Traspie
A walking step with a syncopated cross. Using two beats of music the dancer does step-cross-step beginning with either foot and moving in any direction.
When the dancer stresses the musical accent down to the ground, it is called Traspie. When the dancer stresses the musical accent up in the air, it is called Traspie "falcetti".
(from pascaleyluis.com (http://www.pascaleyluis.com/article39.html))
Using two beats to make a triple step, thus stepping on one beat, then on the half-beat and again on the next beat, is a traspié. It is related to what is called syncopation, syncopa: the stressing of a normally unstressed beat, making a syncopated rhythm.
from Tango-E-Vita (http://users.pandora.be/Tango-E-Vita/tango/walk.htm)
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Traspie (literally stumble or trip) is dancing short, quick steps. If done very quickly some of the steps fall between the beats of music.
One way to do traspie is when leading your partner in an ocho. When she does each pivot step, do three very quick steps to her one, just as she is pivoting.
Another is while moving in a straight line. The man does four short quick steps while she does two, or six very short, very quick steps to her two. He has to do his steps very smoothly, or the woman will feel his upper body weight changes and try to match his quick steps.
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On both of these only the man does traspie. Here's an example that Omar Vega teaches where both partners do it. It's from the view of the woman; the man's part is the same but reversed.
(It's usually a good idea to teach the woman's part first. Not only does she need to know it, but it is what the man has to focus on. He has to lead her part, and once he knows her part often his part becomes obvious.)
Step RIGHT TO THE SIDE, LEFT TO THE SIDE, RIGHT IN PLACE. The last two steps are done on the starting spot, so that it's like a quick side trip with her right foot.
(The man's part, of course, is LEFT TO THE SIDE, RIGHT TO THE SIDE, LEFT IN PLACE.)
This is done in three steps so quick that the middle step is between two beats of music.
Then the woman does the mirror image of the pattern. This is LEFT SIDE, RIGHT SIDE, LEFT IN PLACE. (The man's part is RIGHT SIDE, LEFT SIDE, RIGHT IN PLACE.)
Leading this is tricky, because the steps are so fast. On the first half of the pattern, the man must tilt his left arm up SLIGHTLY and return quickly to the center. On the second half, he does the opposite - tilt his right arm up and return quickly to the center.
I emphasisize "slightly" because too much tilt will pull her off her center in the wrong direction, rather than keep her in the center of the pattern.
This pattern is stationary. To move along the floor, the leader can do the last step of either triple FORWARD rather than in place. Or do both of them forward.
Larry de Los Angeles http://larrydla.home.att.net