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I have heard from more than one string educator that in order to create a warm tone, it is helpful to begin vibrato motion in the left hand before producing sound with the bow.

However, I have also (less frequently) heard that doing so in a group can cause pitch issues. Here are two quotes from Wikipedia's Vibrato page for illustration:

"Wind and bowed instruments generally use vibratos with an extent of less than +/- half a semitone." (50 cents)

"Many contemporary string players vary the pitch from below, only up to the nominal note and not above it, although great violin pedagogues of the past such as Carl Flesch and Joseph Joachim explicitly referred to vibrato as a movement towards the bridge, meaning upwards in pitch..."

So suppose that we have two players, one who starts their vibrato up and one who starts down. Let's be conservative, and say that they only vibrate +/- 25 cents from the center of the ideal pitch. If they play the same note and begin vibrating BEFORE they play, there is a chance that their audience will not hear the same note, but rather two notes 50 cents apart. Unpleasant.

On the other hand, Wikipedia also cites a 1996 study by the Acoustical Society of America (with Wellesley and MIT) which found that the perceived pitch of a note with vibrato "is that of its mean", or the middle of the fluctuating pitch.

And so I ask you: When starting vibrato before creating sound with the right hand, does this cause pitch problems in the split second the sound is beginning to be pulled? Or does this idea of perceived vibrato pitch from the ASA mean that it doesn't matter where the initial pitch is placed so long as the vibrato is correctly centered? Does the fact that this pitch difference exists for a very small amount of time trivialize its magnitude?

Then again, the sine function spends most of its time near its maximum and minimum values; so we could say that, given similar but opposing vibrato speeds, the amount of time the pitch difference is heard is relatively large.

It seems to me that this pitch problem can be avoided if the vibrato is started (centered) in the exact instant (or shortly after) the sound begins to be pulled. But I can't tell if my concern is unfounded, nor can I necessarily articulate what starting with a centered vibrato, even after sound production, would do to fix my problem.

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The mean is not necessarily the mid point. I think that distinction is critical to understanding how pitches with vibrato are perceived –  Fergus Feb 25 at 20:05

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I think you're definitely magnifying the problem beyond it's perceptibility, vibrato is generally much too fast for the instantaneous difference to be heard at all. In fact, it's generally much easier to be in tune with vibrato than without. The natural fuzziness of a vibrated pitch generally makes it blend more pleasingly and there's nothing more difficult than playing perfectly in tune during non vib sections. Vibrato speed, depth, onset and offset should vary throughout a piece based on musical considerations, and I don't think it's possible to reduce it to anything so concrete as the Wikipedia quote's focus on averages.

It's important to note that minute differences in pitch add depth and warmth to a sound—perfect intonation at the frequency level is impossible, but also undesirable. That's why most piano notes are produced by three strings (which can't possibly be tuned identically) and a section of cellos or violins sounds so much thicker and warmer than a solo. [that piano point I crossed out is incorrect, see David's comments below]

Edit to add: I can think of one exception. If you are entering quietly (loud attacks add noise partials that will obliterate any pitch differences) in unison (not octave probably, I mean literal unison) with one other instrument (3 or more players should mitigate most issues), then you might want to coördinate a bit more carefully. Such situations are rare, but they can be a real intonation nightmare.

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Piano strings hold pitch rather well and are mechanically coupled, so of course forced resonance where all three strings vibrate synchronously is quite feasible even if the strings, when struck alone, would have minute pitch differences. –  User8773 Feb 25 at 12:38
    
Hmmm, interesting. But then why, when a piano goes out of tune, do individual keys become 2– and 3–note clusters? Does the coupling only work within a certain tolerance? –  Pat Muchmore Feb 25 at 13:28
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Yes, forced resonance works only within a given tolerance. It's actually a nuisance for tuners since it may mask the minute details of tuning. –  User8773 Feb 25 at 13:33
    
Awesome, thanks for the correction, I need to read more about that. –  Pat Muchmore Feb 25 at 16:04

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