Sometimes it's difficult to work out exactly what's happening when i dance, and it's easy to become too mechanistic by defining exactly what should happen exactly when. But i've always been a little 'uneasy' about the idea of completing all the lowering at end of 3 and no more lowering after that. So i sat down and thought about it more, and lots of tricky concepts sprung up in my mind - i'm not sure i can articulate them (but of course i'm going to try!).
I started thinking "what do i actually mean by beat 1". Because of a musical background, i think of it as the instant i would hit the keys if playing a simple three-notes- in -a- bar waltz. When i place my heel or toe on '1' in a waltz, it plants at this instant. Most dancers seem to dance this way for slow waltz.
Then i split the bar into 1&,2&,3&. And i'm visualising a natural turn followed by a backward step (as a man).(actually, i went through this in the office - fortunately nobody saw me)
On '3' i'm at maximum height and my feet close. On 3& a lot seems to happen. I lower onto the heel of my right foot, but my knees continue to soften as my left foot moves back (i can't take a long stride without softening the knees of course)and then on '1' my left foot is planted (it may have skimmed back across the floor, but it only plants on '1')and on this beat '1' i am clearly at my lowest point.
i guess the technique book is strictly correct (AGAIN!) but at a first or even second reading it could be confusing. I always thought of softening the knees and taking the stride to plant on '1' as somehow part of '1', but i guess it's part of 3&.
Whatever the technicalities (and if you've struggled through this i would welcome any comments, as my dancing needs improving!!)i'm always influenced by 2 visual images, which are worth thousands of words.
The first is a picture of the waltz as a dance with undulating movements (a 'saucer' shape as someone on this site once put it) rather than bobbing up and down.
The second is a teaching wideo i have with Marcus and Karen Hilton showing slow waltz. I once played this in slow motion (almost frame-by-frame) and was stunned at how low he got at the moment of foot plant on beat 1. I thought of that lowering as part of the '1' but i'm now beginning to think of it as the end of 3&.
Do people talk about dancing the way they do about golf?

Yet more on rise and fall..
A post elsewhere talks about the physics of converting the speed of motion (kinetic energy) into rise (potential energy) so i thought about this too, being a lover of physics (it's true).
Skim over the next bit if you don't like maths, but the formulae for these two forms of energy are:
1/2 m times (v squared)
and
m times g times h
m is your mass, v is the speed (strictly velocity for you gurus out there) g is acceleration of gravity and h is the rise.
Putting in numbers, and equating, we get

1/2 times (v squared) = 32 h
now we're working in units of feet and seconds.

for slow waltz stride length of 4 feet occupying 1 beat (an assumption i know), v works out as 6 feet per second, which gives h as 18/32 feet or just under 6 inches.

Of course, this is the center-or-gravity rise, and body rise etc would add to it.
But the other interesting thing is that v depends on stride length, and h depends on v squared. This means that if you increase stride length by 10%, your rise from energy transfer alone increases by 20%.
Of course, as the energy transfer increases, the difficulty of controlling it increases too, but that's another story

Pretty numbers, but since rise is vertical and traveling is horizontal, I doubt that the numbers have any correlation.

Jerry

Ah, but they do. Refer to the classic high school physics textbook analysis or a pendulum.

Jerry - next time you get the chance ,watch some high jump.
The jumper accelerates into the bar (to maximise his energy), softens his knees (sports coaches call this 'lowering the hips') to maximise the efficiency of the leg and thigh muscles, and then takes off, converting the kinetic energy into height over the bar (addding leg muscle action too)
Nobody could jump over a door from a standing start.
As far as i can see, all these concepts apply to dancing - in a slightly different way, of course.
And anonymous is right - it's school physics concepts put into practice.
My original post wsn't just about the numbers - there was an important concept buried in there too!

This is the fourth time in this session. I don't want to hog up all the space here but i will put on once again about a lecture i attended given by Steven Hillier. He said we have a child on a swing. Our two arms are above our head grasping the seat of the swing . As we get to the bottom of the arc there is a moment where we still push the swing on its upward motion before we let go. He went on to say That is that elusive part we are looking for. Nobody can tell you exactly where it is.
Keep looking.

One thing to remember is that when the book talks about 1,2,3 etc it is talking about steps, not beats of music - this is very clear in the foxtrot section where the difference is obvious.

To tell the truth, I quit worrrying about the precise location of the boundaries in the music some time ago. At first, as I had previously been a musician, I was trying very hard to figure it out, but not longer. Today I dance to the music in a way that is more felt than analyzed.

But there are precise boundaries in the steps. For foot passing actions, the end of a step is specifically defined as the point at which the other foot passes on it's way into the next step. Obviously this definition won't literally apply to a closing action - where is the end of a waltz 2, given that the other foot will never pass?

Well, i got out my Marcus and Karen Hilton tape again and studied it carefully (just slow waltz - i know foxtrot is much more complex).
He dances pretty well exactly on the beat - even in the section where they are 'demonstrating' rather than 'teaching'. Of course, there are some parts where there are hesitations for interpretation, but the basic stuff is on the beat (by which i mean that his foot plant is exactly at the point someone would hit the notes in simple 3-notes-per-bar waltz).
So i confess to being a little confused. I like to understand things. I'm a firm believer in a good solid understanding of the fundamentals, even though skilled practitioners (in whatever area, sport, dancing, music etc)may depart from them.
i'm back to my natural turn, this time with a preparatory step (actually, how i start my comp routine).
Prep step left foot forward on 3. Then right foot forward on 1 to start natural turn, followed by left foot to side etc.
If i plant my right foot on 1, it must pass the left foot of the prep step on 3&. The same applies for the moving foot for step 2, which would have to pass the standing (right) foot on 1&
So if the steps end as the feet pass, do the steps end on the & beats?
I guess this post is really about how steps relate to beats. One step per beat, but what's the exact phase?
It's easy to dance with my foot plants on 1&, 2& etc so that my feet do indeed cross on the beat. But my point is this - dancers don't do this, or it would be obvious. AND it would be very difficult for beginners to learn this way, placing their feet on the half beats. The technique book should surely apply to beginners.
i'm beginning to wish i'd never started to think about this!!

In the book BALLROOM DANCING Alex Moore defines that the steps forward and backward do end, from a “time value” point of view, when the moving foot is passing the foot supporting the weight. The end of a side step, when the feet are to close, is approximately when the step has closed halfway towards the other foot, f. exp. the second step of a Natural Turn in the Waltz closing on the third step, or the first quick side step.

I understand that in generally steps end when the mowing foot is approximately at the halfway of the mowing of it. At this point begins the next step by pushing with supporting leg acceleration to the body at the same time you should strike a key of an instrument when playing. To keep balance you must have acceleration at the beginning of every slow step and the first quick step. The second quick and third on waltz are different as you lower and relax on those.

Moore is defining the boundaries of each step for purposes of describing the actions - he's not giving you a point to compare to the music.

Look at the first slow in foxtrot - the point that Moore would call the start of the slow step does not actually begin with the first of the two beats of music, but more around the second. Because what is slow is not really the first step, but the time between the middle of the last quick, and the middle of the first step.