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These pieces are from Victor's piano solo by Danny Elfman (from Corpse Bride by Tim Burton):

Fragment 1

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Fragment 2 (lower stuff is in bass clef)

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Here I want to know what keys on piano keyboard are red notes? My believe is that in the 1st fragment: upper D is E4 (white key) and lower D is E2 (white key) and in the 2nd case it is D4-sharp (black key)? Am I right?

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No, accidentals are never added to the key signature. D# means D# regardless of the key.

  • Why then to write a sharp sign in the first case? There are no naturals in that bar. – LRDPRDX Aug 28 '18 at 13:40
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    Because there was a D natural earlier in the measure, and the notator is just being extra careful that the player doesn’t accidentally keep playing D natural in the other octaves. In the first case, the #s aren’t technically necessary, but helpful. In the second example the # is necessary because the preceding natural is in the same octave. @LRDPRDX – Pat Muchmore Aug 28 '18 at 13:42
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    "Extra clear" confused me =) – LRDPRDX Aug 28 '18 at 13:43
  • Pat is correct. Double sharps, when called for, have their own notation: either two sharp signs ##, or a symbol which looks like a bold "x" x. – Scott Wallace Aug 28 '18 at 13:46
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You have all D#'s in red in both fragments due to the #. Those will be black keys.

The natural on the D in fragment 1 is up an octave (on the 4th line of the staff) and won't effect the D# below (just above middle C) but they give you a courtesy/reminder sharp to be extra clear.

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