How did composers create smooth modulations in a piece? By smooth I mean that when you play it, it sounds very natural, without any sudden and unexpected key changes to remote keys?
The best way to do it is by choosing keys which have the same number of accidentals (parallel major and parallel minor keys) or they have plus or minus one accidental.
For example, if you are in the key of D minor, going back and forth from D minor to F major is very natural. Also modulating from D minor or F major to G minor works fine, too.
Today I would like to share with you my chordal analysis of the Prelude in D minor by Anton Bruckner (1824-1896), late Romantic Austrian composer known for his symphonies, masses and motets who also worked as an organist in his late twenties.
As you sight-read this piece today, pay attention to how the modulations are constructed. In my analysis, you will see chords in Roman numerals (without the notation of suspensions). Before the modulation happens, there is a common chord, for example, I=III which means that in the old key this chord is build on the 1st scale degree (tonic), and in the new key, it's the chord of the 3rd scale degree (mediant).
Notice how after the common chord the modulating chord has to be dissonant - a seventh chord of some sort or its inversion - most commonly ii7 (or inversion) or V7 (or inversion).
If you want, you can use this chordal analysis to transpose this Prelude into C minor or E minor. Even better, you can create your own prelude based on these chord progressions. In this piece, Bruckner only uses D minor, F major, and G minor keys but you can easily expand it by experimenting with C major, A minor, and Bb major for even more colors.
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