Step,* This usually refers to one movement of the foot, Although from a " time value " point of view this is incorrect. ( so it says ). In the case of a walk forward or backward for instance, the time value of the step is not completed untill the moving foot is drawn up to the supporting foot the weight ready to commence another step.
Why not accept the advice , from their videos. and divide the beats into half beats as instructed by both Richard Gleaves and John Wood . We then have an action on each half beat, which we do when we walk normally. In a normal walk we step, then the moving foot comes alongside and we step again. The step when dancing is on the solid beat of the music and the recovery is on that bit which is inbetween the solid beats. Andrew Sinkerson in his lecture which I attended taught the same way. To prove a point about weight distribution. He had us step RF .Bring LF alongside. Lift LF completely off the floor before stepping to the side. The next foot to be lifted was the LF after the closing of the feet and so on. The next step was forward and we did a series of Closed Changes, and eventually Natural and Reverse Turns without any changes to the technique within the steps. So get counting aloud, both lady and man. 1 and 2 and 3 and.

I don't know if this is keeping in the correct order but it has been written that there is nowhere to go on beat three. That is the whole point of a previous argument. Commence to rise at the end of one. Continue to rise on two and three. lower at the end of three. That means continue to rise on three. If the maximum rise is reached on two, you will have nothing to do on three but lower. That is why we close on two ( and ) leaving the whole of three to rise and lower on the third beat.

The maximum rise is reached at THREE. So I would say we stand with split weight at 2 (if a photo was taken), move the foot (that shall close later) at "2 and", close at 3 (highest point), lower at "3 and" in combination with starting the next step.

I agree that to dance the basic waltz in practice we should count the half beats and whole beats, but since we swing our body to the music and the body swings the legs from the back position to the forward position , we keep timing with the swing of the legs. A slow in foxtrot has to be the swing of one leg and not a step?

The question was (paraphrasing) "is this definition in the technique book?". I may not have the very latest editions but AFAIK the answer is no, not in the technique books used for the societies exams, although it is in Alex Moore.
In fact one of the technique books (Guy Howard, used by the IDTA) defines the foot positions and alignment given in the chart as being at the end of the step.

The other manuals are rather vague. I suspect this is because as Anonymouse if the charts were changed to show the position at the end of this definition of the end of the step, then the foot position column would be meaningless.

The current charted descriptions have stood the test of time and are almost universally used for any written description of figures, variations or routines. I would not anticipate any major changes in future editions.

At standard tempo one beat of waltz lasts 660ms. I am sure there will be many opinions on exactly where in that period different actions occur, eg foot starts to move, foot first strikes the floor, toe or heel touches or leaves the floor, mid-stride, weight transfer completes, feet pass, rise and fall, CBM, turn, drum stick hits the drum etc etc.

Adding the & count goes some way to help explain the timing of some of these actions, where it is appropriate to the performance level of the dancers, but it only splits the beat into two 330ms parts so is not the complete answer. It is however a good teaching method for use with suitable students. If it helps both halves of a partnership reach agreement on the interpretation of the music then it can only be a good thing.

Phil. I think the (and ]count at the end of three has always been there but never mentioned untill recent times for the simple reason that if both the lady and the man had their feet together the lady would have been pushed by the man onto her step.So its only natural to feel for the floor behind them. The man also when he is going backwards.

The fundamental reason things seem complicated and confusing is that the technique book isn't precise or accurate enough. And that movements which are judged by their appearance and grace cannot possibly be adequately described in words. There will always be different interpretations.
What does "end of 3" mean exactly? Does it mean on 3&? "End of 3" taken literally means "start of 1" since 3 is immediately followed by 1 in music (for waltz) and we're dancing to the music. Trying to separate "end of 3" from "1" results in differing interpretations. Maybe this is a good thing and allows artistic interpretation.
Best to watch a top dancer and copy what they do.

The timing of good dancers I think is not the step or swing of the leg but {swing cycles} the swing from the top of one position to the top of the next,you might say the the third step of a telemark belongs to the next swing cycle.

"I don't know if this is keeping in the correct order but it has been written that there is nowhere to go on beat three."

No it hasn't. Once again you are making your favorite two mistakes:

First your are substituting different words to create a statement with a different meaning than the one that was actually made.

Second, you persist in treating steps and beats as interchangeable when they are NOT THE SAME THING.

"continue to rise on three."

That instruction concerns STEP three, rather than BEAT three. The rise during step three will occur mostly while the foot is drawing closed and then a small additional amount while changing weight - very little will occur after the closure and weight change.

"leaving the whole of three to rise and lower on the third beat."

Not exactly. Most of step 3's rise is accomplished during the latter half of beat two. Similarly, the duration of beat three must include the leg swing that accomplishes step 4, assuming you want step 4 to land on its downbeat and not sometime after. There's no formal instruction in the book that steps must land on beats, but in waltz it seems to be how people want to dance.

Working backwards, we can conclude that if we are going to land the steps on the beats and all the steps are to have their formal values and boundaries, then the closing completes during the second half of beat two, so that the foot arrives closed squarely on the downbeat of three. Or perhaps its actually more musical not to dance exactly equal timings...

It is probably worth comparing the difference between rise and fall in the Waltz and in the Foxtrot. In the Foxtrot the man will rise at the end of one, up on two and three. Lower at the end of three
Waltz Commence to rise at the end of one. Continue to rise on two and three. Lower at the end of three. If you can do that all your questions are answered.
I think if you go to German Teacher's comments 2/12/08. That just about covers the rise and fall over the three step and three beats in the Modern Waltz for the man.Pay particular attention to the last few words which says "In combination with the starting the next step".
49 words thats all that is needed.