All Ballroom dances have a basic rhythm. The "Syncopation" occurs when the basic rhythm of a particular dance varies. "Syncopations" are normally a temporary variation from the basic rhythm. Syncopations allow for more of a variety of movements in a specific dance.
The Slow Waltz for example, has a 1, 2, 3 basic rhythm (three steps). However, the Slow Waltz "Chasse'" and "Lock-Step" patterns have a syncopated 1, 2, &, 3 rhythm (four steps). Slow Foxtrot has similar "Syncopations" for the "Chasse'" and "Lock-Step", except the basic rhythm for Foxtrot is "Slow, Quick, Quick" (1-2, 3, 4) three steps. This makes the rhythm of the "Chasse'" and "Lock-Step": "Slow, Quick, And, Quick" (1-2, 3, &, 4) four steps. The Slow Waltz has two different step durations in the "Chasse'" and "Lock-Step" elements: two whole beat steps (1, 2) and two half beat steps (&, 3). Slow Foxtrot has three different step durations for these syncopations: a two beat Slow step (1-2), a one beat step (3) and two half beat steps (&, 4).
The Waltz and Foxtrot syncopated rhythms seem a little complicated; but then there is Quickstep. The Quickstep basic rhythm is "Slow, Quick, Quick, Slow" (1-2, 3, 4, 5-6) four steps. However, there are patterns with 4 "Slows" in a row, another with 4 "Quick's" in a row, and still another (Spin Turn with V6), "Slow, Slow, Slow, Quick, Quick, Slow, Slow, Quick, Quick. Quickstep is a major challenge for the leader because it seems as if most of the dance patterns are Syncopations.
Now that we understand that Syncopations" are variances from the standard rhythm of a particular dance, how is it communicated within the partnership? Just to make it a little simpler, let's look at an American Style, Slow Waltz "Chasse"'. The following description is from the Leader's point of view and the Follower's part is a mirror image.
The Slow Waltz "Chasse'" dance element begins in Promenade Dance Position and ends in Promenade Dance Position. The rhythm is 1, 2, &, 3 (R-Whole, L-Whole, R-Half, L-Half). The footwork is: R-Heel-rolling to a ball, L-Ball, R-Ball, L-Ball-lowering to a flat. The Leader's left supporting leg lowers and powers the 1st right foot heel step. The power generated from the left supporting leg creates momentum for the complete element. I call this action "Power and Glide". The dancer's weight is transferred from the 1st (R-heel-ball) step to the 2nd (L-Ball) step. The rise from the 2nd (L-Ball) step allows the 3rd (R-Ball) step to close. At this point in time there is a slight weight change (backwards) to the 3rd (R-Ball) step, immediately freeing up the 2nd (L-Ball) to take the 4th (L-Ball-flat) step.
Wow, this really seems complicated. Let's see if I can simplify it a bit. While standing in Promenade Position, the Left supporting leg powers the whole "Chasse'". Lean slightly back when the legs come together. This causes an immediate weight change so the 4th step can be taken gracefully. Your partner will feel this action and respond accordingly. Footwork and power is an essential aspect in the lead and follow of Syncopations. Simple as that! Be aware that Latin and Rhythm dances have Syncopations as well. Examples are: "Cha Cha Locks", triple turns, etc., etc.
There is another rhythm variation that I personally don't consider to be a true Syncopation but it is somewhat similar. I'm talking about a Slow Waltz or Slow Foxtrot "Hover". A "Hover" is a dance element designed to transition from "Closed" dance position to "Promenade" dance position. It is danced at the higher levels of Ballroom dancing (Silver and above). To me it feels more like a Hesitation or a Suspension of the rhythm rather than a "Syncopation". Actually, it feels just as if you are HOVERING (just as the name implies). As a Leader, it feels as though I am stealing time from the third step to maintain that suspended feeling. It is not uncommon to stay suspended for an additional whole measure of music.
Rhythms, Syncopations, Hesitations, etc. are all part if Ballroom Dancing. Learn them and use them. "Varity is the spice of life", it will make your dancing much more dynamic and interesting.