I am trying to play a song with two voices and something is not adding up in the time signature.
In the image below:
in the first measure, I see a half note rest (circled in red in the upper left) which counts as two quarter notes.
I am not sure if the 1/8 note rest that follows (also circled) is part of that voice but either way the half note rest and the triplet count as only 3 (or 3 and half if you include the 1/8 note rest).
How do I count the upper melody in the first measure?
In the first measure, the upper melody is a half-note rest, followed by an eighth note rest, then three eighth notes, which add up to 8 eighth notes. Those three eighth notes are not a triplet, but simply eighth notes. A triplet would have a "3" indicated above the beam joining the eighth notes.
The lower melody is the dotted half-note triad, followed by the lower eighth-note rest (on the word "the"), then the eighth-notes A and D, also adding up to 8 eighth notes.
So the counting of the upper melody is (1 + 2 + 3) + 4 +.
By the way, "voicing" usually refers to the notes within a chord (vertical), not the notes within a melody (horizontal).
The other answer correctly describes how the notes and rests in each "voice" or "layer" of the music add up, but there is a simpler practical way to read things like this.
In the left hand, you have eight equal length notes. When notes are stacked vertically above each other, they should be played together. That is enough to tell you when to play the right hand notes, without having to work out exactly why the rests are written the way they are.
The notation of piano parts like this can get messy, and often the music is not written with pedantic accuracy if that would get in the way of reading it easily. But unless the notation is really terrible (and in that case, the only option may be to guess what it means!) notes played at the same time point will always be stacked vertically, or as close to that as is possible without the notes colliding with each other.
