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I've only just recently begun learning the basics of time signatures and counting beats, and I'm having trouble applying what I've learned to real sheet music. Consider the second measure in this picture, a screenshot from Recondita Armonia, an aria from Tosca: enter image description here

I believe the 3/4 time signature here means the song has three beats per measure and that the beats in question are quarter notes. But the second measure contains three quarter notes plus five sixteenth notes, which adds to more than three beats. So how is this consistent? What am I missing? Is it that the bars under the quarter notes change their value somehow?

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The thing you are missing is there can be more than one "voice" or independent line of melody within each staff.

Rest above notes, up/down stem directions, and offsetting note heads are ways to indicate more than one voice at the same time in a single staff.

If you use colors to circle the various voices, you will see the passage is a staggered entry of four voices...

enter image description here

If you notated the four voices on separate staves, it would be...

enter image description here

Notice that in the second bar, beats 1 and 2 of the original score you presented there are only three voices - the lower treble, the upper treble with stems down, and the upper treble as rests above and stems up. The fourth voice doesn't enter until beat 3 of the second bar, at which point the three voices in the upper treble staff are two parts with stems down, and rest above and notes with stems up. The in the third bar the score seems to stop notating separate voices and it's just a chord with stem up.

That kind of flexible number of voices per staff changing per bar or per beat is fairly common.

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  • Alternatively, you could split the top stave into only 2 voices: steps-up (except the C#) and stems-down. That'd require some voices to have chords instead of being purely monophonic, but it'd seem more logical to me.
    – gidds
    May 11 at 19:47
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The notes in the treble clef in that measure represent two separate voices. The notes with the stems pointing down are one part, and the rests and notes with the stems pointing up are the other part.

To see what's going on, ignore the notes with the stems pointing up; what's left is three quarter notes, which matches the 3/4 time signature.

Now the harder part is to ignore the notes with the stems pointing down. What's left is several rests and several sixteenth notes, which also match the 3/4 time signature.

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