Haven't heard of purpletime before (although a Google search on it did pull up some interesting hits).
Did you mean "triple time" or "triple step"?
Waltzes typically come in groups of 3 beats with the accented beat being the first beat in each group.
For beginning dancers it's enough to know waltzes are in 3 (usually 3/4 time meaning 3 beats to a bar or measure with a 1/4 note counting as one beat).
Typically counted:
1,2,3,1,2,3... (with a little extra emphasis on the 1's)
Foxtrots, jives, cha chas, rumba, tangos are written in 4/4 time):
1,2,3,4,1,2,3,4... (emphasis on the 1's again and called quadruple time)
Try counting the above out loud emohasizing the 1's to get the difference. ONE, two, three, four ONE, two three, four...
A little more advanced possibly than you need to know but waltzes are possible in different groupings as well. I.E. 6/8 or 12/8 time (6 or 12 beats to the bar with an eighth note getting the beat).
In 6/8 you'd count:
1,2,3,4,5,6,1,2,3,4,5,6...with 1 again getting strong emphasis and 4 slightly strong emphasis:
ONE, two, three, Four, five, six, etc.
Hope this helps.
OB