Your manual probably reads that you should use "premium", or some certain AKI (antiknock index, what we used to call octane rating) number, for optimum performance. That means no reduction in fuel economy or power output.
It also probably reads that you can use some mid-grade fuel, or (again) some certain lower AKI, as a minimum. However, you will find less than optimum performance. The reason is that the engine will occasional ping in certain conditions (load, acceleration, temperature, etc.) that will make the computer reduce the spark advance and change the fuel mixture.
This will lower your fuel economy, at the very least (it also lowers power output, and is not good for your combustion sensors, etc.) So think about this: if you save 10 cents per gallon, that's about (at today's prices) 2.5% of the cost of your fuel ($0.10/$4.00) -- you will certainly experience more than that reduction in fuel mileage, so you're actually losing money from that decision.
And absolutely No, you cannot change the timing on your car. Sure, when distributors could be manually "rotated" to change the ignition timing, that could be used to prevent ping (but it retards the spark and reduces economy and power). However, in our newer cars, the timing is controlled by a computer based on the position of the crankshaft (i.e., flywheel), and rotation of the distributor (if even possible) has no effect.
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