What specifically is the speed of a dance? What does "SPEED" really mean? Is it miles per hour, feet per second, how long the song, number of steps taken, how big the dance floor or what? I am defining "SPEED" as how fast the two-headed four-legged animal moves.
Most Ballroom dancers think that only the tempo of the music indicated by mpm (measures per minute) determines the speed of the dance. mpm is the speed of the music not the dance. Although tempo is one factor that has a bearing on the speed of a dance, the tempo of the music actually dictates the dancers weight changes.
In the standardized Ballroom dancing, the music for each dance has a specific tempo range. An example of a tempo range for a particular dance might be 28 to 30 MPM. The physical dance step elements are designed to be executed in this defined range. That is why it is so important that the music have the correct tempo for a particular dance. It is possible to dance at tempos outside the specified range, but the dancer doesn't get the intended feeling of that particular dance. If the tempo is too fast, there isn't enough time between the steps to develop the character of the dance. If the tempo is too slow there is too much time for what is supposed to happen between the steps. In my opinion, the real dancing (the development of the feeling) happens between the steps (Latin motion, Rise/fall, power, connection, etc.).
Let's look at a Slow Waltz (1,2,3) at 30 MPM (30 makes calculations easier). Each beat would be a weight change: 3 beats per measure at 30 MPM equals (90 beats) 90 steps per minute (assuming no syncopated elements). Is this the SPEED of the dance? Not quite there yet. There are other factors that also influence the SPEED of the dance. Let's assume for simplicity's sake, that all of the steps are forward. If the dancer takes steps 1 foot long, he/she would travel 90 feet per minute. If the dancer takes steps 2 feet long, he/she would travel 180 feet per minute. The size of the steps also has an influence on the speed of the dance.
Let's now look at a Slow Foxtrot (Slow, Quick, Quick) at 30 MPM Each beat is not a weight change. The Slow is 2 beats and the Quicks are 1 beat each, resulting in 4 beats per measure at 30 MPM equals (120 beats). There are still 90 steps per minute because of the Slow, Quick, Quick timing, (assuming no syncopated elements). The timing characteristics of the dance (timing of the steps in a measure) has an influence on the SPEED of the dance too.
Let's compare Rumba and Cha Cha. Rumba (Slow, Quick, Quick) at 30 MPM. The calculations are the same as Slow Foxtrot but this time we won't analyze the distance component, but we will look at leg/foot speed. Basically we have a Slow weight change followed by 2 Quick weight changes (90 steps per minute). Cha Cha (1,2,3,4,&) at 30 MPM. The "1", "2", "3" of Cha Cha are whole beats. The "4", "&" are each ½ beats for a total of 4 beats but 5 weight changes (150 steps per minute). As seen in this example, Rumba and Cha Cha have the same tempo of 30 MPM but Cha Cha has 5 weight changes (two of the steps ½ beats) at 30 MPM equals 150. Rumba only has 3 weight changes in a measure (one step a Slow) at 30 MPM equals 90. The leg/foot speed is faster in Cha Cha even though the tempo of the two dances are the same. The frequency characteristics of the dance (number of the steps in a measure) has an influence on the SPEED of the dance as well.
The skill of the dancers also has an effect on the speed of the dance. An accomplished dancer usually wants to dance to the slower end of the tempo range of the music so he/she has time to develop the feeling between the steps. The newer dancer usually wants the slow end of the tempo range because he (the leader) needs more time to think between steps. Pattern dancers usually want to dance to the faster end of the tempo range because he/she doesn't know what to do between the steps. There are also dancers (usually Pattern dancers) that just dance while the music is playing, instead of actually dancing to the music. Typically Pattern dancers dance faster than the music being played.
Now we have an idea of what determines the SPEED of a dance. The tempo of the music, the size of the steps, the timing characteristics of the dance (timing of the steps in a measure), the frequency characteristics of the dance (number of the steps in a measure), skill of the dancers, etc. After all of this, it still isn't very clear as to what SPEED actually is. I define "SPEED" as how fast all the parts of the two-headed four-legged animal move, either in unison or separately.