I'm trying to figure out how long I should rest between exercising a particular muscle group.
Have any studies been done that correlate the muscle-mass gain with the number of days between sets?
I've heard 72 hours, but I don't know where that number comes from.
What you're actually asking about is "recovery". The term "rest time" usually applies to the time between sets within a workout. For example, if you'd do several sets of squats, you might rest anywhere between 2 to 5 minutes or even more depending on the intensity between those sets.
Mark Rippetoe likes to underline in his works (Starting Strength, Practical Programming for Strength Training) that strength and muscle are not built by lifting weights, but by recovering from lifting weights. The weight lifting constitutes a stress to the body which forces an adaptation. Initially, after the stress is applied, there's a period of reduced performance, during which your body is recovering. At that point performance is below the original baseline. As recovery completes, supercompensation occurs: in order to guard itself against a repetition of the stress the body adapts, increasing strength through muscle hypertrophy and other mechanisms. Performance now rises above the original baseline. If the stress is not repeated, detraining starts to occur and a return to the original baseline begins. Here is a diagram showing this effect.
So what must happen is that the new training stimulus is provided within the window of supercompensation, when heavier weight can be used, this constitutes a new stress that the body is not adjusted to, and the cycle repeates with a higher baseline.
If the stress is repeated too soon, when recovery hasn't completed, overtraining occurs. Trying to lift heavier weight when you're still in the reduced performance zone will work against you, since you're likely to miss reps and are actually shoving the baseline lower. Wait too long, and you're not getting the benefits of the supercompensation window. If a beginner would only train each muscle group once a week, progress would likely be very slow or absent. There's plenty of people who do the exact same thing for years in the gym with little to show for it, since they're missing the crucial aspect of increasing the baseline.
The answer to your question, then, is what the time frame between the stress and the maximum of supercompensation is, which would be the optimal time to repeat training. That is going to be dependent on a lot of factors. First of all, the level of training. A beginner will usually fully recover and adapt within 48 to 72 hours, since the weights used are still low in an absolute sense, and so far from their physical limit in terms of strength in a relative sense. This is why a simple linear progression (weight increase each workout) and about 3 full-body workouts are concepts you'll see in many of the most popular beginner workout programs. For an intermediate trainee, where linear progression is no longer sustainable, things become more complicated. A single workout probably can't induce sufficient stress for enough adaptation to occur, so it's no longer just a matter of choosing the right recovery time. Stress from workouts needs to be accumulated in a way that uses multiple parameters, such as the intensity of an exercise (number of repetitions and percentage of max weight used), the number of sets, the way these cycle and more. Recovery will no longer be just a matter of how much time there is between workouts, but also what the workouts consist of. The Texas Method, for example, utilizes a scheme where one day is a volume day, a second day is a light day that doesn't inhibit recovery and adds no new stress but keeps neuromuscular efficiency up, and finally an intensity day which, driven by the recovery from the volume day, allows for setting new personal records and driving the baseline up.
Apart from those things, other factors will influence recovery such as adequate sleep, nutrition, the normal daily level of activity, personal life and stress... So in the end it's hard to say "this time frame of rest is optimal" because it will be a very individual matter. It is constantly going to vary depending on your level of training, program adherence, life factors and training history. I'm hesitant to go for actual studies, because they're frequently flawed in this respect. A lot of them work with untrained individuals or groups that are too coherent, who are going to respond very differently than you or I might, or someone with an athletic history.
For the true novice, however, the vast majority are going to be capable of recovering and being ready for a new training stimulus within 48 to 72 hours. So that is why you'll see beginner programs often consisting of 3 full-body workouts per week. The edge between overtraining and suboptimal volume hasn't become as sharp yet for these trainees, so things can be quite simple. Once you're past that phase, you should dig into some literature regarding programming (the aforementioned Practical Programming for Strength Training by Rippetoe & Baker is a good read) and have developed the sense to figure out whether you're doing too much or not enough. There's going to be recommendations that tend to work well for the largest portion of trainees, but there is, and can be, no single recommendation that is going to be optimal for everyone, in every situation.
