During my 20's I worked as an attendant and group therapist on locked psychiatric units. My primary responsibility was to insure the physical safety of the patients, which meant closely monitoring the emotional state of patients who might become violent with themselves or others. Over time I learned to pay close attention to tone of voice as an indicator of mood, more so than the verbal content of speech. Listening closely to tone of voice was also very important in understanding what was going on under the surface in group therapy sessions.
The flip side of all that attention paid to the voice tone of others was trying to always insure my own tone of voice was not accelerating a volatile situation, but rather helping to keep things relatively calm.
Those experiences led me to be more conscious of something I think we all do on a mostly unconscious level, i.e. make judgments about the personality and state of mind of others based in part on their tone of voice, and that we use our own tone of voice as an underpinning to expressing ourselves through speech.
It's my idea that when the neuroscience gets sophisticated enough, we'll see that the tone quality of your music springs from, and affects the listener in, deeper and more primal parts of the brain than the rhythm, melody and harmony. When you make music, your tone sets the stage for whatever else you do.
(As a side bar to this discussion, there's the question of the tone of piano players. It would seem that, more than wind and string instruments, the tone of a piano resides more in the piano than the player. That's largely true, but the hammer action means that strings can be hit with different amounts of force and at different rates of acceleration (see correction below), exciting the strings in subtlely different ways. Along with that, high level players can control the dynamics and the temporal sequence of every single note to such a high degree that individual styles can be developed and appreciated.)
UPDATE - Jonathan West corrects me in the comments:
By the way, you're wrong about the piano. By the time the hammer hits the string, it is no longer attached to the key and so it is in free movement and has no acceleration due to the key. Being in free movement, the the sound made by the hammer's action on the string varies from one note to the next solely on the speed with which the hammer hits.
What pianists and others think of as tone on a piano is derived from timing and use of pedals, and also from different degrees of force (and hence loudness) applied to different notes of the same chord. To a great extent, the idea of varied tone on the piano is a cognitive illusion fostered by the player - one which the player himself may be unaware of and honestly believe in.
All of what Jonathan says is very well put, especially that last sentence. During my time as a keyboard major in the late 70's I convinced myself that there was something more than simply the speed of the hammer affecting the tone of the note, and had come up with my faulty explanation involving acceleration. There is the acceleration created by gravity as it works to pull the hammer back to its resting position, but that's a constant rate involving the number 32. So maybe what I'm feeling is how that interplay between gravity and the force of the keystroke allows for super fine tuning of the hammer speed.
Jonathan is also absolutely right to mention pedaling, which I'd not included and which has immense effect on a player's tone. Oftentimes a hammer is hitting a string still vibrating anywhere from a little to a lot from a previous hammer stroke, and pedaling controls the amount of that vibration.