Hello Alex,
Sorry for the delay in getting back to you.
Most commercial meters will have a time-constant switch that makes them average over a longer period of time, but they generally only go up to a few seconds at the most.
Measuring the peak loudness in a whole song is easy enough - just keep an eye on the meter and note the highest level. (Digital meters will often do it for you.)
Measuring the average loudness is going to be more complicated.
One way to do it doesn't take any special equipment or require a computer. But, it takes some time. Basically, you randomly sample the song at several different points.
You could generate around 10 random numbers (for example, using this web site
http://www.random.org/nform.html ) between 0 and the length of the song in seconds. Then play the song while looking at the time on your CD player and at the meter. When it gets to each of the random times you've listed, look at the meter and write down the value. (For reasons we can discuss if you like, using really random numbers rather than just picking numbers in your head is a good idea. Humans are notoriously bad at making up numbers that are truly random.)
From that, you can estimate the average loudness in the song, and you can also figure out the uncertainty on that average value.
One caveat - if you do this, remember that a dB is a logarithmic unit. You'll need to convert back to linear units before doing any math with them and then convert to dB again afterward. (For example, the mean value of two points, one at 100 dB and one at 90 dB is actually 97.4 dB, not 95 dB!) If it's not clear what that means, let me know.
The mean of the linear values will give you an average loudness. A measure of the uncertainty on that value (often called the "error on the mean") will be given by the standard deviation of your measured points divided by the square root of the number of points. You can find formula and explanations for the "mean" and "standard deviation" in most high school statistics textbooks and online. If you have trouble finding it, let me know.
A good way to report the numbers might be to do all your math in linear units and then convert both (mean + uncertainty) and (mean - uncertainty) to dB. You can then report the value as something like "85-88 dB," which tells your reader how accurate the measurement is.
If you want a better measurement, take even more random points.
A second method is to record it onto a computer through a microphone and then use audio software to calculate average values.
For example, the free program audacity (
http://audacity.sourceforge.net/ ) will allow you to make a power spectrum of the song. That gives you the amount of power (relative to some arbitrary zero value) as a function of frequency.
How to turn something like that into a single metric for measuring "loudness" will depend on how much time you want to spend on it.
The simplest method is to pick a moderate human-speech frequency (somewhere in the 400Hz-1KHz range) and calibrate your computer only at that one frequency. Then assume that the response is flat over all the frequencies you care about. That will let you plot your power spectra in absolute units.
In reality, the response of both the meter and your computer microphone aren't exactly the same at all frequencies. Most meters have settings for "A-weighting," "C-weighting" and similar things. A-weighting artificially decreases the meter's response to very low and very high frequencies in an attempt to simulate the response of human ears. I think C-weighting is supposed to be constant over the meter's range. Try switching between them during the music and see how much difference it makes. If the change is small, then calibrating at a single frequency is probably fine. Most eletret condenser computer mics are pretty uniform over the range you care about.
Once you have a power spectrum in absolute units, you can do a couple of different things:
1 - Just display the power spectra themselves and don't try to come up with a single "loudness" number.
2 - Estimate the average loudness by eye. (Maybe let a couple different people try it to get a sense for how accurate this is.)
3 - Export the power spectrum as a text file and use something like a spreadsheet program to calculate an average. This is more accurate than #2, but takes more work.
For reasons we can discuss if you decide you want to do something like this, the right way to add the numbers in a power spectrum to get a total value is start out with linear values (rather than dB), square every number, add them together, and then take the square root of the result. Then use the formula for a logarithm to turn that into a number of dB.
If you decide you want to do that sort of thing and that very brief intro doesn't give you enough to get started, let me know. I'd be happy to fill in some details.
Good luck,
Erik
