Here's a dilemma that's been going round in my head for a long time.
Let's talk slow waltz - first 6 steps of natural turn as a man. RF forward on 1 DW and turning. LF to side on 2. close R to L on 3 and now backing LOD. LF back on 1 (beat 4 of the 6 steps)and turning. RF to side on 2(5). Close L to R on 3(6) now facing DC.
The technique books define the end of a step as being that moment in time when the moving foot passes the standing foot (i know this doesn't apply to every step, but i'll use it for the steps it does apply to).
So RF forward on 1, DW and turning. LF to side on 2. Let's stop there. As my left foot swings past my standing right foot, this instant is the end of step 1. My left foot keeps swinging for a while and then plants. At the moment of planting, we are some way into step 2 by the technique book definition, but all dancers i've ever watched would plant that LF pretty well EXACTLY on the second beat.
so this means that the 'steps' (as defined by the foot plants - OK i know these aren't everything )don't occur on the beat of the music, but occur in fact mid-way - roughly - between the beats.
So this concept leads onto another important point:- "Lower end of 3" as the technique books explain for waltz. End of which 3? beat 3 of the music or step 3?
In my example of 1-6 of natural turn in waltz, the step back with my LF for step 4 is taken at the end of beat 3 because i only plant my (left) foot on beat 4. The technique book says that this action is in fact part of step 4 and so can have no lowering. The fact that all top dancers i watch do in fact continue to lower in this action suggests that either they are treating is as "end of 3", or they are 'massaging' the technique book a little.
The technique book is confusing (in my view) in insisting that the transitions between steps occur mid-way between beats of the music.

Maybe this dilemma has been circulating in my head for so long that natural background radiation has corrupted some of the ideas and confused me. Maybe i needn't be worrying about it at all, but it must make it the devil's own job to teach beginners.

Phil. Lower at the end of three means just that. You lower with the music and lower at the end of the step at the same time. Having said that one the top dancers has been criticized for dancing slightly behind the beat taking more time, I think, on beat three.

Hi onlooker. Thanks for replying so promptly.
I should have said more about how i view beats in music.
Imagine tapping out the beats in a waltz - you would tap each beat to coincide with the onset of, say, the left hand accompaniment of a simple piano accompaniment. The onset of the energy in each beat, which is usually clearly audible in straightforward music, would define the start of each beat. This is how musical notation works. And all dancers i've watched make their foot plants to coincide with these energy onsets. It would be difficult to deliberately dance otherwise i think (though i've never actually tried it).
Since the foot plants don't define the starts and ends of steps (they are defined as being the points at which the moving foot passes the standing foot, where this is applicable), it's not possible to lower at the end of step 3, and at the end of beat 3 (with the music) coincidentally. That's the dilemma for me

Phil . I have always been told that on step, and beat three, in the Waltz I have two things to do on the one beat, and that is I am at my highest and my lowest on the same beat. I was also told that as the person going backwards I need to prepare much earlier. In other word get the foot moving before beat one has struck. Also flex the supporting knee towards your partner at the same time. If not a person could be pushed onto the step and will never get a full extension of the moving leg. Another thing that comes to mind. Don't get too high on two otherwise there is nothing to do on three but lowering.

Actually you've identified the difference between the rhythm dances and the (body) swing dances. In the rhythm dances, the footfalls are timed to the music. In the swing dances - foxtrot being the classic example - the body movement is timed to the music and the foot falls are necessarily off time. The disparity isn't as big in waltz, but it's still there.

It would be no surprise if most of the dancers in many venues are using rhythm timing for all styles as the alternative is not widely understood.

Phil, you have discovered that everything is not exactly as described in the books. I suppose, it is to keep the books from becoming too technical, but as you noticed it creates confusion. Basically everything you said is correct. The confusion arises as to the meaning of "end of 3". If the down beat of 1 starts the beginning of 1, then the very end of three is immediately before 1. If you wait until the very end of 3, then obviously you don't have time to do anything while still in beat 3 region. So if you want to do something at the end of 3, you have to start somewhere after three and use the time up to the end of 3. As you noted, observing the professionals, this is what they do. Actually most of them start lowering immediately after 3, reach a low about the middle of 3, and hold this low position through 1. Is this correct? I don't know, but it looks pretty good to me.
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"The technique books define the end of a step as being that moment in time when the moving foot passes the standing foot ..."
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I'm not sure exactly what concept they are trying to convey here, maybe it doesn't seem logical for the definition of a step to end at the moment of contact of a foot, still having a lowering action yet to be completed, and they are saying to complete the step you have to finish the lower action. However, time wise this can't be the same "end of a step" we are talking about above. If the end of time for one step is also the beginning of time for the next step and coincident with foot placement (waltz for example, not foxtrot). Obviously, your feet can't be passing at the same time you place your foot.

Small correction to my last post regarding: "The technique books define the end of a step as being that moment in time when the moving foot passes the standing foot ..."

The lowering action has been completed (not thinking correctly before). That occurs between 2 and 3, and the end of three is end of the step. But it is after your feet pass. So the conclusion is still the same: your feet can't be passing at the same time you place your foot. However, this definition does make some sense, you have "essentially" completed the step.

It's easy to prove that when the technique talks about something happening at the end of a number it means the end of the step, and not the end of the beat - just look at a dance other than 3 count waltz where the step numbers and beat numbers don't line up. For example, a quickstep natural also says lower end of three, but that's somewhere between beat four and five because the timing is SQQ and not 123.

We also need to look at what the book means by lowering. Watch a classic couple perform any step that ends with passing footwork and you will see that loss of altitude commences before the book's lowering. Watch a step with a closed finish and see that loss of altitude must continue after the point where the lowering is supposed to end. So clearly when the book says lower, it is talking about some particular body action, not gain or loss of altitude in general. That body action is essentially foot rise - this is all that the book specifies, not really so much knee bend and not at all the height change due to leg division. So for example in our natural turn, we lower out feet at the end of three, but then we continue to bend our knee and loose altitude as we move into the next step. This is okay as long as we move with control that will let us be on the verge of gaining alitutude again by the time step four is placed - it's falling into the next step that is forbidden, while swinging through a lower point between the steps is actually desireable.

(But it's not precisely foot rise, because it's a quality you can still have on steps with "no foot rise" - it's really a sort of pushing up from the feet that can be achieved off either the heel or the toe, whichever is in contact with the floor. Note that you rarely have this rise without your knees fairly straight - generally feet rise last and lower first)

Anonymous
Many thanks for this post which, i think, answers a lot for me.
You've explained very well the technique book's version of 'lowering' and that has helped to reconcile my thoughts about a few things.
I still believe that there is a fundamental problem caused by step boundaries not coinciding with beat boundaries. Maybe it's the scientist/engineer in me (that i will never be able to remove, even if i wanted to) that wants everything to be consistent. And i still think of beats rather than steps, which possibly is causing me some problems.

As an aside, but related topic, it's interesting that some conductors regard the beat as the point at which the baton stops going down, and others as the point midway during the stroke.

Jerry