Harsher and softer are hard terms to quantify. Does the small speaker look defective? If you are talking about cutting some of the hi frequencies from the small speaker you can do that electronically.
I suspect that the difference in perceived sound is due to frequency response or possibly an unwanted resonance. You could drive each speaker separately with an audio oscillator over a range of frequencies (and volumes), and either detect harsh sounds by ear, or even better, use a good microphone and a scope (or distortion analyzer). Once you determine what is actually causing the "harsh" sound, you might be able to do something mechanical to the speaker enclosure to reduce resonance, or use a filter (or compensation network) to produce a more pleasing sound.
If you want to try Paul's suggestion, you can download my Daqarta app. It uses your sound card to generate test signals, and to analyze the mic response. You can read about how to use it for frequency response and distortion measurements here (copied from the Daqarta Help system):
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You can probably do everything you need within the
30-session/30-day trial period. After that you won't be able to analyze input signals unless you but the program for $US29, but the signal generator is free to use forever whether you buy or not. You can still use that to listen for resonances or "bad" frequencies, for example.
Best regards,
Bob Masta DAQARTA v4.51 Data AcQuisition And Real-Time Analysis
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Scope, Spectrum, Spectrogram, Sound Level Meter FREE Signal Generator Science with your sound card!
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