You happen to be asking a question that I am researching for an upcoming Tutti Celli article. Explaining how to create vibrato is one of the tougher challenges for a cello teacher. One of the problems is that there are differing opinions on how to do it. Some say you should bunch your fingers around the playing finger to give it added strength. Others say that you shouldn't do this because you are limiting your mobility.
Phyllis Young in her book, Playing the String Game, has devised some valuable imagery:
1. "Let's see if you can make your arm so relaxed that all that fat on the inside of your uppoer arm will shake like Jello! Hang loose." Hopefully, you aren't offended by this imagery.
2. "Let's see you move your left hand as though you're shaking dice. Every bone in your hand will rattle! Now try vibrating again, using this same kind of motion."
3. "Sometimes, when I think of a cello vibrato, I envision two parallel wall about three feet apart. I see a weightless ball thrown against one wall. It immediately bounces right back to the second wall, which in turn sends it back to the first wall. I have a feeling this could go on for years."
Another image that may help is the "ointment technique." Place the pad of your middle finger on a table in front of you. Imagine you are rubbing ointment into the table, but don't let your finger slip back and forth. Feel the pad of your finger flexing over your finger bone as you go back and forth. Feel your first finger joint flexing a little. Notice that your whole forearm moves. Feel how relaxed your arm is. Once you get this feeling, try getting the same feeling on the fingerboard.
Louis Potter, in his book, The Art of Cello Playing, has a nice two page explanation too. He gives exercises which may help. He emphasizes that the vibrato is a motion of the entire forearm. Do not vibrate with just your wrist. Don't role your wrist either.
Maurice Eisenberg, in his book, Cello Playing of Today, recommends the following introductory practice:
"Close up the fingers into the palm of the hand. Hold the forearm over the strings at second position level, so that the cuff or inner wrist rests on the strings and the fist is just beyond them. Then rub the arm up and down, slowly and very lightly, with a movement directed from the elbow."
Victor Sazer, in his book, New Directions in Cello Playing, recommends removing "the thumb from the neck of the cello to maintain a consistent, unwavering vibrato."
The speed and width of vibrato should vary both for technical and musical reasons. Vibrato on the lower strings should be slower and wider than on the upper strings. A slow and wide vibrato sounds funny in the upper range. A fast and narrow vibrato in the lower range can hardly be heard. Vibrato should be wider and faster the louder you play as well. Also, musically speaking, vibrato should have vary depending on the musical demands of the music to avoid monotony.
To help get control of the speed, use a metronome and vary the number of "shakes" per beat.
Play long notes with gradual crescendos from piano to forte. As you get louder, wider and speed up the vibrato. Then start loud and diminuendo, narrowing and slowing your vibrato as you go. Then do a long note with a dynamic swell in the middle, which combines the above actions.
Make sure you aren't clenching your fingers or hand or tightening your shoulder as you play.
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