How does Nick finally explain the charm of Daisy's voice in The Great Gatsby? In what sense, then, is Daisy connected to "His Father's business, the service of a vast, vulgar and meretricious beauty"?
Nick expresses the notion that the charm of Daisy's voice is derived from the fact that she is incredibly wealthy. Her voice is "full of money," says Jay Gatsby. It is in this moment that Nick realizes that Daisy's attraction and Gatsby's fascination with her have their roots in the fact that she comes from a wealthy background and has married into wealth. Symbolically then, her voice has the ring of "a king's daughter." She is "the golden girl," "high in a white palace."
The implication is that Daisy is no ordinary girl. She is special and far removed from the common and mundane. Money makes her grand and different. It is money which makes her almost unattainable, like the fabled princess who lives in a high tower. She is "golden" because she is precious and she is a "girl" because her attraction lies in the fact that she exudes a vitality commonly found in those who are not burdened by financial constraints, who can exercise almost their every whim.
To Jay Gatsby, then, Daisy becomes the object of his romantic ideal: the fairy princess, and he, her prince charming. Only, Jay has to work hard to attain a position to be worthy of her and it is because of this that he had to go about his "Father's business."
Jay's "adopted" father, Dan Cody, had introduced him to wealth and its power. Dan Cody was in the business of money and for Jay to realize his dream, he has to attain wealth, and this is exactly what he does. In the process, he changes his name from the ordinary and insignificant James Gatz to the pretentious but more memorable Jay Gatsby.
The "service" that Jay has to offer is his commitment to obtain vast wealth, relish the vulgarity of it and become its servant. His relationship with wealth leads to his audacious, over-the-top parties, his friendship with characters from the underworld (Meyer Wolfshiem et al) and fleeting associations with vulgar, pretentious individuals.
Wealth's beauty is "meretricious" - it is deceptive and paints a false image, it is a lie, just as Jay Gatsby's wealth is a lie, for he obtains it through criminal means. However, obtaining this wealth is what Jay Gatsby felt compelled to do to, once again, be with Daisy. He tragically discovers that his dream could never be, for Daisy tells him that he "asks too much."
In the end, James Gatz dies alone, forsaken and abandoned.
Here is the quotation that addresses that question directly:
" 'Her [Daisy's] voice is full of money,' he [Gatsby] said suddenly.
"That was it. I’d never understood before. It was full of money—that was the inexhaustible charm that rose and fell in it, the jingle of it, the cymbals’ song of it...high in a white palace the king’s daughter, the golden girl."
--The Great Gatsby
The charm in Daisy's voice is described by Gatsby as being full of money. Overall, Fitzgerald used The Great Gatsby to criticize his contemporaries, especially those of the east, or New York City, for being overly concerned with money to the extent that they seem to worship money and material wealth more than God.
So when Nick describes Gatsby as a "son of God" going about "His Father's business," (note the capitalization of His Father) he is saying that Gatsby has created himself like Jesus. Gatsby left his real father, a poor farmer, behind and completely erased him from his past, so, like Jesus, he has no father but God. In the Bible, Jesus goes about His Father's business (King James Version -- Luke 2:49: "And he said unto them, How is it that ye sought me? wist ye not that I must be about my Father's business?") But in The Great Gatsby, the god that people worship is money, and going about His Father's business for Gatsby is the pursuit and spending of great wealth.
So when Gatsby says that Daisy's voice is full of money, it means that for him, Daisy is a part of the wealth he is collecting. Perhaps Gatsby found it too easy to amass his fortune, and he revels in the higher challenge of acquiring Daisy. Not because he loves her, as he believes, but because she is a living symbol for him of money.