What is not understood about the V, Waltz is. If I don't start facing diag to centre I will over rotate the Natural Turn. The same with the Reverse. If I started the Reverse facing diag to centre I will over rotate.
Where it sometimes goes wrong is the alignment at the end of the Reverse after the Forward Change. Get that to finish diag to centre and you will be technicaly correct. Try not to do Reverse Turns on the short sides of the Ballroom. If you have to, try not to do heel turns instead of back side together.

In case the previous response (from Polished) causes confusion step 1 of a natural turn is facing line of dance having turned 1/8 to the right between the previous step and step 1. Step 1 of a reverse turn is facing line of dance having turned 1/8 to the left between the previous step and step 1. This is according to the British Dance Council and is the technique also adopted by the Imperial Society of Teachers of Dancing (ISTD) and the United States ISTD.

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Before you take one step in a V. Waltz make sure you know where you should be facing to start the Natural Turn and the Reverse Turn. The Natural Turn should start facing Diag to Centre.
The Reverse Turn facing the LOD. This is throughout the dance and especially after a forward change.

"I'm not sure what is meant by "the most characteristic version" but the amount of turn achieved in the chart forms of the natural and reverse turn is one whole turn for each figure."

The most characteristic execution of Viennese Waltz as a dance would curve around the short side using natural turns which turn less than a half turn.

Therefore, in actual practice the amount of turn commonly used in the natural turn is NOT the same as that used in the reverse turn, but a bit less.

A full half turn natural feels different that the under turned one usually employed.

"Cutting corners as a matter of course is frowned upon"

Going fully into the corners in Viennese waltz does not fit with the flow of the dance which is more naturally oval in shape.

The amount of turn isn't the point, but in case the previous response (from anymouse) causes confusion I'm not sure what is meant by "the most characteristic version" but the amount of turn achieved in the chart forms of the natural and reverse turn is one whole turn for each figure. This is good technique and is the amount of turn expected in examination. Of course the natural turn is underturned at the corner but not "around the short side" or any other side. One could achieve a sort of arc by dancing three naturals in succession, the first and last each cutting a corner. Cutting corners as a matter of course is frowned upon by examiners, however.

http://www.goballroom.co.uk

"Although the amount of turn is the same of course, the reverse turn feels "tighter" than the natural turn therefore and this is reflected in the different foot positions."

While the difference in turning in the two directions in the hold should not be discounted, the amount of turn in the most characteristic version is not the same either.

If you are dancing reverse turns down the long side they will have to complete a full 1/2 turn, but if you dance natural turns around the short side each one can be under-turned to add up into a nice graceful arc the width of the room.

Of course some like to curve their reverse turns around the short side, but that's a different story.

The reason why both gentleman and lady close in the natural turn but cross in front in the reverse turn is that in the case of the natural turn we are turning towards the open side of the hold but in the case of the reverse turn we are turning towards the closed side*. Although the amount of turn is the same of course, the reverse turn feels "tighter" than the natural turn therefore and this is reflected in the different foot positions.

*In the normal hold, from the gentleman's point of view the left hand side of the hold is described as open even though the body position is closed.

http://www.goballroom.co.uk

"A more sedate form of the V. Waltz was danced at 90 beats per minute, evolved in America about 1834 and was originaly known as the Boston."

Some would argue that the Boston is the origin of the modern ballroom slow waltz.

From the Histoty of Ballroom Dancing.
A more sedate form of the V. Waltz was danced at 90 beats per minute, evolved in America about 1834 and was originaly known as the Boston. The Boston has the distinction of being the first Ballroom Dance to be done with the feet parallel rather than turned out in Ballet. The present form of the dance was derived around 1910 in England. Strausse wrote the song The Blue Danube in 1867.
Just for the record the demonstration of the Viennese Waltz I saw in Vienna was a distant cousin to the one I know.

I'm curious as to why a 'lock' is danced in the reverse sequence whereas, in the natural sequence of the dance, no lock is performed.

My teacher says "...because that's the way it is". NOT SATISFACTORY!!!