: Simplified notation for two-note tremolo Does first and second bar mean the same thing? If no, is there a simplified notation for the first one?

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These two bars don't denote the same thing. The first asks the player to alternate the two notes. The second asks the player to repeat the two-note chords.

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There are two different types of tremolo indicated in your example.

The first bar, where the tremolo lines are placed between notes, requires the rapid reiterations (here, in 32'nd notes) of the alternating notes indicated. The first tremolo requires that we alternate between middle C and its octave (higher) in 32'nd notes for half a measure. The second tremolo requires that we alternate similarly between E's.

The second bar, where the tremolo lines are written through the stems of the notes, require that we play the notes rapidly in unison. So, with the first tremolo in the 2nd measure, we play the middle C and its octave in unison, in 32nd notes for half a measure. And similarly for the second tremolo on E.