However, my mind keeps going back to a concept of timing. Even the skaters have to spin at a rate that matches or compliments the music they are skating to.
Just making sure we're talking about the same element here -- In ice skating, it's called a Scratch Spin -- whereby a solo skater will spin around and around on a single spot. Typically the skater will draw his arms and legs inward, causing the timing of each consecutive turn to speed up. Since the music is not also speeding up, it is impossible that each spin is matching the individual counts in the music. To appear musical, the spin may begin and end on a particular count, but everything in between is ultimately just a blur.
Music is a fascinating and complex subject in dancing. Certainly a large part of it is based in simple mathematics. But it is a mistake to discount the human component, as music is, in fact, an art form. Sometimes in other art forms, mathematical precision can, in certain contexts, be perceived as less artistic. Likewise in dancing, rhythmical precision may be perceived as less "musical".
There is a device used in orchestral music known as a "run" or "swell" often played by various combinations of strings (i.e. violins, violas, celli & basses). It is notated in a very unorthodox manner: Rather than dividing a group of beats into perfect, symmetrical parts (e.g. a group of eight 16th notes over two beats), they'll squeeze any seemingly random number of notes into the phrase. For example, you might have a run of 17 notes over two beats, where in theory each note should get 2/17ths of a beat. In reality, every musician interprets this slightly differently, and what you hear is a musical "effect" which has no exact pitch, but a general movement upward or downward (or some combination thereof), which evokes a certain feeling.
Incidentally, string and harp runs happen to be a great complement to runarounds. Choreographers take note: If you are choreographing to a Waltz that has a long swell of at least two measures, it's a perfect place for a runaround!
At any rate, needless to say, context is everything in art and music. There is typically a logical explanation behind every departure from the "rules". And when you're breaking rules of rhythmic precision, the justification will probably have something to do with perception. In music an especially in dancing, your brain selectively filters information in ways that allow it to accept -- or even prefer -- an alternative to rhythmical precision.
Your brain goes through this process each and every time you set foot on the dance floor. When you concentrate on your foot rhythms, you are probably unaware of all of the other various parts of your body that may or may not be "off-time", such as the swing of an arm or the twist of your body. Body mechanics are so complex that it is impossible to be aware of every individual movement at once. And even if you could be aware of everything all the time, it is impossible to make every single aspect of every movement perfectly rhythmical at the same time. And so we make choices, and do our best to draw the spectator's attention to the elements we've chosen.
When you dance a runaround, your first job is to draw the spectator's (and for that matter, your own) attention away from the foot rhythm. If you simply "can't get past it", it's likely you don't truly want to, which is ok because art is, after all, a matter of taste. But if that's the case, I suggest you tell your teacher it's not for you. However, assuming you do want to conquer the hurdle, you have to start by accepting that foot rhythm is not the point of this movement, and take your mind off of it by distracting yourself from it. The best way to distract is to concentrate on other things, such as the speed of the whole body (i.e. as fast as possible), or other rhythms such as arms, hands, head, etc.
Regards,
Jonathan Atkinson
www.ballroomdancers.com