‘Whisper Not’ is in the key of D minor, the natural, relative minor to F major. We have seen a couple of songs in “harmonic minor” keys (Link). In this case the 7th degree of the scale is not raised so the piece takes on a smoother texture (the sharp 7 drives harder to the tonic). In fact the piece begins on a minor VII chord (softer yet) setting up a temporary IV – II – V – I sequence to G minor. The sequence is then repeated to the D minor tonic.
The ‘B’ section reflects the same chord changes as the ‘A’ section but adds some rhythmic contrast with nice little punch chords.
To get started improvising on ‘Whisper Not’ you might like to try something like Example 2 in the left hand.
Example 3 has a couple of tone groups to try. The first seems to work over the first three or four bars the second over the next four of five.