7.37Harmonizing by ear without knowing the key initially

Suppose someone sings a melody.

First find a note that feels like tonic.

Then test major/minor.

Once you suspect the key, identify:

I, IV, V

on the piano.

Now accompany experimentally.

If most of the melody works, you're probably close.

Then refine.

This is much more efficient than searching all 12 possible roots randomly.