Arnold Schoenberg · section 40 of 44

Modulation Continued

Since modulation into the second circle of fifths rests on a more distant relationship than modulation into the third and fourth, it is more complicated. We shall therefore deal with the latter first and set the former aside for the time being.

Starting from C major and A minor, the keys of the third circle of fifths upward are A major and F-sharp minor, those of the fourth, E major and C-sharp minor; downward, those of the third are E-flat major and C minor, those of the fourth, A-flat major and F minor*).

*) “Upward” is to be understood as meaning in the direction of increasing sharps or decreasing flats; “downward” means in the direction of decreasing sharps or increasing flats. It goes without saying that one must then sometimes think of G-flat major as F-sharp major, of C-flat major as B major, of D-flat major as C-sharp major. And so it turns out that D-flat major is four steps of the circle of fifths away from A major going upward, and eight going downward.