In Chopin's polonaise in A-flat major, op.53, in the second section the key changes from A flat to E major. What type of change is this? Is it from the flattening of the sixth (F-flat major), or was it made some other way?
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You're exactly right! It's technically a motion to ♭VI, which would be F♭ major. But in order to make it easier to read, he spells it in E major (♯V).
F♭ isn't in A♭ major, but it is in A♭ minor; thus this is an example of mode mixture.
The modulation is created by the common tone between the original A♭ tonic and the new E tonic. A♭ becomes the chordal third (G♯) of the new key to create a smooth modulation.
This move to ♭VI is really common in the Romantic era. Schumann's "Widmung" does the exact same modulation, and in the exact same key!
