The problem only arises because beats per minute and bars per minute have the same abbreviation.
That's not the only problem. In fact, that's not even the biggest problem with bars per minute.
The real problem with bars/measures per minute, as I mentioned before, is its tendency to mislead. Far more important to musicians than being more accurate, beats per minute is more truthful.
I already used the Waltz/Foxtrot example, so here's another one: Tango, Samba and Paso Doble can be written in 2/4 or 4/4. Let's say a Samba has a tempo of 100 beats per minute. If it's written in 2/4, its tempo in measures per minute is 50, but if it's written in 4/4, its tempo in MPM is 25. Most dancers would be fooled into thinking that a Samba in 2/4 played at 50 MPM is twice as fast as a Samba in 4/4 played at 25 MPM. Because of their lack of understanding of time signatures, they don't realize the two songs are exactly the same speed.
Tempo measured in beats is always the same, no matter what the time signature. 2/4, 4/4, 6/8... It doesn't matter. 100 bpm is always 100 bpm, period. On the other hand, tempo measured in bars per minute changes depending on the time signature. One music label lists their Viennese Waltzes as 60 mpm, while another lists theirs as 30. Add to that the fact that most dancers have no concept of time signature, and it's a recipe for confusion.
If you disagree, try this fun little exercise: Ask 10 dancer friends to answer the following questions, and see how many of them answer correctly.
(1) Which is faster, a Foxtrot played at 30 bars/minute, or a Waltz played at 40 bars/minute?
(2) Tango "A" is written in 2/4 at 60 bars/minute. Tango "B" is written in 4/4 at 30 bars/minute. Tango "C" (A Vals-Tango) is written in 3/4 at 40 bars/minute. Which Tango is the fastest? Which is the slowest?
(3) A Slow Waltz and a Viennese Waltz both have a tempo of 30 bars/minute. Is the Viennese Waltz the same speed, twice as fast, or half as fast as the Slow Waltz? (*Bonus question: Why?)
My guess is that 9 out of 10 dancers would flunk this quiz. On the other hand, if you were to present the same exact questions using beats per minute instead, 10 out of 10 would answer correctly. What does this tell you about the problems inherent in using bars as a measuring tool for tempo?
Regards,
Jonathan