What I have in mind here is the situation where we're moving from one chord/tonal area to another. If you take a tune like "So What" where we go from Dmi7 to Ebmi7 there's certainly no overlap as far as the chord tones go. If we consider, however, the scales used then it's a whole different story. If we're using seven note scales, keeping in mind that there's only an available twelve, then there has to be at minimum two notes which will be the same (no matter what scales they are, so long as they're both septatonic). If you write out the tones for the above mentioned chords (using dorian in both cases) you'll see what two notes are the same (in bold):
D Dorian: d e f g a b c
Eb Dorian: eb f gb ab bb c db
And of course knowing which notes are common helps us to build links between the tonal areas (if so desired).
On the other hand the most tones in common would be six (because if all seven are the same we haven't moved from one area to anotherFN 1), because traveling around the circle of fifths by the shortest distance -- either right or left on the circle -- only alters the key signature by one accidental.
There is an interesting situation that can be imagined (and in fact can happen ) which might contradict what's been said regarding having at least 2 tones in common. We might travel from C# major to Db major, for instance, and if you look at those two scales you won't find any common tones:
c# d# e# f# g# a# b#
db eb f gb ab bb c
However if we listen to the two scales (equally tempered) we won't hear any difference! This is because they are enharmonically equivalent, and in fact no tonal movement has occurred at all.
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1. Leaving aside something like moving from Ami7 to Cmaj7 where there are two different scales (aeolian and ionian), because here the overall collection of notes is the same.
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