A note raised in pitch by two semitones, sounding enharmonically a whole step higher. So, a “D##” sounds the same pitch as a “E.” Double sharps are generally used to indicate accidentals in a sharp key; for example, a sharp 9 in the key of G# would be spelled A##, while a sharp 5 in an F#7 chord would be spelled C##. Yes, you could spell that C## as a D, but it makes the chord harder to recognize and a D technically would be interpreted as a b13, which indicates a different flavor for soloing and accompaniment.
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