Speaking out of the box and therefore probably out of my mind — you could in theory, open a new message and use the microphone on the right side (normally used for speech dictation) to record any sound source such as a short tune from the radio or iTunes and then send it as a sound file. Now the question is whether the system allows or recognises music as it's purpose is to identify speech and translate into digital language.
Well, I tried it out. I can't say that my wife was particularly excited to get a text with a music file containing "Abide with me" at 11pm; but in the interests of scientific enquiry, I can confirm that this does work. So you can send a song via text, but only in the way I described. I don't sense a Nobel prize coming my way, but it works...
Ian
EDIT: one senses an opening for karaoke parties. No, I never said that.