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I've been listening to music for a long time using the cheapest headphones of any type, on all devices until ~2010 when I noticed that on PC the music has more of a stereo feel to it than on tiny mp3 players. Then I bought a pair of ~80 usd headphones (don't remember the brand but the point was it wasn't the cheapest, and it was entry level price) and it sounded a lot better, and I could distinguish new detail which I previously wasn't aware existed in my favorite tracks. If connected to phones or mp3 players though, it also brought out a little bit more detail, but not as much.

Then I bought the cheapest internal Sound Blaster PCI-Express audio card I could find and then I found out there was even more to hear in my favorite tracks. The low frequencies became notably more powerful, but not in the way that blocks out the high frequencies and drowns out all detail, as you'd get if you play around with equalizer software on builtin Realtek AC/HD codecs. Compared to any portable device with a 3.5 jack this is night and day. But why is that exactly?

What electrical characteristics allow the discrete audio card bring out more detail and significantly improve low frequency sounds without losing all detail of higher frequency sounds? What does the cheapest PC audio card have that portable music players and even high end phones don't?

For comparison, Realtek ALC 892, HD and AC'97 all produce inferior sound in my opinion to all of the dedicated audio cards I've listened to.

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Well, apparently there can be a lot of factors: a better signal definition (how small are the bits that count; good chips allow for a true 20bit sound, while a lo-end will struggle hard to achieve even a 15bit resolution — and is likely to fail at that;) how wide is the actual passband of DAC filters; linear and non-linear distortions introduced, the stability and precision of the clock—the geometry (and isolation) of the analog schematics and materials used; the quality of all the physical contacts, esp. in the plug, as small contact surfaces introduce extra resistance and create sparkles, and thus generate noise and lower the amount of content (same probably goes for the wire lengths.) Even the AC current itself creates humming noise, so how good is your main unit power plug's phase portrait filtered on the way to your phones matters too.

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