I am sketching out a sonata, the first since the disaster of a sonata I wrote about a year ago, and after sketching the Intro and the Coda of the 2nd movement, the intro is in B-flat major (the key signature of the sonata), and the Coda sounds best to me in F sharp major. These keys share no common chords. I tried using a Neapolitan chord to quickly modulate to B major (IV of F sharp major) but the modulation seemed so jagged that it interrupted the cheery nature that I was trying to create throughout the entire movement, and was simply out of place surrounded by playful and consonant music. I tried the whole tone scale trick that almost always seems to work, but again, the jagged modulation interrupted the nature of the piece (I am trying to make the 2nd and 3rd movements as light and enjoyable as possible so I can finish with the destructive/violent finale). I tried using all three augmented 6th chords, but always ended up in the tonic key of F. How do you make these sudden, massive modulations without causing it to become too jagged?
It's interesting you cite these two keys, B♭ and F♯, because these are famously the two keys used in the first movement of Schubert's D960 piano sonata (although he sometimes spells the second key as G♭). You may check this piece out to see what he does; once it's a direct modulation, and another time he uses an enharmonically spelled fully diminished seventh (Bdim7 becomes E♯dim7, then he just places a C♯ in the bass to make it a dominant of F♯).
But more broadly, there is one big thing to consider: strengthening the cadence in the new key. There are multiple ways to do this, but I'll mention two.
- Set up the cadence beforehand with a very clear predominant–dominant–tonic motion. So often the satisfaction of attaining a new key is directly connected to how well the cadence is set up. One way of clarifying this is by prolonging the predominant area; expand IV, ii, ♭II, etc., in the new key before moving to dominant.
- Instead of (or in addition to) the above, really prolong the dominant. This often happens in sonata movement in the retransition that precedes the exposition: one of the reasons the exposition is so effective is that it resolves the long prolonged dominant that preceded it. A similar situation could happen here: the move to F♯ could be made more effective and convincing simply by prolonging the dominant, thereby making your listeners want and expect the F♯ tonic that much more.
Not that distant. If you spell it as B♭ to G♭ majors, the modulation looks a lot less violent!
There's no common chord, but there's a common note, the tonic of B♭ major becomes the 3rd of G♭ major. And "chords with roots a third apart that share only one common tone and have the same quality (both are major or both are minor)" are so pleasing that they have a special name - 'Chromatic mediant'.
Let the melody linger on B♭, then this is a classic case for 'just do it'.
According to Schoenberg's comments on modulation, one needs to "neutralize" the previous key; by that, he means emphasize the notes that are different between the keys to confirm the modulation. Simple example: going from C major to G major entails making sure an F# stands out early (thus the idea of entering a new key from its dominant or at cadencing in the new key soon.) He also suggests that using a V/V (my notation, not his) in the new key helps. For more distant keys, more notes need to be used. Going from C to A means using F#, C#, and G# prominately.
Another suggestion (I don't know where I got this from), is to use and Augmented Sixth in the new key to introduce its dominant. The double half-step movement strongly suggests modulation. One can play some (seemingly) secondary dominant in the first key and then treat it as a German Sixth in the new key (and vice versa). A French Sixth works well too (if a 7b5 in the old key is available on some note) as there are also two tritones being resolved with the double half-step motion. Neutralization afterward is still useful to confirm the new key.