In practice for string or wind players, the difference in key relations is a real difference. Per E, a D# in a line is a leading tone. A solo violinist or somebody, the first chair fiddle, is going to give it an extra amount of 'leading' in terms of intonation (sharper).someone called simon wrote:
The notes sound the same, but they must have the correct name if you're talking theory and notation etc, or everyone will get hopelessly confused.
A composer will tend to write an Eb if the next note is the D below; that descending movement is going to be intoned flatter more often than not. So there are contexts in which you might see 'both versions of the note', and they will be intoned differently, significantly.
for a keyboard player, they're stuck with 12 notes. A deficiency in terms of intervals in harmony, because a lot of the intervals are compromised in 12 ET. Which gets to be another topic... Wind and string players adjust their intonation in concert with the ensemble, to get the purest harmony. This is why samples can be pretty deficient in orchestration. (VSL addresses this with various intonations and a mode of operation to utilize this.)