not fighting with each other, etc.
- A natural pendulum moving equidistant from its axis, or center of the movement. A fly swatter is a good example of such symmetry. Altering the equal distance from the center makes it difficult to return to normal. Have a firm connection between the fingertip and the fingerboard to insure theres no slippage.