This is the handout, minus a few diagrams, that I give my students when beginning to need vibrato. I usually wait until they have stabilised their LH shape and spacings, and have started to shift from 1st to 3rd Position and begin working on tunes as well as Simandl.
VIBRATO
Vibrato is one of the two things the left hand can do to add life, beauty and interest to your sound. It is caused by rolling the fingertips towards and away from the bridge along the string. The motion is slightly faster on the way up and decays on the way down, with "rubber" shock absorbers at each end. Wind players often use Haa Haa Haa to helpfind their vibrato. The H goes up faster than the aaa goes down, a bit like a rounded saw tooth shape (in my missing diagram)
Sufficient time must be spent around the pitch of the note for the pitch to be centered and stable, so don't wander too sharp or flat. The width and speed can vary, usually slower and wider as pitch goes down to the A string, and a bit faster and narrower progressively going up the G string.
There are two components in the vibrato motion,
(1) the hand tries to move parallel to the neck (because the finger end is stuck on the string this motion will twist the finger and and roll the fleshy pad on the fingertip),
(2) the hand is cupped with arched finger over the string and opposite the thumb (this forces the whole forearm into a rounded motion that pivots around the thumb and causes the finger end to roll).
Cellists can often develop a "wrist vibrato" by rotating the two forearm bones, the Radius and Ulna, like twisting a door knob. I don't recommend this approach, that can produce a very fast brittle-sounding vibrato that is distracting for the listener and doesn't allow notes to sing.
(3 missing diagrams)
The motion of throwing the hand towards the bridge comes from right back around the shoulder by rotating the upper arm likw an axle. The forearm moves like a crank around the axle. But picture the axle being not quite in line with the upper arm but diagonally across to part way up the forearm. This allows the elbow to counterbalance the hand movement and provide some of the "rubber" bounce. Try holding your hand in front of you with a 90 degree bend in your elbow. Move your hand up and down as though you are shaking the contents of a bottle and observe the way your moves and feels. Or hold a little tin of Tic-Tacs in your hand and listen to the K-chuck K-chuck sounds.
Vibrato is one of the harder things to teach. Some people naturally fall into it and others struggle. Some of the ways into finding a nice vibrato could be
(1) resting your hand in "piano playing position on a table or on your bass upper rib. Rest on your 2nd finger pad and move your hand parallel to the table top. Observe that your finger will move sideways and twist and that the fleshy end rolls. Everything tightens at each end of the motion. Now add a (slight) rolling motion of your hand by moving your forearm. Observe that the fingertip now rolls more widely backwards and forwards. Try translating this blend of actions to the bass neck around C on the G string with only the 2nd finger pressing the string towards the opposing thumb. The change of "geometry" from table to neck is awkward because directions of movement have changed and the weight of the arm must be supported (partly by hanging weight through the neck back towards the shoulder). The thumb centers the rolling movement.
(2)An intermediate step could beto use your right forearm as a practice neck held upright in front of you so that you can observe the actions that make the vibrato.
(3) In the playing position and with the left thumb about opposite C on the G string, open your left hand wide with fingers high above the string. Rythmically throw the hand wide in an arc around the thumb with straight wrist so that the fingers strike the string at each end of the movement, well above the thumb with the index finger and well below with the pinkie. The whole forearm moves widely but does not twist (as in wrist vibrato). Now press the 2nd finger down on C and observe that this tightens and narrows the gross rolling action. Relax the wrist a little and feel the heel of the hand thrown towards the bridge like a gentle hammer, creating the Huh in Haaa. The wrist and fingers tighten at the end of the movement to create the "bounce" and the rebound creates the aaa. The gross arc is not only narrowed but flattened as the finger end twists a little and the pad moves sideways to take up slack.
(4) Do a glissando up and down between two notes on the same string with the 2nd finger, eg between Bflat and D on the G stringor F and A on the D string. Stop the ending note by "nipping" between finger and thumb and use this to go on over into vibrato for a few Haaa Haaas as the note tails off. Stay relaxed and feel the bounce that starts vibrato. Repeat the gliss and nip over and over.
(5) Strap a small container of Tic-Tacs or rice to the back of your hand and listen to the sounds as you do vibrato, like a sort of rounded
K-chuck K-chuck sound
Work towards keeping the vibrato going, like a perpetual motion (very like the feeling of dribbling a basketball, trapping the bounce with your hand and pushing the ball back down over and over again). Then aim at being able to start and stop vibrato at will, and vary its shape width and speed according to musical context.
Vibrato can help notes avoid sounding crushed when using slower bow speeds with more weight. It seems to help increase the back pressure from the string to the bow. It also helps play closer to the bridge with fuller tone
I generally don't advocate using vibrato on the E string, where it is already hard for a bass section to produce clear rich-sounding notes in tune. The E string is vibrating at about 41.7 cycles per second on bottom E and 55 cycles on A. It takes about the first 10 cycles to establish full tone. A 4 cycles per second vibrato on a 43 cpsnote that can take a quarter of a second to speak fully can end up making a mess. Better to play simple notes with great intonation and tone?
Listen to other instruments and singers, especially Basses and Baritones. Observe the vibratos that are ugly and distract your ear from the music and the vibratos that add quality to sounds.
DP
ps You are right, Bass Tutors don't help much with Vibrato. I hope my own long-winded explanations above are a help.