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.

I can't agree with this. What you are saying is "the first step is slow, so there is a "slow" between the middle of the last quick and the middle of the first slow" (have i understood you correctly?).
The middle of the last quick is exactly that - in the middle of the last quick and therfore not part of the first slow.
My original point on all this is that most dancers - even advanced dancers - plant their foot on the note because the note defines the beat (i was talking about simple 3 notes-per-bar waltz, and still am just for the moment) yet the technique books effectively place the step boundaries on the & beat (between the notes) which can be danced no problem, but is a source of confusion for those learning.
Transferring my comments to foxtrot (and taking a big risk!!)i would maintain that i plant my right foot (first step of feather) on the beat and so the preparatory act of moving the right leg past the standing left leg, sliding it across the floor (with my body following appropriately, in case anyone points it out!)takes place during the previous & (usually 4& in my case). Of course, i do attempt subtle rhythmic variations to interpret the music - with limited success - but this is the essential timing i use as a base. I'm prepared to do this differently if i can be convinced that good dancers do it differently, but from videos i've watched, i'm yet to be so convinced

The footfalls in good SQQ foxtrot are VERY approximately on 2, 3, and the & after 4. But nobody times the feet to music - we time the body and the feet do what they have to in order to enable this.

Just when I thought it was safe to come outside. Low and behold we were made to do a change of direction in the Foxtrot with only three slows, and not four. So how did we manage to come out in rhythm, I hope you can follow this because this is what you are watching without realizing. Count this way slow slow then quick on the left foot which is normaly a slow. And a quick on the first of the feather which is also normaly a slow followed by the normal two quicks. I even watched in a major competition on tape a professional do a Natural Turn. At first I couldn't figure out how he got away into his Feather so quickly untill I took a few more looks at it, and also counting with my new found knowledge. After that I took nothing for granted and can pick out competitors who syncapates a Open Telemark to come back into rhythm which is 1234 and not 3412,

Some teachers encourage their students to count the Modern Waltz in half beats
with the foot closing, on a (and) count. Leaving all of three to reach your height and lower on an (and).
It was recomended that in pracise both should count aloud.

Hi Anonymous

I have been injecting your ideas/concepts in my system for the past about four years with gratifing results.

Thank you.

However, I am now anonymous too because I found myself in traumatic situations for doing things that the "experts" did not understand.

Some of them have now discovered the website.

Keep up the good work. In this life you are not usually rewarded in a monetary way for divine contributions made to the development of the species.

You are an agent of the great master. When he is pleased with you, there is the peace that passeth understanding.
The technique here is that you don't go after it.

I am positively sure that there are countless people all over the world who have benifetted from your good work

Thanks again.

Something that has'nt been mentioned before and that is. Lowering in the Modern Waltz. If you allow your body to lower it will always beat the knees, and out pops the bottom. So stay up to come down, and stay down to come up. In other words use your undercarriage not your upper body. That will get rid of your bottom sticking out. and your shoulders lifting.