I'm going to take a shot at interpreting this poem. This is my interpretation, so if it doesn't bode well with you, well, whatever.
We are presented with a mind whose reality is filled with disharmonious noise, clatter. He see's evidence of this clatter in lines 3-6, evidence of disharmony.
Somewhere, out of the noise, out of the clatter, there is a realization of a non-clatter, a quiet. He realizes that this quiet has always been an option, he just hadn't heard it because that is its nature. Now that he realizes that the quiet is there, he can hear it in the breaks between clatter.
It's in lines 9 and 10 that he realizes that silence exists, lines 11 and 12 is him actually listening for the quiet in the noise. I'm thinking here that the Whistling is what signifies that there are only short bursts of silence.
Practicing now in his daily life he finds his mind tends to be filled with clatter in the mornings. as his curiosity in the elusive silence grows so does his focus in listening to the quiet which drives out the clatter.
Finally, in line 17, she hold out her hand, presenting to him the choice: Clatter or Quiet ?
Will he allow himself to be assaulted by noise or will he transcend to this quiet place?
The last line is his answer.
Nice! That's not quite it, but it's close. Clatter is used to represent the noise of the busy world, all the things in life that keep you busy, distracted and not focused. The quiet represents the focus in life, the clarity apart from the distractions. The whistling is the calling to that clarity that you, so often ignore in life.
Choosing to take that stand and focus on the clarity and "silence" when being called is a tough decision because it may mean you have to change what you're presently doing, amidst the noise and "clatter".
Finally, the question is... does all that clatter really even have any meaning - your destiny is the calling - the quiet, the focus.