Thank you, Starise! I'll definitely look that book up! Thank you, Jeff, for your input, also!

Thinking about tempo and more specifically, our ability to perceive a change in tempo, we can speculate that there is an evolutionary advantage in being able to detect very slight changes in the timing of external events (that is of course, if you believe in evolution).  OK, we may not want to apply the concepts of natural selection when we are talking about the change in tempo of the knock at your front door when the drummer is delivering your pizza but, what about the footsteps of an approaching predator?  I think we can make an argument about the importance of a timely response on your part when you hear an increase in the stride frequency of the approaching Bigfoot (i.e., it is starting to run faster).  Also, I suspect that your chances of survival are even greater if you don’t have to spend a lot of time thinking about certain auditory cues.

At what point can people detect a change in a stimulus such as tempo?  A study at the University of Central Oklahoma by Kim Thomas shows that the threshold of change in tempo necessary for test subjects to detect the change is 8% (6% for one study).  The study used test tones and tempi of 43 and 75 bpm.  There is a fairly comprehensive research article by Guy Madison from 2004 on the topic and if you like statistics and technical jargon like “isochronous sequences” (that is what I am naming my next band) this article is for you.  In addition to his own research, Madison discusses and reviews a number of related articles by other authors.  A bit of an over-simplification of his work but, he shows a 2.0 to 4.5% difference necessary to detect a change which he states is consistent with earlier work from other researchers ranging from 2.5 to 6.0% (I THINK I am interpreting it correctly).  As a side note the technical mumbo jumbo for the point where we can detect a change is called the “just-noticeable difference”.

Also, to help understand how we respond to a slow versus a medium versus a fast tempo we use the Weber-Fechner Law.  The Weber-Fechner Law says, if you consider the point at which people can notice a change in a stimulus, the measured values that correspond to the change are a constant percentage of the reference level.  Or, in other word, and this is my interpretation of the Weber-Fechner Law through a hypothetical thought experiment, if a listener just detects a change in tempo of a song originally at 100 bpm when it is changed by 10 bpm (either to 90 or 110 bpm) then, if the Weber-Fechner Law holds, that listener will just detect a change in tempo of a song initially at 200 bpm if it changed by 20 bpm (either to 180 or 220 bpm ).  In this hypothetical example, the changes from the original tempi are both 10%.  Or, in “other other” words if we are able to detect a 10% change, that 10% will apply to any tempo so, we can just talk about percent.  As far as I can tell, the results in the studies above follow the Weber-Fechner Law.

I am also in the middle of reading Daniel J. Levitin book called “This Is Your Brain On Music” and I too highly recommend it.  In it, he discusses an academic article he co-authored in which he asked research subjects to simply sing they’re favorite rock / pop tune.  His results showed that on average, people could sing a song from memory within 4% of the recorded version.  He speculates on this observation, the ability to accurately recall a tempo, by stating, and I quote “the neural basis for this striking accuracy is probably in the cerebellum”.  For those of you who don’t know the first thing about anatomy (like me), take the time to peruse the Wiki article on the cerebellum (I did).  An important point to take away from his speculation is that the cerebellum has a “direct role in motor control” and motor learning.  The Kim Thomas paper also alludes to the time frame of neural firing (tens of milliseconds) and processing time of the brain but that discussion is over my head (pun intended).

You can certainly make an argument challenging the applicability of these various studies to real world music listening situations but, I think the range of the numbers, from 2 to 8%, suggests that we really can accurately and precisely determine variations in tempo and recall a tempo from memory (excluding drummers of course).  Saying that you feel a major difference between say 120 bpm and 123 bpm (that’s 3%) may be pushing it but in the context of these studies it seems feasible.   As a side note, by accuracy I mean getting the “correct” number and by precision I mean getting the SAME number (not necessarily the correct number) repeatedly.

Is there a relationship between heart rate and a preferred song tempo?  There is not a whole heck of a lot of coherent material out there when you search the correlation of drug use, heart rate and music tempo (gee, I wonder why … sorry Ben) but, there is some solid research investigating the relationship between exercise, heart rate and music tempo.  For example, the work by Costas Karageorghis looks at music preference, specifically the tempo, during what he describes as a long duration workout (on a treadmill) while maintaining a heart rate of 70% of the test subjects maximum heart rate reserve.  He doesn’t give a value for the heart rate in the article so, through a little research and guess work on my part; his test subjects probably maintain a heart rate in the vicinity of 155 bpm.  His study contains songs that he calls “medium tempo” (between 115 and 120 bpm) and songs he calls “fast tempo” (between 140 and 145 bpm).  The bottom line is that his study shows a preference by the participants in his study for music at the medium tempo over songs with a fast tempo or even a mix of songs at medium and fast tempi during exercise while maintaining a specific elevated heart rate.  He also reviews earlier studies by another author that arrive at a different conclusion for a slightly higher heart rate (75% of maximum heart rate reserve) and discusses the possible source of difference in detail.

I don’t think the research answers the question directly in terms of correlating a value for heart rate to a value for tempo but it does suggest that we are in our comfort with tempi around 120 bpm when we are intentionally exerting ourselves and our heart rates are on the range of 150 bpm or so.