How would I play the notes that are side by side in the same line?
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As far as playing is concerned, play the notes once and hold it for the largest of the two time values given.
This kind of writing is done when the music is for more no. of voices than staves used. Within a staff, if there are two voices, first voice's note stem goes up and the other voice's goes down. When writing for two voices, time signature has to be satisfied for both voices seperately and independently.
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