What is the meaning of the following type of notation?
All I know regarding the stem location is the common rule of going down below the third line and up otherwise, but I'm not familiar with the one in the screenshot.
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Usually, that is the way the same note is written, when both soprano and alto voices sing/play the same note. In other words, for the rest of that treble clef, there'd likely be two distinct lines, one with up stems, the other with downstems. Up for the soprano part, down for the alto. That's all assuming it's an A in the treble clef.
Were it the bass clef, it'd be a C note, as part of the tenor and bass lines.