New answers tagged modulation
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We can go considerable modulatory distances by using secondary dominants of closely related what would be minor keys as secondary dominants of major keys instead.
One such example that gets you from A flat major to D major with 2 intermediate keys would be this:
A♭: I -> V7/iii = C: V7 -> I -> V7/vi = A: V7 -> I -> V7/IV = D: V7 -> I
As you ...
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We can re-write the question as how one makes x+y+z=6 mod 12 then reinterpret the numbers as scale steps. A quick answer is -2-2-2 or 2+2+2 moving the harmony by whole steps. Another is 1+2+3 (in some order) making moves of a minor second, a major second, and a minor third; this can be done as -1-2-3.
Other possibilities are +4+5-3 or 4-3+5, etc.
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Consider that a commonly used key change, or probably modulation here, is up a semitone. That's easily achieved, and used often, as the pivot V of the new 'key' contains one of the old tonic notes - the tonic itself.
That would take us to key A major. That happens to be the V of the target key - D, so it's quite simple to move into that. Thus, two simple, ...
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