Great question. I've often wondered how a Ford and a Chevy engine of similar size and configuration can sound different. Obviously mufflers and headers can make a difference but excluding the impact of those, the actual engine configuration apparently makes a difference.

Googling I found this:

Basically, it's firing order that gives it the cadence.

1) Essentially no common automotive engines have two cylinders firing at exactly the same time.

2) A four cylinder engine has a 1342 firing order with one cylinder firing every 180 degrees of crankshaft rotation. A four cylinder engine would be perfectly balanced only if it had infinitely long connecting rods. Only in that case would the velocity of a piston as a function of time be described by a pure monochromatic (single frequency) sine wave. Only in that case would the forces generated by the acceleration of the pistons near the bottom of their stroke exactly balance the forces of the pistons near the top of their stroke. With finite length connecting rods the piston velocity contains harmonics (multiples) of the fundamental frequency of the sine wave describing the motion of a piston. Engineers would call these Fourier components. Others often refer to these as secondary vibrations. Unlike the fundamental, some of these do not balance out, so there is some residual vibration.

3) A straight six has a 153624 firing order with one cylinder firing every 120 degrees of crankshaft rotation. A straight six is perfectly balanced.

4) A V8 can have various firing orders. But, there is still just one cylinder firing every 90 degrees of crankshaft rotation. A V8 is two four cylinder engines arranged at 90 degrees to each other, sharing the same crankshaft. In that sense a V8 shares the imperfect balance of a four in the plane of each bank. In addition, there is a certain component of fore-and-aft rocking vibration which arises from the fact that though each connecting rod shares a crank journal with the corresponding rod on the opposite bank, they of course are offset on that journal by their thickness. The off-beat of the V8 exhaust note arises from the fact that, no matter what the firing order is, the firing on a given bank is not even. Since in almost every case the exhaust is fed into one exhaust manifold for each side, and then into one pipe for each side, there is an off-beat. If you combine the exhaust from the outer cylinders on one side with that from the inner cylinders on the other side, you get a nice even sound. Think of the
bundle-of-snakes exhaust on an F1 car or an old GT-40. They gave a nice ripping canvas sound. Alternatively, think of the nice honking sound a big four barrel carb on a V8 makes when you floor it. The intake manifold on a V8 connects the intake ports in a manner identical to the way a bundle-of-snakes exhaust system connects the exhaust ports.

5) A V12 is commonly arranged like two straight sixes with 60 degrees between them. One cylinder fires every 60 degrees of crankshaft rotation. Think of it as evenly splitting the 120 degree firing interval of each bank taken separately.

6) I'm not familiar with V6s. I assume that a 60 degree V6 should fire every 120 degrees and sound like a Corvair. The few 90 degree V6s made by casting 3/4 of a V8 are pretty raggedy

Cars with carburetors (vs EFI) can add variation to the pressure waves produced by introducing air&fuel unevenly. They can also change the evenness by firing the spark plug on the exhaust stroke (wasted spark).

I was surprised that I couldn't find a website that offers "sheet music" or waveforms of different engines. I did find several articles on how Harley Davidson motorcycle are designed to produce its distinctive sound.

I also found new sounds for the empeg. http://www.autospeak.com/library.htm