And then you watch Ray Chen, or his teacher Aaron Rosand, or lots of other players and you realize these are not Suzuki kids. They're blitheringly skilled violinists. Ray's thumb comes way up on the other side of the neck, but that could be because he has long hands.
When I was a kid there was a local guy who taught violin lessons -- he was not my teacher but sometimes I wish he had been. Anyway his thumb was double-jointed and the neck of his violin sat on his thumb which formed a right angle at the joint -- it looked so weird to me but he was totally comfortable. That's why I remembered it.
@Neil I'm not sure Menuhin would be my go-to for the fundamentals of technique.
I went through a lot of opinions on thumb use but after studying my thumb itself I came to the realization that that digit is a lot smarter than all the pundits. Obviously, there are basics to thumb use as there are to all aspects of playing the fiddle (I think the main purpose of basics are to help stop you becoming committed to a method that can not be used to build on - that prevents future growth. One example perhaps is letting the neck of the fiddle fall completely into the thumb-index space - I have yet to find a use for that!). However, once you are past that point Elise's method for thumb training is - teach it as many actions as possible - play with it forward, backward, sideways. Teach it to support the fiddle and the fingers using its side, its tip, the sideof the tip and anything else you can think of. And then let it be. For a particular action your thumb will figure out the best option from all the ones you have taught it. Its really like a well trained pet dog - you give it a goal but then it figures out the simplest way to complete an instruction in a particular circumstance...
This place needs some livening up!
I learned to have the thumb straight (optically; I have to bend it a bit; otherwise it looks bent backwards), low and opposite the first finger. My main thumb problem in years 3 to about 5 of violin playing was tensing it up. Eventually I got over that.
Only recently I found (inspired by the discussions on this forum) that "liberating" the thumb from its "first-finger lock" helps with extending the hand (which I need to do to play a minor third with fingers 2 and 4 in first position).
Of course this all depends on the size of your hand and fingers and how your muscles work. You want to avoid strain as much as possible. I know violinists and violists with small hands who do a beautiful job and they often play the lower positions with most of thumb under the neck.
The placement of the thumb along the neck will depend on what you are trying to do with the other fingers; opposite 2nd, 1st, 3rd finger??? I think all bets are off in the really high positions and the thumb must go where one needs it to - which really is the "rule" anywhere on the fiddle.
So the problem is to learn what works best for oneself - and that might actually be hard to do without expert guidance - especially if one has already learned to play sub-optimally!
But coming back to the point of the thread, I agree with Elise even though I use a shoulder rest, whereas she does not. I particularly liked her statement that the thumb is smarter than it looks (or some such).
For instance, when shifting up over 4 strings the thumb just follows the hand and goes in a diagonal direction. In shifting downward, though the thumb leads the hand.
Exercise: Play without the thumb touching the violin. (You can place the scroll against a wall to support the violin). However, the thumb will probably still stiffen. So, better yet, while playing move the thumb in circles, still not touching the violin. This assists in making it independent of the other fingers.
Exercise: wrap a band aid around the first joint of the thumb to immobilize it. You will instantly notice when the thumb starts to clutch.
Exercise: “Numb the thumb.” place the thumb so it is behind the index finger and play. This immobilizes it. If you do this exercise for several minutes when you put the thumb in a “normal” position it may feel paralyzed, which is what you want.
Early on, I would play with my thumb high and bent as James Ehnes does, but at the time, I was having issues with my pinky collapsing, and I found that my hand being so high over the fingerboard made the problem worse. So I lowered my hand, developed strength in my pinky's PIP joint, and now I have a curved 4 all the time.
Anyway, I think the player should be able to forget the thumb is there most of the time, with it only guiding shifts and providing necessary stability in the hand. The thumb can make or break a lot of left-hand techniques!
But my second teacher told me to scratch those, and just think about the placement of the whole palm. Need more support for pinky stretchy? Whole palm forward to favor it. Shifting? Wherever the palm needs to be, the thumb follows in a neutral position.
I find the second way more intuitive to me.
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There's a video on YouTube about how the left thumb is used. Most violinists keep it low, to support the violin neck a bit.
Others leave the thumb high in a way that it even rises above the fingerboard. Yahudi Menuhin critiqued a young Corey Cerovsek in a MasterClass for having a high thumb.
There are a plethora of YouTube videos on left hand posture. In particular, here's a YouTube video on high vs. low thumbs:
Here's another on the Menuhin' critique mentioned above: