Need help with the notation in Beethovens Pathetique 2nd movement. Bars 20 and 21.How are these played? What notes are played forthe ornamentation.
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You are going to play something more or less like this - it's called a "turn":
I say "more or less" because ornaments are meant to be tackled rather freely within the duration they have to fill, so these specific durations may be taken with a grain of salt. The up-and-down of the S-curve tells you to go up a step, return, then go down a step and return. Accidentals above or below apply the upper or lower auxiliary note respectively.
Turns can be placed in two places: between a note and its successor, or directly above the note...
... which produces something like this...
...(bearing in mind what I said about fairly free execution within the duration of the note - these last two examples are from Wikimedia). The difference is that the turn between the notes starts on the main note; the turn above the note starts on the upper auxiliary.
Von Bülow's "instructive edition" (first published 1875, https://imslp.org/wiki/Special:ImagefromIndex/30364/torat) suggests playing the turns a bit faster than @Patrx2, but the general principle is the same.