My understanding is that the waltz grew out of an Austrian folk dance. Of course, the aristocracy of the time couldn't be caught doing a dance so simple that a peasant could do it, so they deliberately made it more difficult. Others claim the waltz has Italian or French roots...do a little searching on the 'net under "dance history waltz," and I'm sure you'll find lots of info and theories.

Phil. The music is eight bar phrased. if you start with eight bars of a Natural you will strike your Forward Change on 123. Your next music will be 223 which is the first of you Reverse.
If you started with a Reverse and completed your eight bars you would be hitting the first of the Natural on 223. It doesn't matter how you do it it doesn't fit. Do you want to stay in phrase. Then only do Natural Turns. Or all Reverse Turns.
I wonder why nobody has ever thought that nine bar phrased music would solve the problem. What do you think.

"I wonder why nobody has ever thought that nine bar phrased music would solve the problem"

I suspect 9 bar phrased music would sound rather un-musical to our 2,4,8,16 bar trained ears, and it would feel uncomfortable to dance to, and could be very difficult for musicians to play.

Also, we would probably mentally split the 9 bars into 3 x 3 bar sub-phrases. This would mean that every other turn would be out of phase!?!?

An example "fitting" sequence
Bars no in [ ]. Man's steps:
[1] 1-3 Nat. Turn
[2] 4-6 Nat. Turn
[3] 1-3 Nat. Turn
[4] BACKWARD change
[5] 4-6 Rev. Turn
[6] 1-3 Rev. Turn
[7] 4-6 Rev. Turn
[8] fwd. change

Now you could say "but at [5] the Rev. Tun is started bachwards" but the appearence shown by the movement of the whole couple swaps at [1] and [5] as you would like it.
And who says all accentuations have to be for the man? In this sequence lady gets the [5].
The problem of choreographing V. Waltz in phrase is the restricted RHYTHM of the steps. And that may have been appeared because of the high bpm-musical speed where it would be uncomfortable to dance something else than "1, 2, 3".

Also, the Reverse Fleckerl-Contracheck-Natural Fleckerl combination does the same; which suggests the following at least gets the man back to 123 on the forward step: Natural Turns - Closed Change - Reverse Turns - Reverse Fleckerl - Contracheck - Natural Fleckerl - Natural Turns.

In your wildest imagination-- could you visualise ANYONE moving around a floor , completing sequences, with the feet closing on every third movement ??----- with never having heard music to match ?

Its a generally considered fact, that the earliest form of music, was the drum . Surely the " sound " of something, fires the imagination .

Logic dictates, that one would not compile a series of movements, and then say-- " lets write some music, to fit that "

The steps belonged to another damce. Then Chopin and a few others wrote in 3/4 time long before the Blue Danube.

Which goes back tio the original premise-- music first ( the drum )One could say that " dancing ", could be performed without music-- but is that convoluted logic ?

Not only is it convolted. It's very complex.

It is my understanding that the V Waltz that is danced today was begun in the 1880's. The waltz as a ballroom dance dates back to the 1820's. In the 1860's the waltz was a dance done only rotating to the right where the man stepped diagonally around the woman on his left foot and then pivoted on his right foot, followed by three small right left right steps as the woman does the pivot steps around the man. The man starts by facing the outside wall and the woman faces in. By the 1880's the man faces backwards to start the dance and it allows for left turns and other variations. If you do an internet search, there are teachers and videos for Vintage Dance.
Waltz music predates the dance. There are English Country dances from the 1700's that are done in Waltz tempo.
Steve