Martin, I'm not really certain about those $30 players(suspect they're okay)but the typical $100 players all have 8X oversampling(and have had for years)which allows relatively gentle filtering to remove the response beginning above 20KHz and reducing it to below audibility by 22.05KHz, so there's no harshness as a format. Of course individual recordings can be lousy, but that has nothing to do with the digital process itself.

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Enjoy the music, not the equipment.