I'll tell you guys what I've discerned on this subject, but don't take it as gospel, because I'm still learning, and I might be wrong about some of this. But, from what I've read on the subject:
The harmonic relates to how many times the pressure tuning wave travels back and forth along the intake tract. The theory goes something like this: the air/fuel mix has mass, and therefore momentum as it moves down the intake tract towards the valve. At the end of the intake stroke, as the valve is closing and the piston is starting to come up the bore, the momentum of the air/fuel column is still trying to fill the cylinder. When the valve slams shut, the air/fuel mix is still coming and builds up pressure against the valve. Since the valve is shut, this pressure wave can't go anywhere and so is reflected back up the intake tract until it reaches the plenum, then it reflects there and goes back down to the valve. The pressure wave travels at the speed of sound in the intake tract, which is generally considered to be somewhere around 1250 feet per second, if I recall correctly.
Once the pressure wave makes it back to the valve it has completed the first harmonic. The same process repeats itself again and again. By the time it arrives back at the valve the third time (third harmonic), the intake valve is open again and the pressure wave helps to ram the air/fuel mixture into the cylinder. So, the pressure wave travels at a specific speed, and at a given RPM if you change the length of the intake tract, you change the time when the third harmonic pressure wave arrives back at the open intake valve.
There is an ideal time for this pressure wave to arrive, and it seems to be the subject of some disagreement, at least among the papers and books I read on the subject. There are several different formulas out there for calculating the ideal length of the intake tract, but the inputs for all of them are the engine speed in RPM, and which harmonic you are aiming for. Some of the better ones also include intake duration as an input, in an attempt to take into account when the intake valve closes (which starts the whole harmonic process), and the rest seem to just use some typical value.
Tuning for the third harmonic is supposed to give the best results, with maximum torque available over an RPM range of 1000 or so. Sheet metal intakes are typically designed to tune to the third harmonic. Single plane intakes typically average tuning at the fourth harmonic; I say average because some of the runners are longer than others, so they may tune at different engine speeds. The fourth harmonic is not as good for torque as the third, but from what I've read the torque range is a little broader, maybe 1400 RPM or so. The old early 1960s Chrysler crossrams tuned at the second harmonic, which gives even more torque than the third, but is much more difficult to package.
The fourth harmonic intake design in my post above is designed to tune at the same RPM as the original third harmonic design. But it will also tune at the third harmonic, just at a higher engine speed. So, this manifold will tune at the fourth harmonic around 7000 RPM, and at the third harmonic at around 8900 RPM. In between those RPM levels, say at 8000 RPM, the pressure wave will have a detrimental effect on power production. So, if you time the pressure wave wrong, you will lose horsepower, not gain it. This is why all the hardcore racers pay attention to runner length, and try to optimize it for whatever RPM range they are running at the track.
I hope that explanation helps. To me, a little empirical testing on the dyno, once I have a couple of these things put together, will go a long way towards really dialing in the runner lengths. Formulas are fine, but some real horsepower numbers will take a lot of the unknowns out of this process.
