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I'm a complete noob when it comes to sheet music and I have a (probably) very stupid question regarding this:enter image description here

The way I see it, the notes and pause don't add upp to 4 beats? First a dotted quarter, 3/8ths of the bar, then an eighth pause, 4/8ths, then an eighth note, 5/8ths, followed by half notes, 9/8ths?

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The dot above the quarter note is a staccato articulation which doesn't affect its rhythmic value. It's still a quarter note. If the dot was to the right of the note it would change its rhythmic value.

The sample has two voices. The top voice (sticks upwards) has a half note rest followed by a half note.

The lower voice (sticks downwards) has a staccato quarter note followed by an eighth note rest then an eighth note tied into the following half note. The eighth note rest is vertically misaligned - it should be further up the staff.

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    I think the eighth rest is further down the staff to indicate that it corresponds to the lower voice. But it's so far down, and the lower voice in such a high register, that it's more confusing than helpful in this particular situation. – Kevin Dec 7 '17 at 0:14
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    I'd agree with @Kevin that the eighth rest should have been placed somewhere around the 2nd or third staff line. – Carl Witthoft Dec 7 '17 at 14:43

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