I'd like to know the differences between the words "sadness" ans "suggestiveness" in the following excerpt from the Chapter 8 of The Great Gatsby and how these new tunes could "sum up" all that; in others words, are "sadness" and "suggestiveness" used with negative connotations (sad choices implied - suggested - by her luxury life) or could "suggestiveness" refer also to "promises", "hopes"?
"For Daisy was young and her artificial world was redolent of orchids and pleasant, cheerful snobbery and orchestras which set the rhythm of the year, summing up the sadness and suggestiveness of life in new tunes."
These terms are used with some degree of irony in this passage, though they speak to Daisy's situation.
First, sadness and suggestiveness are not used as synonyms here. (These terms would be difficult to align as synonyms in any circumstance.) Rather, they convey two contrasting ideas that together create a sort of lyrical idea.
"Suggestiveness" here relates to the idea of promise, as you interpret it correctly. Suggestiveness refers to that which remains "unstated" yet which is indicated, hinted, promised, suggested, intimated, etc. Life is suggestive, as it were, because life is largely unknown, especially for Daisy who has experienced only a small slice of life in a small part of the world.
A translator might reasonably choose to replace the term suggestiveness in this passage with "poetry".
With this said, we can see the irony that comes from the contrasting ideas presented that describe Daisy's life at the time. In an "artificial" atmosphere of "cheerful snobbery", musicians conjure ideas of the other side of life; feelings and experiences that are not present in this world. In the midst of formalized and gaudy material happiness, Daisy encounters an idea of ethereal and disembodied sadness and beauty.
These abstractions are like dreams to Daisy, attractive but unreal. As a character, we can generalize these dreams and her relation to them and say that Daisy is always, figuratively, standing in the middle of an opulent party and wondering what it would be like to be elsewhere, with other people - another person. What if life were different?
This attraction to the dream of "what if" is with Daisy from the day of her wedding when she sobs drunkenly in her room before fixing herself up to walk down the aisle. It is with her when she visits Gatsby's house and cries over his "beautiful shirts".
Suggestiveness and sadness describe Daisy's daydreams. We should also consider the facts of Daisy's life, which remain unchanged despite these desires. For Daisy, the "what if" that is somehow conveyed in the music at the party is never attained. It remains abstract, like the music, expressing but not "realizing" a different way of life.
Daisy remains in the trappings of wealth and remains, like Gatsby, the dreamer with dreams unfulfilled. We might ask if her dreams were as real as his, but clearly we see that each of them held to a fantasy that would not leave them.