Is this what you need, meaning specifying not duration but the start and end of time interval of a note?

Sound[{SoundNote["C", {0, 2}, "Trumpet"], SoundNote["G", {1, 3}, "Piano"]}]

That was an example from the docs: SoundNote >> Scope >> Timing

http://reference.wolfram.com/language/ref/SoundNote.html

Experimenting with random specs, here are a few ideas:

inst={"Trumpet","Piano","Organ","Violin","Voice"};
Sound[
    Table[
       SoundNote[3RandomInteger[{-5,5}],
       Sort[RandomInteger[{0,9},2]],
       RandomChoice[inst]],
    15]
    ~Join~
    Table[
       SoundNote[3RandomInteger[{-5,5}],
       {#,#+.5}&@RandomReal[{0,9}],
       RandomChoice[inst]],
    15]
]

Gadzooks, Vitaliy Kaurov, I know I can start and end notes if I know AHEAD OF TIME when then will start and end and put them in a list. Look think of it this way, what if I were simply trying to play one note, and then when the user hits a key, it plays a note over the first note. How do I do that? I don't think I can, because when the second note plays it stops the first, and I didn't know AHEAD OF TIME that the user would push the button, so I can't just put it all in a list from a table.

Similarly and closer to what I'm doing let's say I'm trying to use the digits of pi to specify start and times. I don't know long the song will go on for so I don't know how many digits I will need ahead of time so I want to play the notes AS the digits are computed, not afterward. Look at my second code example, it uses While, so it goes on forever/indefinitely picking random notes.

In your code, you knew ahead of time what notes would be played. I do not. I'm playing an infinite stream of notes. Does that make sense or not?

P.S. George Woodrow, thanks, I look forward to the eventual new functionality.