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db is not a measurement, but a multiple ie- the difference in 90 and 93 db may be subtle. The difference in 130 and 133 db, not so much.
Why do we believe 3 db is barely noticeable? It's simply not true at high volume where we expect to hear a difference.
On the other hand if you're trying hard to discern differences in volume or tone between two similar sounds, you can often detect a mere 0.5 dB of difference.

Also, I was totally under the impression that the human ear could only discern changes of 3 or more decibels. Where did you hear otherwise?
That would be from Bell Labs, who invented the decibel scale in 1928. After testing a thousand or so people the minimum average change audible to them was classified as 1 decibel (a previous standard was called the MSC). It took place at a specified frequency and intensity, so it doesn't hold true for all frequencies and intensities.Also, I was totally under the impression that the human ear could only discern changes of 3 or more decibels. Where did you hear otherwise?