The Tyranny of mathematical bow division.
What I mean by this is we are often taught to use the bow in an apparently simple progression that corresponds to -written music.- IE musical notation usually has two or four beats and therefore we are often systematically taught to use whole bows, quarter bows and half bows in various combinations and this is supposed to be the simplest starting point. Anyone who cannot get it is then written off as being less talented or whatever.
However, as the aforementioned writing make clear in different contexts (Jee Won was referring to beginners, Clayton to presumably advanced players struggling with the Bach Prelude) it is not actually the printed page but the nature of the bow and how its sections relate to various parts of the arm which is as important and actually quite a different thing. If one actually analyzes this then the simplest bowings e.g. the ones with the least number of components being learnt are ones that take place from the heel to balance point, heel to square, the square zone and close to the point. If these uses of the bow, and which part of the arm performs them are not made clear from the start then trying to work on mathematical subdivisions of the bow is very hit or miss. The student or even advanced player will simply not have an adequate sense of the role of the upper arm in isolation (although this is never completely true) or the forearm and how they blend into seamless units at a later stage which can be sub-divided as mathematically as one wishes. The next step is of course artistic sub-division!
I suspect it is in part frustration with unused or incorrectly used upper arm that leads to an occasional over emphasis on the wrist in string crossing. As Clayton states in his most recent blog `the wrist is…never used for string crossing.` However, I have seen many times exercises in which one plays for example two slurred and two separate on alternating strings described as `wrist exercises,` yet even at high speed they are quite playable with the upper arm doing the slur and although it might sound a bit odd, the bow doing the crossing for the two short notes as a kind of reflex action within a gentle but glue bow hold which allows for the kind of movement.
At a higher level the problem in the notorious bariolage passage of the Prelude is actually that a player has never felt the independence of the upper arm as a string crossing machine working in tandem with a laterally moving forearm. Rather the organism is doing some kind of screwy spiral. The only option at the point is to isolate this movement and then reintegrate. It takes patience, but then that is what the Christmas Vacation was invented for.
I agree that using the good part of the arm according to the part of the bow should be the first thing essential to be taught. When I think too mathematically, my arm often mooves wrong. They also said such things in the books I'm reading now if I remember correctly. 1st select the area of the bow for x area in the score, then analyse the arm motion required (of course amount of bow and pressure too...).
yes, Clayton is something of the extreme in his simplification of playing;) There are actually excellent exercises in Basics which practice the very tehcnique you refer to. Now you have it you can explore all angles of the question. When I studied sevcik at RCM my teacher was quite adamnat that sevcik opus 2 was for arm training and opus 3 for the wrist and I had to do all of both. He would make me draw little diagrams of the wrist patterns for each verison of an etude. You have to take things with a pinchof salt. If you are going to apply the concept of `the faster the note the smaller the unit of bow arm used` then certain things are going to played from tewrist and by default ther eis going to be some kind of wristy string crossing goin on.
If you're playing the second movement of the Handel Sonata No. 1 in A major, there's a place where if the arm is positioned for an A-E string level, the counter-clockwise movements of the wrist are easier so I would qualify the statement to say that the appropriate arm level for the strings to which you are crossing greatly eases whatever wrist movement is made and makes it more efficient. Obviously too much wrist motion can result in bad angles for the hair on the string and weaken the tone, a tendency happily completely absent from Nathan Milstein's video of his stellar performance of Bach's Preludio from the 3rd partita. The wood of his bow consistently stays at an angle that keeps excellent contact of the hair with the string. This factor, in addition to proper placement and distribution of the bow goes a long way to making the tone project with clarity and openness.
Take a look at Milstein's efficient wrist movement at about 15-16 seconds into this video. In the famous bariolage passage it's clear he's using very efficient arm movements to cross the strings.