Why 96 beats per minute, and not 95? Why 124 or 132, and not 125 or 130?

What is it about those exact tempo markings that makes them used by so many composers out there? Is there a justification somewhere I can look up? Maybe a theory book?

Not sure if there are any texts out there about this specific subject, but there have many studies in number theory out there on the subject of number theory and why we choose some of the numbers we do for things.

Some are based around factors of 10 (largely because of the number of fingers or toes we have), while some are based around the idea of being divisible by two (humans are bipedal, have two of most things, anatomically), etc. The word digit actually has its root in the Latin word for finger.

I'd be willing to bet that exact numeric choices of tempo could possibly be traced back to the latter of the two.  I don't think you'll find an answer in a textbook, but doing some research in number theory might produce some interesting results. 

When I was a lad taking piano lessons (and still buying records...), I remember using a mechanical metronome like this:

  [img]http://www.musix.com.au/images/metronome.jpg[/img].

These metronomes didn't give you every increment of BPM. You can kind of see this in the photo, but depending on the tempo range, the notches for adjusting the weight on the pendulum might be spaced at increments of 2 BPM (at slower speeds) to 8 BPM (for faster speeds). For me, I know those stock tempos on my old wind-up metronome still stick in my head. So using those can be a force of habit for some.

All the more fun to rebel when writing a cadence at 121 bpm these days! :)

Because I enjoy challenges and finding obscure knowledge I started doing a little research. It turns out that the conventional tempo markings date all the way back to the original portable metronome invented by Johann Nepomuk Maelzel in 1816 (he actually stole the idea from another inventor Dietrich Nikolaus Winkel). Beethoven was the first major composer to indicated metronome markings in his scores and the marking[i] M.M. = 120[/i] actual refers to ";Maelzel's Metronome"; not the contemporary interpretation of ";Metronome Marking";. Maelzel's original metronome had the rates of 50, 52, 54, 56, 58, 60, 63, 66, 69, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 126, 132, 138, 144, 152 and 160 and later was expanded to include 40, 42, 44, 46, 48, 168, 176, 184, 192, 200 and 208. This was written about Maezel's metronome markings:

[i]In order to determine a scale of musical beats per minute, it was necessary to establish how many degrees of speed are needed to accurately indicate the beats of all possible musical tempi, from the fastest prestissimo to the slowest lento.

After having examined the works of all the classical composers, Ma��lzel is convinced that in the slowest lento, there are more than 50 eighth notes per minute, and in the fastest prestissimo, there are less than 160 eighth notes per minute. Consequently, the numbers 50 and 160 were adopted as the two extremes of tempo. The intermediate numbers will be found to be sufficient to indicate all the other degrees of speed of each tempo.

The author has found that the number 80 can be considered as the medium term; adagio with MM eighth note = 80, andante with MM quarter note = 80, allegro with MM half note = 80, and presto with MM whole note = 80.

One will notice that, on the metronome, the number 50 is followed by 52, and 60 is followed by 63, and so on. The author, from experience, knowledge in mathematics, and especially by the certain and invariable laws of measurement, has demonstrated that it would be pointless and an unnecessary complication to include the intermediate numbers. The difference in effect from one number to the next, for example 50 to 51, 60 to 61, and even to 62, is not noticeable.

What difference would it make to perform a piece marked as MM eighth note = 50, at MM eighth note = 52 instead; only a quarter note in the time of a minute; an imperceptible difference even to the most trained ear, and certainly, a duration for which one would not be able to add or remove from the merit of the musical material performed during a minute.

It is for this reason that the numbers from 50 to 60 proceed in steps of 2, those from 60 to 72, in steps of 3, those of 72 to 120, in steps of 4, those of 120 to 144, in steps of 6, and those from 144 to 160, in steps of 8. By the way, the numbers 100 to 160 are just double those from 50 to 80, and they indicate a tempo exactly twice as fast as the latter. So, if the quarter notes indicate a given tempo with 50, 58, 66, etc., one could mark the eighth notes of the same tempo with the numbers 100, 116, 132, etc.[/i]

It is believed that he chose M.M. = 80 as his reference tempo from Johann Joachim Quantz who said the human pulse is 80 beats per minute. So the markings that we use today are founded in long held traditions and are still found on the Maezel style metronomes that are sold today.

[i]";A metronomical performance is certainly tiresome and nonsensical; time and rhythm must be adapted to and identified with the melody, the harmony, the accent and the poetry��_";[/i] - Lizst


Sources:
http://en.wikipedia.org/wiki/Metronome
http://www.greschak.com/polytempo/ptts.htm

You made that whole thing up, didn't you?

Man, that's more information than I was expecting but answers the question completely. Thanks!

Slightly off-topic, but I have this theory that the untrained person cannot hear deviations in tempo within 5 beats (at a relatively moderate tempo). In other words, if the group slows down by five beats, it drives the band director nuts but the students and their parents may or may not notice.

Chew on that.

I have an old metronome like Jim had, but it only has words on it: adagio, largo, etc.  It's starting to ";swing"; the beats now though.

I'm pretty boring when it comes to tempo selection.  I have used maybe 4 or 5 different ones over the last 10 years.  I think some work really well for drumming and/or marching and some don't.  In commercial music I usually use tempos that make it easy to write 10, 15, 30, or 60 seconds of music.