Sorry, I'm NOT Jonathan, but I think I understood your question and are able to give the answer:
The "Clapping Moment" is the number, so your graphic interpretation has to be:
1 -------- 2 --------- 3 ----------

So usually a step starts (by the impulse/drive from the 'old' supporting leg) BEFORE the beat is heared. An 'and' belongs to the preceding beat. So a rhythm of 1 2 & 3
is:
1 -------- 2 ----&---- 3 ----------
Here the & divides the second beat from a 1/4 note (is a beat in 3/4 measure called that way in English?) to two 1/8s notes (half beats)
Some figures require an "odd" division of beats, then we count "1 a 2", where the 'a' marks a half "and", which is a 1/16 note:
1 ------a- 2 --------
e.g. a Jive Chassé or a Samba Basic (int. style).

Good observation. Yes, in music, the beginning of a beat is the moment it first strikes. The duration belongs to the same beat, right up until the moment the next beat strikes. That includes any "ands" and "a's" occurring within that span of time. So when we speak of the "and of two", for example, we're talking about the "and" that occurs after, and therefore belongs to, beat two.

Movement in dancing does not always work so mathematically. Also, it's based largely on perception. For example, your perception of the moment a step begins may be different than someone else's. But let's say, for the sake of argument, we've decided it's the moment one foot passes the other and begins to move towards its next position. And if we also suppose that the foot strike is the moment that defines the beat, then in order to be perceived as "on time", we must begin the step sometime during the previous beat.

This is probably the reason you perceive the "and" as belonging to the previous beat.

By the way, this concept isn't limited to steps. Almost all movement is organic, with no true beginning and end points. It's all a matter of perception. Whatever you consider the end point of something, it's also the beginning of the next thing. If you're trying to hit a specific pose or line on the downbeat, you need to move towards it during the previous beat, and then presumably past or away from it afterwards. In other words, like taking a step, part of any movement occurs during the end of the previous beat leading into the "target" beat, and some of it occurs after the initial strike.

I hope that makes sense.

Regards,
Jonathan

Jonathan. Am I right then to say that when the music first strikes that our heal begins to take part weight depending on how we hear the music.

Yes, with a few noted exceptions (the "slow" step in Foxtrot being the most notorious), most steps are perceived to be on time when the foot strike hits the beat squarely. By "foot strike" I mean the moment the foot stops moving and begins taking weight.

I wouldn't bother mentioning the heel, since not all steps are heel leads. And for those that are, the amount of time between the moment of foot strike and the lowering of the toe is negligible.

Regards,
Jonathan

Jonathan
Did you really mean to use the word 'negligible'?
I won't be doing any serious practice till tomorrow, but just dancing a few steps in my lounge (don't worry - the neighbours can't see me!) i roll from my heel onto the ball and then toe as my weight comes over the foot, which would be possibly half a beat in slow waltz natural turn, for example.
I was pulled up at a recent practice for landing too abruptly on the third step of a curved 3-step (slow waltz) and going from my toe onto the heel very ubruptly before moving back on the next step. I'd never noticed it myself, but when i softened the movement and controlled the heel lowering it made a big difference and felt nicer. I'm sure none of this is new to you!!

"i roll from my heel onto the ball and then toe as my weight comes over the foot, which would be possibly half a beat in slow waltz natural turn, for example."

If you take the action of the heel lead properly, with the leg moving as a consequence of the body action and not flying out on it's own, then the time between the late point when the ball of your foot flips up so that your heel lands first, and when the ball lowers again as your weight is arriving, will only be a very small fraction of a beat.

"I was pulled up at a recent practice for landing too abruptly on the third step of a curved 3-step (slow waltz) and going from my toe onto the heel very ubruptly before moving back on the next step. I'd never noticed it myself, but when i softened the movement and controlled the heel lowering it made a big difference and felt nicer."

Apples and oranges, step 3 is nothing like step 1. Step three starts your downswing, and you want to control that so as not to get going so fast or so down that a clean step 1 after it would be impossible.

It's an interesting fact, but when lowering toe-heel to continue forward, you actually do have to get into the heel fairly quickly and do most of the lowerin with your knee. If you supported your whole weight in your toe, your weight would have to move backwards against the travel to get to your heel again, and that would not be good.

Except that you are checking your travel in the curved 3, so this is what you want - you want to absorb your motion in the toe and lower with control. You then send your weight the lenhth of the foot in preperation for the driving action of the next step , in which you will push from this standing heel as your release its toe.

Hi Suomy
"the time between the late point when the ball of your foot flips up so that your heel lands first, and when the ball lowers again as your weight is arriving, will only be a very small fraction of a beat."
At the point my heel lands, my body is roughly mid-way between my two feet. This is instant 1
At the moment my weight is over the standing leg and my foot is rolling onto ball-toe - let's call that instant 2.
What's the time interval between instant 1 and 2?. I don't think it would be a very small fraction of a beat.
And when i do this type of movement, i can feel that there's a time interval of about 1/3 of a beat (hard to be accurate)
However, i'll get my Andrew Sinkinson tape out again and study this very point. Hopefully, i'll learn something to improve my dancing

"At the point my heel lands, my body is roughly mid-way between my two feet. "

Your body should be substantially closer to your front foot. If you keep it equidistant, then you could well feel that the foot would lower more slowly, but this would be miscoordinated dancing because you are allowing the body to lag behind the foot, rather than precede it.

Substantially closer to my front foot? This is not what i'm seeing on the Sinkinson tape, which i've just been studying in close detail. It's his teaching tape 'Come Dancing' -the slow waltz section. He starts with a natural turn and i played it frame-by-frame (20 frames per beat) to measure as accurately as i could how he controls his foot plant. For the right foot plant on 1 there is about 1/5 - 1/4 beat between the initial heel strike and the foot going flat. It would be longer than this before the weight rolls onto the ball of his foot. His body moves over the standing foot almost exactly 1/2 beat after the foot plant. The same thing happens with a reverse turn.
The detailed timing on his natural turn is very interesting though.
If my body were 'substantially' closer to my right foot (for the step on '1') wouldn't i be over this foot very early in the beat, and my body flight be curtailed into beat 2? i might try it to see what happens. However, Sinkinson doesn't appear to do this.

Phil. If it helps this is the latest bit of information given to me. It has come in a round about way to me from a former Blackpool winner. That is, on the sole of our shoe we have four points in a square. On the heel we have the same.We must use every point on our shoe. A person can talk on and on about when to put what part of the shoe to the floor. It all comes to a mstter of timing. When do I put the second row to the floor after a heel lead which has the first two points down. And now the other four which are on the sole coming onto the last two. All this to tell a person that they must use the whole of the foot. Let's not forget that we have two feet with both of them working. Isn't that a much simpler way of explaning the use of the whole of the foot.