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It's not the difference between C# or Db per se, it's a function of what note in the chord it is occupying.

I’m responding to this part of the parent’s post: On all fretless instruments, including most bowed strings and the human voice, enharmonic equivalent notes still have different pitches. The subtle differences in intonation is incredibly important and noticeable on the violin, for example.

Would that not just manifest as... you feel like you're out of tune, so you adjust minutely?

Yes exactly, and one would intonate it slightly differently by ear depending on what role the note has in the current harmony is the idea.

Presume a base note of A is being played and the violin plays a C# functioning as the major third of an A major chord. The ear would want to play the C# justly intonated to the root note A, or maybe a compromise somewhere between equal temperament and just intonation.

See for example https://music.stackexchange.com/questions/113812/violin-tuni...

there's a lot of nuance. A lot of playing it by ear. :)

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