Use of FFT in a window / Alternatives.

Hello all,
I am half way through writing an audio transcription tool that is supposed to read polyphonic music and obtain the frequency/length of each note in say a simple piano melody.
I have written a basic FFT function that finds the frequency of a single note by finding the max peak.
FFT windowing would allow me to do this over a longer recording (so i'm told). But i was wondering if it sounds feasable to analyse a recording in the time domain to obtain the notes, then passing them one at a time through the function I wrote earlier. I can provide code if necessary but im away from my desk at the moment.
Its more of an opinion im after than solid code, does this sound like a reasonable approach?
Thank you.

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