To further complicate matters, there is also the engine's powerband. The engine makes more torque at some points than others, so a gear ratio that keeps you in the "torquey" area longer will have feel than a gear ratio that keeps you in an area where there is not as much torque. Think of it like running the revs too high before shifting. As you go past the torque peak, you feel like you are losing torque. The same goes for operating too far below the torque peak (although you will get a better feel here, since you get an increase in accelleration, not a decrease).
That's the idea between more and closer gears: to use the rear ratio and transmission ratio, combined with tire size, to keep the engine operating in it's powerband. The more the revs have to drop with each shift, the longer it takes you to come back up to the powerband.
For example, you have a 2.64:1 first gear, a 1.75:1 second gear, a 1.34:1 third gear, and a 1:1 fourth gear (all eventually multiplied by the rear end ratio, of course). That means your revs need to drop 33% when you shift 1-2, 23% when you shift 2-3, and 25% when you shift 3-4.
If you had a '63 Sting Ray with the base 3-speed manual, you'd have 2.47:1, 1.53:1, and 1:1. That would mean a 38% drop on the 1-2 shift, and a 35% drop on the 2-3 shift. The smaller of those two is still larger than the largest of your splits. And that transmission doesn't have as aggressive of a first gear, so it won't give the same multiplication.
The 4-speed allows a smaller split between ratios, and a larger overall spread of ratios. A 5-speed or 6-speed allows even greater variety.
And that's just the fun with manual transmissions. Automatics have the addition torque multiplication factor of the torque converter to worry about (my owner's manual, for example, lists a range of ratios for each gear, to try and give the driver an idea of what the car will behave like).
Joe