It has been my experience that musicians, especially drummers, have a hard time understanding how to ballroom dance (move physically) to the music. There is a misconception between "musical beats" and "ballroom dance movement". I believe it is because of how different the physical action of a "drum strike" is to the physical action of taking a "ballroom dance step". The assumption seems to be that they are the same when in fact they are very different.
Let's take a look at taking three forward steps in Foxtrot using the Slow, Quick, Quick timing. The music is written in 4/4 time (figure 1a) and the speed of the music is 30 mpm (measures per minute). This would make each measure 2 seconds in length (fig.1b). The Slow, Quick, Quick, is equivalent musically to one ½ note and two ¼ notes (fig.1a). The ½ note would then be 1 second in duration and the ¼ notes .5 seconds each (fig.1c). I will compare a pianist and a drummer playing the three musical notes and a dancer moving to the same three notes.
The pianist (fig.1d) "depresses" a key to begin the ½ note tone and "releases" the key one second later to end the ½ note tone. The pianist would do the same for the ¼ notes except for depressing the key and holding it for just .5 seconds per ¼ note tone).
The drummer would raise the drum stick in anticipation of the beat and strike the drum at the start of the ½ note (fig.1e). The duration of the drum strike is measured in milliseconds (duration depends on the type of drum, tone, etc.). In percussion there's no ability to sustain a sound, therefore, a drum note of a specific length actually means striking the drum at the beginning of the note and doing nothing for the rest of the notes' duration.
The definition of a Foxtrot forward "step" in ballroom dancing is: "A complete weight change from one foot to the next concluding with the free foot beside the other." The weight change (step) is initiated at the beginning of the note and is not completed until the end of the note. Commencing with the left foot (fig.1f), the ballroom dancer would start moving the left foot on the drum beat at the beginning of the ½ note (at the same time that the pianist ½ note tone starts). The step would be completed (free foot beside the other) at the end of the ½ note when the tone ends 1 second later.
The ballroom dancer must dance the same way a piano player uses the keys to play notes. As the key is depressed the dancer starts to move. When the piano player releases the key, the dancers step (weight change) is complete with his/her feet together. Using our example, let's compare the drummer to the dance movement. The drum strike (fig.1e) at the start of the 1/2 note would start the dancers ½ note step and the drum strike at the beginning of the ¼ note would complete the ½ note step and simultaneously start the ¼ note step. Even though the drum strikes are on different notes, they effectively start and stop the ½ note movement because drum strikes have very little duration.
The ballroom dancer has to develop the ability to understand how to listen to the music and move accordingly. Once you can achieve this, the Foxtrot will have a very smooth and even movement as it was intended to have. The same it true for West Coast Swing, Bolero and other dances that use this type of movement.