I'd say that music and language overlap. They share some common properties such as rhythm, tone, inflection, pitch, volume, etc, and each has some unique qualities as well. Language is primarily a means of communicating explicit information. If say the eagle flies at midnight, it may mean that a raptor will take flight one minute after 11:59 PM, or it may mean something else by some agreed upon code, but it typically conveys a specific idea.

Music on the other hand is a direct experience of sound waves. Our ears pick up compression waves in a medium, typically air, and our brains produce neurological sensations that are direct analog signals of the compression waves. The human brain is capable of discerning and appreciating a wide variety of sounds with a great deal of subtlety, varying from one individual to another. Music is the art of creating combinations of sounds that are pleasing or at least interesting. (For example I don't find Penderecki's "Threnody to the Victims of Hiroshima" to be especially pleasing, at least not in the same way as Bach's Air from the Orchestral Suite No. 3 In D Major, but it is interesting.)

A writer can draw on musical qualities when composing. For example the sentence "It's got a lot of glottal stops" has a staccato quality. (And if you say it with a Cockney accent, it's got a lot of glottal stops.) Naturally when writers are creating lyrics to go with music they seek to exploit the musical qualities of language. For example Chuck Berry's lyrics often manage to be both conversational and yet rhythmically pleasing ("Well early in the morning I'm a-giving you the warning: don't you step on my blue suede shoes"). Rhyming is another example of a musical quality to language. The appreciation of rhyming does not depend on the meaning of the words, although the meaning may add to the impact of the sentence.

But a writer can also distinguish his work with techniques probably beyond that of the musician, punning being one example. The apprehension of the humor of a pun is an interpretive act by the brain. I may enjoy a Brazilian singer's performance despite no knowledge of Portuguese, but I may miss out on the deeper wit of the lyrics.

The guitarist/singer/songwriter Mark Knopfler (formerly of Dire Straits) has a voice on the guitar that I find very expressive. Often, his long solos seem to borrow from the inflections of storytelling, with a gradual buildup of tension and pace leading to a climax and then a denoument. (cf "Tunnel of Love" from the Dire Straits recording Making Movies.)