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It depends on various factors, which format are your song files? what bit rate is the file? how long are your songs?
Apple considers audio quality from 128kb/s AAC format sufficient and that songs will be about 3.5 minutes long. With these assumptions it should hold 4,000 songs. If you use MP3 format these files are larger than AAC and fewer songs will fit. If 128 kb/s doesn't sound good enough and you choose a higher bit rate to improve audio quality that too will mean fewer songs will fit. If your songs average longer than 3.5 minutes that too will mean fewer songs. Naturally if you install applications, load your iphone up with pictures and video these too will reduce the number of songs that will fit. The 16 GB must be shared by the operating system, applications, application data, images, and videos as well as songs.
However the iPhone 16 gig has roughly 14.2 gig free when you take it out of the box. It's going to depend on how many apps, photos, videos, contacts, etc you also have saved on the phone. My iPhone 4 16 gig has almost 2000 songs on it and lots of everything else. I think I have around 2 gig free yet
16 GB = 4000 songs
