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