Beethoven spelling a D#7 chord with a G-natural in 2nd movement of Emperor Concerto -- why?

Question

In Beethoven's Emperor Piano Concerto, 2nd movement, there is an unusual spelling -- normally I'd expect the G-natural in the 1st violins in the 7th measure (top right of the image) to be spelled as a F-double-sharp; the same spelling is used later in the movement when the piano has the same melody and chords.

And also in the master's handwriting...

Do we know why Beethoven might have decided to spell it this way?

One reason I'm asking is it reminds me of the unusual pitch spelling in his 5th Symphony 1st movement, where the flutes and 1st violins alternate between D-flats and C-sharps respectively; there I see it as the composer wanting to emphasize that the two groups of instruments are still having a dialog despite the fragmentation of the motif.

EDIT: He seems to be doing it with a vengeance: in the fragment below, where we have Flute, Clarinet in A, Bassoon, and Piano, notice that the clarinet, being a transposing instrument, actually has the "correct" spelling, whereas the 3 other instruments, flute, bassoon, and piano, all have F#-G-G# -- it looks as if there's something special about these three notes, but I'm not sure how one would figure out the mystery...

Answer 1

The short answer is that it is easier for the performer to read.

But another, more intriguing answer to this puzzle is that the construction of harmony was not reliant on block chords until more than a century after Beethoven.

Beethoven (and his contemporaries) would have thought of those excerpts as being contrapuntal, each instrument acting as its own musical line.

Thinking one musical line at a time, aka looking at the score "horizontally", the accidentals you describe are normal convention for displaying a rising chromatic pattern. It is easier for the musician reading the music to see a G in that position rather than an F##.

However if we think "vertically", and look at how all the crotchets line up on every beat as a defined chord, that G should indeed be F## to fit inside a D#7 chord.

But this was not Beethoven's thought process.

Answer 2

This isn't much of an answer. More of a comment about the "sharps for rising chromatic lines" practice.

In Mozart's Fantasia in C minor, K.475 there is a chromatic scale over an F7 chord resolving to Bb...

...the rising chromatic line does not always follow the practice of using sharps.

That's from https://imslp.org/wiki/Fantasia_in_C_minor%2C_K.475_(Mozart%2C_Wolfgang_Amadeus), first edition, the monograph doesn't actually notate the complete line.

The segment A♮ B♭ B♮ rather than A♮ A♯ B♮ makes sense because it's moving to a tonic of B♭. But that doesn't explain segments like G♮ A♭ A♮.

It could have been G♮ G♯ A♮ B♭ B♮ to both use sharps for a rising chromatic line, and also maintain B♭ for the tonality, but it wasn't written that way.

My point is old scores don't always follow the practice of sharps for rising chromatic lines. I think it is a more modern practice.

This doesn't explain why Beethoven used G♮ when Fx makes more sense harmonically. But you can at least drop the "sharps for rising chromatic lines" part of the question, because apparently that was not always the practice.

I would guess G♮ for the sake of white key convenience on piano, but that is easily contradicted by Beethoven solo piano scores, and the inconsistent spelling in the various instrumental parts.