If you think of a typical sine curve (graph) ... the note being "vibrato-ed" has a y coordinate equal to zero ...
The "maxima" is the most positive y value.
The "minima" is the most negative y value.
The extent of the vibrato is sum of the maxima and minima (absolute values).
The smoothest, most pleasing vibratos have maximas and minimas that are equal ..
Ex) Max = +20 cents ; Min = -20 cents therefore the extent is 40 cents.
The ear/brain will detect the "dead center" of the pattern as the "note" being played ...
In general the lower the frequency, the greater (wider) the extent and the higher the frequency, the lesser (narrower) the extent.
Comparing folks like Mel Torme to Judy Garland is really enlightening.
The "speed" of the vibrato is measured in Hertz (Hz) ... waves per second.
Typical vibrato rates range from say 4 Hz to 7 Hz.
Most greats (singers, violinists, 30's steelers) have rates just about 6Hz.
In general, the lower the frequency the slower the rate ... the higher the frequency the higher the rate.
Again, comparing folks like Mel Torme to Judy Garland is very enlightening.
The time that elapses between the picked note and the beginning of the vibrato cycle is the onset.
Here there is tremendous variation ... and frustration. One of the most difficult aspects of vibrato is knowing when to apply it. Different places in a phrase require different onsets.
Generally, notes with short duration (quarter & half notes) need faster onsets than whole notes, etc.
It takes years to develop a "classical" vibrato ... I'm still tryin'
My biggest "Tip" on Vibrato
No matter what musical "era" or "genre"... all the great vibrato-ists have/had one thing in common ...
A whole number of oscillations per vibrato cycle ...
Most will speed up the vibrato toward the end of the cycle to accomplish this ...
Easy to say ... hard to do !!!
Here is an example of what I mean ...
Say you reach the end of a phrase on an A note.
One typical "vibrato wave" would begin dead center on the A note ... then move to say ... (+)30 cents (sharp of A) .... then back "through" A to (-)30 cents (flat of A) ... then back to A (dead center).
Start dead center ... go sharp ... go flat ... back to dead center = 1 wave (oscillation).
No matter what rate (generally 4-6 Hz) or extent (usually 20 to100+ cents) ... an accomplished player/singer will incorporate a whole number of waves (1,2,3,4,5,6 ...etc.) into the sustained note's vibrato.
Depending on the tempo of a song ... the artist will generally use his/her "natural vibrato frequency" ... and then speed up that rate to complete a whole number of waves ... as needed.
Of course, this is natural to the great players/singers and they certainly don't really think about it ... its more of a "feel" ... a "complete-ness" ...
Regardless if it is a violin, flute, steel guitar, tenor or Theremin ... the acoustical properties of vibrato are fairly consistent. Not only with the basics (rate/extent/onset) ... but with the more complex issues like harmonic involvement through-out the cycle, dB changes associated with rapid changes in pitch (fundamental and overtones), etc.
Something that has not been mentioned yet and is one of the primary reasons for the use of vibrato ... is Auditory Attention Deficit Disorder (AADD)... I made that up ... ha,ha
The brain has a very short "attention span" and grows weary of a stagnant note fast. The vibrato gives the sustained note needed variation to keep the brain interested.
For that matter, the brain will soon loose interest in a machine-like vibrato (consistent rate and extent). That is why master musicians employ a variety of rates and extents in a single piece ... Got to keep the audience on the edge of their seats
In particular, I remember comparing Sarah Vaughn to Ella Fitzgerald ... Vaughn's had a much longer onset time (note held longer before applying the vibrato). Once she started though ... the extent was much greater and rate was a tad slower.
A whole number of waves/cycle and an even-ness between the maxima (sharp) and minima (flat) combined with variations of onset and rate were the hallmark of the greats.
Sampling poor examples (my own playing) showed irregular wave functions (ie. not smooth sine curves), deviations from the "dead center" of the note being embellished ... and worst of all ... changes in rate that were inconsistent.
Mine would ... start fast, then slow down, then speed up ... Yuk
Hey, I'm workin' on it.!!!!!
The exciting players like Andy Iona will vary the rates .. but always in a "build-up" way. A "pure" note followed by an increase in both rate and extent .... very hard to tell in "Real-Time" (easy to see in the 3K Hz range of a sonogram) ... but flat out thrilling to hear.
I love that era !!!