Width, speed, and character
Vibrato is not one setting. It has two independent dials — how far the pitch swings (width) and how fast it swings (speed) — and you turn them to fit the music. A player with one vibrato for everything sounds the same in a lullaby and a fanfare.
The two dials
Width. The working range is roughly a fifth to a third of a semitone — a narrow shimmer. Push it toward a full half-tone and it reads as dramatic, hot, Romantic. Pull it in and it reads as controlled, clear, Classical.
Speed. Roughly 5 to 7 wobbles a second for expressive playing. Slower feels broad and singing; faster feels intense or brilliant.
They're independent — wide-and-slow, wide-and-fast, narrow-and-slow and narrow-and-fast are four different sounds:
Width follows the dynamic
The most natural pairing: more vibrato in loud playing, less in soft. A forte wants width and energy behind it; a piano wants a narrow, still shimmer — sometimes almost none. This links straight back to Stage 5's dynamics-with-the-bow: as the bow gets faster and heavier, the vibrato opens up with it; as the bow eases, the vibrato closes down.
Try it
Try
On one long note, play the four combinations above, naming each one's character aloud as you do it. Then play a phrase you know twice: once imagining it as a lullaby (narrow, slow, quiet), once as a love song at its climax (wide, warm, loud). Feel your hand actually change the dials.
Hear it
Two recordings: a period-instrument Mozart slow movement (narrow, cool, selective) and the Tchaikovsky or Bruch concerto slow movement (wide, warm, continuous). Same instrument, opposite ends of both dials. Neither is "better" — each fits its music.
The usual mistake
One vibrato, applied to everything — usually a medium-fast, medium-narrow default that never varies. And confusing "more expressive" with "wider": a narrow, faster vibrato can be more intense than a wide slow one. Expression is choosing the dials, not maxing them.