RandomFiddler said
  If you pay attention to singers (not the operatic type, mind you), you'll notice that they use vibrato as an occasional embellishment.   

I sort of agree with your basic assertion, although I might qualify it ("it depends on the type of vibrato"), as you do with the above comment. In baroque music we read that vibrato was an occasional embellishment, or even a type of ornament, but we have to be careful with historical writings, as their word "vibrato" might not mean exactly the same thing as ours - after all, modern uses of the words vibrato and tremolo can vary. Sound is subjective. Forums are a form of writing, and require care in interpretation.

So it's possible that vibrato is simply insufficiently varied, rather than overused.

I've said before, start with fast vibrato, then slow it down - slow vibrato is harder. Perhaps few people bother learning slower vibrato - they have other things to learn first, such as continuous vibrato between separate notes (this can induce a "constant vibrato syndrome"), and then perfect intonation, which in theory should be possessed before someone learns vibrato, although vibrato is also a good aid to fine-tuning your intonation.

Err, welcome to the forum, btw. There's an introduction section somewhere.

RandomFiddler said
Am I required to do a public introduction? 

I'm not sure, but it would be polite - see what a mod says.

Let's add a little more complexity.

Correct vibrato profoundly affects the timbre of your instrument. You'll hear the difference when you practise it. You should be practising to hear the timbre alteration - the hand movement is merely a means to this end. Quality of hand movement is essential for this. The slower the vibrato, the less it affects timbre. So that you won't hear it and you won't get quality of movement. With fast vibrato you will hear the difference. Then you will know what you are aiming for in slow vibrato.

Singers are a different kettle of fish. Diaphragm "vibrato" is mostly about amplitude variation, whereas violin "vibrato" can only be frequency variation. But there are singers who attempt frequency variation in their voice. Their degree of success is frighteningly varied. I spent 6 months developing diaphragm vibrato on the oboe under the supervision of an LRAM. People such as self-taught saxophonists develop throat vibrato because they don't have a teacher. Singers presumably use their throats to emulate pitch vibrato. James Gallway diagnoses his vibrato as throat vibrato, which surprises me. It would seem, if he hasn't misdiagnosed, that he wasn't given any formal training in it at college.

AndrewH said
It always depends on context. 

It's the same with trills - slow music demands slow trills. You save the "doorbell trills" for fast music.

Jim Dunleavy said
...diaphragm vibrato...definitely affects both amplitude and frequency because it affects the speed of the air stream. 

The end result almost certainly works out that way, but that's not the theory.

On the oboe one crescendos by blowing harder which makes the note sharper, but also one relaxes the embouchure to neutralise the pitch increase, as well as facilitating greater reed vibration. Diminuendo is the reverse of this - tighten the lips, which sharpens the note, and reduce the air flow, which flattens it.

You then practise regular cresc, dim, cresc, dim, slowly for zero pitch variation and then gradually speed it up over 6 months. I don't know if it would be practised this rigorously on the flute. I'd imagine it is more easily achieved.

So in theory there's no pitch variation, but, as we probably both agree, at top speed it's probably unavoidable, as the lips don't come into it any longer.

I feel pretty sure that the worst operatic warblers don't achieve the effect by diaphragm alone. I'd have thought it was a vocal chord thing. Maybe I'm wrong.

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Incidentally, when we did Prokofiev's Duenna in 1979, my oboe teacher was first oboe and I was second, and he said that in orchestras in the tuttis he didn't bother with vibrato.

I asked about this in my community string orchestra, and the conductor likes everyone to use vibrato to maximise the richness of the sound.