Danthurs has it right, low octane fuel is definitely causing the detonation. Detonation can cause engine-killing damage to pistons, especially when driving "spiritedly."
Operating an engine against the manufacturer'* requirements is not saving you money - it is almost certainly costing you money. Consider the following arithmetic example. Let'* say 89 octane costs $3.10 per gallon and 93 octane costs $3.35. That is 8% more for premium fuel. Your car will not only run a whole lot better on the premium fuel, it will also go more miles per gallon. For premium fuel to pay for itself, your miles per gallon would only need to increase by 8 percent. If you get 23 mpg on 89 octane, you would only need to see that increase to 24.8 to recover the increased price for premium.
Using low octane fuel in an engine that is designed for higher octane will cause detonation. Most of the time, you will not be able to hear the detonation. When you can hear it, it is really severe. But, even light detonation will be detected up by the knock sensors in your engine and "reported" to the PCM. The PCM will respond instantly by retarding the ignition timing to protect the engine from damage. This will result in seriously reduced performance and DECREASED FUEL ECONOMY.
If you drive 15,000 miles per year, at 23 mpg average, you will spend $2,022 for 89 octane fuel. If there were NO mpg benefit for using premium fuel, you would spend $2185 per year for premium, or $163 more per year. This works out to about $3 per fill-up. The engine will last longer, run better, accelerate MUCH more quickly, and generally be a lot more fun to drive and own with the proper fuel. The resale value of the car will be higher if it is running better. And, if you do break a piston, the cost of replacing it will quickly wipe out all the "savings" you thought you were accruing by abusing your car with low octane fuel.
The best fuel economy I have enjoyed in recent years was in a 1991 Corolla 5-speed. If I drove under 65 mph, the little car would give me 40 mpg. Compare that to 30 mpg in a good running L67 Bonneville that weighs 1000 pounds more, provides much more comfort and safety and you see why so many of us love this 3800 engine.