Piano Forum

This is something I've experimented with.  During the height of the pandemic, I regularly tried to practice Paganini caprices with just my left hand, and I was stumped trying to find a solution to a double octave trill in one hand in one of the slower parts of a caprice.  The easiest solution is to trill the bottom note (as it stands out more than the top trill due to it occupying more of an extreme to the ear).  Sometimes I try to do that while alternating as quickly as I can the notes of the trill with the thumb of my left hand (something like triplet eighths or even sixteenths depending on how fast your thumb is; if you can do sixteenths there will be more of an illusion of a double trill) while trilling the bottom notes.  Another thing I've thought about here is alternating trills between the top and bottom notes, depending on the music above (so if there's an upward skip in the melody to trill the top notes there to emphasize the upward movement, but then go back to the low notes trill as the melody descends).  I've also practiced doing tremoli as samjoseph noted.  Something like the fingering 5241 (G#, G#octaveup, A, A octave up), although the artifice of this bugs me because it's like playing staggered octaves of the root note and the trilled note, which takes away the trill feeling to me, so sometimes I practice 5142 (G#, A next octave up, A, G# next octave up)  so there is a constantly octave displaced trill-like tremolo happening.   There's no perfectly elegant solution unless your hands are huge or you can move either your thumb or fifth finger incredibly fast, but I think just trilling with the lower note and giving the illusion of movement with a thumbed upper note is fine, and good rotation can make the tremolo work.