Unusual key relations you nevertheless hear quite often

[Maestro267]

It always amazes me how many times music in E flat major winds up in B major. The two keys sound very distant from each other. The most famous example is probably Beethoven's Emperor Concerto, whose slow movement is in B major. And of course the numerous examples of slow movements of C minor works being in E major.

Other examples?

[Jo498]

I don't know how often this is. But it seems that with Beethoven (and sometimes late Haydn) an extension of harmonic relations between movements (or contrasting sections) was achieved by using flattened/sharpened keys a third below or above home key, or similar ones. E.g. Haydn's last piano sonata E major slow movement in E flat major, F# major slow movement in the D major quartet op.76/5.

It becomes fairly common in Beethoven (although the more traditional dominant/subdominant for e.g. slow movements is still more common). Ab major slow movement in the C major piano concerto, E major in the c minor, B major in the Eflat, Bflat in D major quartet 18/3, F major scherzo in A major 7th symphony (with trio in D maj IIRC).

It seems that at least some later occurences were directly inspired by Beethoven. Weber used the same key relations for the slow movements of his piano concertos as Beethoven's 1 and 5. Brahms used E major slow movements in the first symphony and the piano quartet op.60 (although here it might have been more trivial, if that work was originally planned in c# minor with E major as obvious parallel key for a slow movement).

[71 dB]

As someone who understood nothing about music theory just 5 years ago, but has gotten into it during the past few years, I am surprised how easy it is to modulate to other keys, even distant ones. I always thought it is something very difficult, but it isn't. There are so many tricks to use: Secondary dominants, common (pivot) chords, common (pivot) notes, chromatic mediants, vii°7, augmented 6th chords,... ...let's just say that I am not impressed anymore when a piece of music modulates to the other side of the circle of fifths.

[amw]

It always amazes me how many times music in E flat major winds up in B major. The two keys sound very distant from each other.

Flattened sixth relationships took off in music during the early Romantic era as an expression of subjectivity, precisely because they do sound so distant and therefore "fantastic", while in fact being very easy to resolve back to the tonic via moving a half-step back down to the dominant. Schubert probably did this most extensively on the small/local scale, and others followed, but the origins go back to Haydn and, as mentioned, Beethoven.

And of course the numerous examples of slow movements of C minor works being in E major.

This is somewhat more radical, seeing as the mediant relationship of C major to E major/minor traditionally works because of the use of the third as a pivot tone—in C minor, obviously, this pivot tone is absent. Most of these examples are therefore directly inspired by the, at the time, possibly unprecedented use of E major in the slow movement of Beethoven's third piano concerto, which Beethoven then felt the need to justify in the finale by beginning the main theme with Ab-B (the two notes in harmonic C minor that are shared with E major).

[Jo498]

There seems a difference between brief/transient modulations within movements and the typical keys for contrasting sections or middle/slow movements. AFAIS most of Bach and Mozart is rather "conservative" in the last respect with dominant, subdominant or alternate/parallel minor/major accounting for almost all slow movements' keys.