Is there a reason why it should be Eb as opposed to D#?
First, D# and Eb are not the same notes and cannot be used interchangeably. This is a common mistake beginners make. These notes are
enharmonic, meaning they have the same pitch, but different names depending on the key signature and context in which they are used. For example, If a C major triad is spelled C-E-G [R-3-5], to make it a C minor triad, we always
flat the 3rd [R-b3-5]. There is no point in which the note "D" would ever be considered a third of any chord in which the root is C. Flattening (lowering a note one half-step) the third of a C major triad gives us a C minor triad, which is spelled C-
Eb-G [R-b3-G]. Calling it C-D#-G means you are no longer talking about a C triad at all because at no point is D or D# EVER CONSIDERED THE THIRD OF ANY CHORD IN WHICH C IS THE ROOT NOTE.
If we look at the scales corresponding to each C chord:
C major scale:
C D
E F
G A B
C natural minor scale:
C D
Eb F
G Ab Bb
If C is the tonic (starting point of the scale), at no point does either C major or C minor produce a C triad in which D or D# is a third.
This is the context I was talking about. Sharps and flats are not arbitrary, if I am calling something C#, it means I am
raising the note C a half-step, which is NOT the same as Db
which means I am lowering the note D a half-step. Context ALWAYS matters when using enharmonic notes, especially if you are trying to "make the information in the article as underwhelming as possible while still allowing people to make progress" as you said.
