What does the horizontal lightning bolt over the C sharp mean?
Also, what do the double grace notes (the two semiquavers joined by a beam) mean?
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For pieces such as this one, Chopin's Waltz in A minor, you can often find recordings and follow along with the sheet music in order to hear how the performer plays such ornamentation. There is such a recording included here: en.wikipedia.org/wiki/Waltz_in_A_minor_(Chopin) – Neal Jan 26 '18 at 17:31
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See also music.stackexchange.com/questions/33573/… – Richard♦ Jan 26 '18 at 18:03
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Including the piece and edition that the picture is from within the question is usually helpful (event though Neal was able to pull it out). – Dave Jan 26 '18 at 20:26
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If I'm reading things correctly, in this piece the upper mordent should be realized starting on C# as per Tim's answer (music.stackexchange.com/a/66166/2639); the question linked to as a potential duplicate indicates the older (Baroque) realization which would start on the auxiliary note. If this is the case I do not believe that these are duplicates (in that the correct/accepted answer on the linked question is not the correct answer for this one). – Dave Jan 26 '18 at 20:32
It's an upper or inverted mordent. Play C#, the next note up in the key/scale, then C# again, all squashed into when the C# would be played normally.
The 'double grace note' is pretty well the same thing, just written out as played. I guess the tune's in A major, so why the F is sharpened, - don't know. Maybe it's in A minor, and modulated, rather than change the key sig., the composer used accidentals.
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Yeah, it almost looks like there is no key signature, but it moved to A major via A minor. – Richard♦ Jan 26 '18 at 16:30
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That Chopin sure did like accidentals. I always wondered why he even bothered with key signatures. – jjmusicnotes Jan 27 '18 at 12:15