Actually, the inherent signal-to-noise ratio or dynamic range of the CD standard is very high. Consider this admittedly qualitative "thought experiment":
You have a well-recorded CD with a track that is designed to demonstrate the full dynamic range of the format. The track begins with a "minute of silence", then has music that starts out very soft and gets louder and louder until it reaches "peak level". You also have a high-power, low-noise amplifier, and speakers that can play at very high dB level with low distortion; state-of-the-art, "money is no object" gear. Set up in (of course) a quiet listening room.
OK, start to play the track. Turn up the volume control until the background noise in the "minute of silence" is just barely audible. Now keep listening, without touching the volume control again. I bet that in this experiment, most listeners would run out of the room (to protect their ears) before the music reached the peak level.
Or, here is a demo that could actually be done in my home. Take a well-recorded CD with a symphony by a composer (like Bruckner, Mahler, Shostakovich) that contains passages from "whisper soft" to "loud as possible" (using the full resources of a large orchestra of 100 or more acoustic instruments). Now start listening on high quality headphones. Don't even worry about "background noise"; just find the softest passage in the symphony. Turn up the volume until you think that soft passage is at a nice, reasonable, level where you don't have to strain to hear all the notes. Now, keep listening without touching the volume control until you get to the loudest passage
You won't forget the lesson "CDs have inherently wide dynamic range"
However, many actual CDs are nothing like the CD standard. Especially in rock and pop music, the trend has increasingly been to record everything as loud as possible, as close as possible to "peak level", so the music volume is far far above the inherent "background noise level" of the CD, but the music is very compressed and distorted by "clipping" at the peaks. Those not already familiar with this trend might ask "Why would the (pop music) industry deliberately abuse digital recording technology in that way? Are they all crazy, or what!?" I can't answer that, but apparently a lot of people like their CDs loud, compressed, and distorted, because those loud CDs sell well, and the recording industry keeps making them.
http://www.avsforum.com/avs-vb/showthread.php?t=778779