"Tempo is a measure of speed, so that statement by itself, without further explanation, is self-contradictory."
Tempo is a measure of RATE, not of speed. But the important point is that tempo is not a measure of a dance - it's a measure of paramater of the music.
"Foxtrot in particular is specifically characterized by variety of rhythms."
Yes, but there's one fundamental default rhythm. Call it potential swings per minute or something - it's the same for a waltz and a foxtrot at the same number of measures per minute, even though the tempo of beats (which are quite unimportant) are different.
"You can substitute Dancing a weave (mostly quicks) followed by a change of direction (all slows) doesn't make the dancer change tempo..."
None of which are swing figures. What you've done is basically stepped outside the pace of the dance by substituting something else. Which is a fine thing to do, but the pace of potential swing figures (SQQ in foxtrot, 123) in waltz is still there in the music, even if you've chosen to briefly substitute something with a different rhythm.
"That is why DANCERS often prefer measures per minute - because this gives the APPLICABLE SPEED OF THE DANCE.
Which depends entirely on the rhythm, something your methodology unfortunately can't seem to separate from tempo. "Applicable speed of the dance" can change constantly, because the rhythm can change constantly, but this has no bearing on tempo."
No, the applicable speed stays the same. Syncopation does not make the dance faster, it merely makes it more complicated.
"And defining tempo as "applicable speed of the dance" (a definition I have yet to encounter in any dictionary I've read) is inaccurate"
Read again, the passage of mine you quoted: "Which is to say, that tempo is NOT an applicable measure of the speed of a dance" See, I didn't define TEMPO as the applicable speed of the dance. I said that what was important was the applicable speed of the dance, of which TEMPO IS NOT A MEASUREMENT. On the other hand, at least when comparing waltz and foxtrot, the number of measures per minute IS an applicable measurment.
"Take the example of American style Rumba and Cha Cha, which happen to be of very similar, if not identical, tempi. How does MPM do a better job than BPM of telling you that Cha Cha "feels" faster than Rumba when a person dances to the prescribed rhythm? Either way, the numerical value tells you that the tempo is the same (Both dances are 31 MPM or 124 BPM). So that shoots a hole in your theory that MPM is somehow a more accurate measure of perceived speed than BPM."
Okay, in latin syncopoation changes the pace. But latin tends to be unduly preocupied with such noise anyway
Take a look at Continuity Smooth, a subject with which I'm sure you are familiar. We can come up with a classic sequence of open natural and reverse turns that is equally characertistic for both waltz and foxtrot. Dancing it at your proposed 30 mpm foxtrot and 40 mpm waltz, are you going to try to tell me with a straight face that the waltz isn't faster? Of course it is - because it is the number of characteristic swing actions per minute, not the number of beats per minute, which determines the applicable speed of these dances.
"So tell us, what have you determined should be the defining quality of this "applicable speed"?"
It referes to the characeristic action of the dance: in waltz and foxtrot, the swing over 123 or SQQ (actually, over 3-12 or Q-SQ, but that's another story).
In latin it would probably be the half-basic.
"Of course, these are all silly questions, but that's because they stem from a silly definition of tempo."
It is NOT A DEFINITION OF TEMPO!
It is a definition of SPEED. 35 mpm is too fast to be comfortable in swing foxtrot, and it is too fast to be comfortable in waltz - because it is the same speed of action in both cases.
"Such silliness can be avoided by understanding that tempo is simply a measure of the speed of the music, while rhythm is something a dancer or musician simply superimposes on top."
Right, but missing the point. The speed of the dance is not it's rhythm, it is the number of it's characteristic element occuring per unit time.