Hi Physicist Dancer,
Your analysis is quite good, as it pertains to Waltz Box actions where the 3rd step is closed. The only thing I would add to that is more specificity on the 3&. You've separated everything into half-beats except for beat 3, but that too could use additional information, namely:
3: Vertical lowering
3&: Progressive lowering
The lowering between 3 and 1 is neither perfectly separated from the progression, with the path of travel in the shape of an "L", nor is it taken exactly concurrently, with the path of travel on a straight diagonal line from beginning to end. The best description I can give for the path would be one that is roughly parabolic, commencing straight down, overlapping for a brief period of "scoop", and continuing into a slight downward diagonal toward its final point of mid-stride.
The space of time between 3 and 3& is therefore primarily a vertical lowering, mostly in the form of heels lowering to floor. You do want that vertical lowering to overlap slightly with flexing knees to soften the transition, but exactly where that overlap moment falls with respect to the 3& is up for debate, and in truth probably doesn't matter. If the mechanics of the movement are correct, it will fall where it should.
The space of time between 3& and the following 1 is for moving the body forward or backward into the position we want to achieve at mid-stride. Through the flexing of the appropriate joints (knees, hips, ankles, etc), as well as the division of the legs, the body should arrive in a position at mid-stride that is slightly lower than where it began, which is why I describe it as "progressive" lowering. (Some might disagree with my choice of nomenclature, but the mechanics are correct).
One more thing I'd like to point out is in your analysis is the description of 1& being the "same level" as 1. If 1& marks the end of the step (which itself is debatable, but we'll save that for another thread and assume for the sake of this discussion that the beginning and endpoints of a step are when the feet pass), then count 1& is the exact endpoint of the step. Therefore the language "commence to rise at end of 1" suggests that the action of rising should begin slightly prior to that point, and that you would be at least slightly higher on count 1&, at least in the legs if not the feet, than you were on count 1.
The truth is, many of today's competitors don't quite dance it exactly according to the book, and your analysis does actually represent more accurately what's going on. So if your goal is to dance more like a competitor, "same level" is a good description of count 1&. But if you plan to take an exam and want to match your verbal description as accurately as possible, you will want to be just slightly higher on 1& than you were on 1.
Which version is "correct?". Depends on who you talk to. I study with both camps, so personally I think they both are, in their own way. How you dance it, I suppose, will depend on who you're trying to please.
Regards,
Jonathan Atkinson