Bandsaw blades require tension and lots of it to consistently produce straight, uniform cuts, especially in thick or dense stock. Most blade manufacturers recommend 15,000 psi to 20,000 psi for a common carbon-steel blade.
However, bimetal, spring-steel, and carbide-tipped blades are much stronger than carbon-steel blades, so manufacturers recommend a much higher tension: 25,000 psi to 30,000 psi. Why do bandsaw blades need so much tension? For beam strength. The tighter the blade is stretched, the more rigid it becomes and the less tendency it will have to deflect in the cut.
You only need maximum tension for the most demanding cuts, such as sawing dense hardwoods or stock of the maximum thickness that will fit under a saw's guides. In simpler circumstances, you can back off the tension a little.
All blades, regardless of width, require the same amount of tension for maximum beam strength. The variable factor is the amount of pulling force needed. For example, it takes approximately 200 lb. of force pulling on a 1/4-in.-wide by 0.025-in.-thick blade to create 25,000 psi of tension. Conversely, a 3/4-in.-wide by 0.032-in.-thick blade will require approximately 800 lb. of force to create the same 25,000 psi of tension.