Perfect pitch is an acknowledged musical skill - the ability to hear a note and name it.
Is there a corresponding skill that applies to tempo, to be able to hear music playing and say precisely what the bpm is?
For people claiming this skill, what level of accuracy is possible?
I know a professional conductor who can pretty much nail it right on.
It's just like perfect pitch, in that it's something you learn to do by being exposed to a ton of music and having reference points ingrained in your memory through sheer repetition. They're not magical skills that you're born with and either have or don't have.
You can probably find 120 pretty accurately, since it's march tempo. Just sing Stars and Stripes Forever or Washington Post. You can probably sing your favorite songs extremely close to their original tempo, so now it's just a matter of looking up what that tempo is to develop another reference point. Then you just keep going.
I've worked with quite a few dance band drummers who hit the correct tempo for particular dances - and believe me, serious dancers can tell if it's not right! It's sort of the opposite of what the OP is asking, but could very easily work the other way round. Basically, it's experience, the more you do it, the more consistently right it gets. Having said that, most people seem to be capable of singing/playing well-known songs at the recorded tempo, so if one knew a song at, say, 100b.p.m., it should be possible to judge another tempo from this reference point. More like relative pitch.
By coincidence, in last week's Boston Symphony program book (for Thursday November 12 through Saturday November 14) it says of Bela Bartok that "He was equipped with an uncannily accurate inner clock and he could tell when music marked to be played at metronome 112 was in fact going at 111 or 113."
I don't know if that is true or not. His piano pieces have a metronome marking at the top and a timing in minutes and seconds at the end and they never match up.
I don't think anybody is a "born natural" at this, but one well-established way to become better at it, already partly mentioned by MattPutnam, is to find a set of reference points.
Matt's example of famous march music as a reference for 120 is a good one because those marches are always played at the same tempo, and to experienced ears sound "wrong" if played faster or slower. That's the catch - if you don't hear famous marches all the time so that you can reproduce them in your mind and nail the tempo, they won't work for you. The trick is finding strongly-rhythmic pieces of music, some fast, some slow, some medium, that are already "burned into your brain", and using them. For example, if you were watching TV in the 1970s and the Hawaii Five-O theme is stuck in your head, then listen to the beat of the bass drum and you have 88. If you don't know Sousa's marches but you know "Thriller" by Michael Jackson, well, that too is at 120. It doesn't matter what kind of music you use - what matters is that you know it really well and it never changes.
Don't use, for example, a national anthem or a children's song, because different people sing those at different tempi and they all sound OK. It needs to be music that "just sounds wrong" if the tempo isn't perfect.
To check the tempo of a song you find, get a free metronome app for your phone, borrow a friend's metronome, or whatever. Many of the phone apps have a "tap" function that will tell you how fast you're tapping the screen.
Here is an interesting combination, and coincidently I started both interests in the same year (age 35 in 1995). I'd played percussion in grade and high school, 17 year break and took up tenor and bass in local bagpipe band. The bass is THE metronome, and works closely with the Pipe Major. Most of our marches were 86 BPM, and I eventually could hold that as the day is long. Now, move to other interest = CLOCKS! And, I can tell if they are in beat perfectly. Best example - guy says I just have to get a machine to put regulator grandfather clocks 'in beat' = there is exactly one second between the 'tick' and the 'tock'. This is harder to do because of the 'long' time of silence between each beat, but I got it within 1% according to the guy's reading metronome. I was bummed that I missed it, be he said the instrument write up said that reading variability could be as much as 3% 'off' and still spot on due to environmental factors, age of the antique clock, etc. So I really didn't need that $500 machine.
Own a clockshop now, and am constantly trying to explain to owners putting their clock 'in beat' when they get it home. I remind them of their early music lessons, and 8'ths are 1 and 2 and 3... and 16'ths are 1 e and ah 2 e and ah.... and just fit it into their clock's beats to make sure are exact. Have discovered that some people have the beat equivalent of a 'Tin Ear' = hugely and painfully off from true, and they don't hear any difference.
The answer to your question depends on your definition of "perfect".
I believe the only way to even achieve perfect tempo, much less possess the ability to listen to a piece of music and accurately determine the exact tempo, is with a computerized click track or quantized drum track. Even a metronome might be off a millisecond from perfect due to it's mechanical limitations.
Having said that, I am sure some folks have a unique ability to get pretty close by listening to the music. But even recorded music is not always in a "perfect" tempo.
To illustrate my point - as a songwriter I often use software and hardware to create demos of my original compositions. I know that if I use a live drummer, no matter how good he is and even if he is playing to a click track, the drum track will sound more realistic and organic than if I use a quantized drum sample that plays in perfect time. Somehow the listener is able to perceive perfect tempo in a drum track (but won't be able to tell exactly what the bbm is) and it sounds artificial compared to the imperfect timing of the best real drummer.
In real life, since music is often played slightly out of perfect tempo (unless a click track or metronome is employed) or at an imperfect tempo at best, I don't know how valuable it would be for someone to be able to say "Stop the music - we are supposed to be playing this song at 160 bbm and you people are playing at 161 bbm - we need to slow it down a bit"! Just sayin .....
If perfect means within a few bbm, then yes there are a few folks who can get pretty close.
