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What are some good ways to figure out what notes are being sung? I can always tell when more than one note is being sung, but telling the difference between 2 and 3 separate pitches is very difficult for me, especially when a song is not a capella.
I actually have a specific song I am transcribing and cannot tell if I am catching all of the pitches, but this forum seems to frown upon asking for specific help like that.
When I teach dictation (=transcription) in my classes, I emphasize that it's not 100% an ear-training exercise; a big part of dictation is critical thinking. In most cases we can reason our way through what the difficult pitches are just by looking at the context and thinking about our own understanding of harmony and harmonic progression. Far too many students think that dictation and written theory are completely separate exercises, when really they're two sides of the same coin.
I recommend dictating the outer voices first. In almost all cases I recommend dictating the bass first and then the uppermost (soprano) voice, but occasionally there will be an excerpt where the soprano line might be easier than the bass.
Once you have that outer-voice framework, take some time thinking about the implied harmonies and the implied progressions. If your outer voices are a C and a G, for instance, there's a decent chance the middle voice will be an E or an E♭. Sure, it's possible the inner voice might be a C♯—and you may run into that occasionally!—but the odds are that you'll be building consonant sonorities.
You can also take this time to identify the qualities of individual chords. If you have a B in the bass and a G♯ in the soprano, and you hear a major chord at that point in the music, you know the middle pitch must be an E.
By approaching dictations in this way, you limit the possibilities of the remaining pitches, and in many cases you can narrow the options down to the exact pitch you're seeking.
As David mentioned, this takes years of ear training practice however... a few tips to help.
Practice relative pitch, a very good app I'd suggest is Tone (has an orange background with a white wavelength as the icon).
As for actually transcribing your example: pick out the soprano line (or top line) first as this is generally very easy to hear. Then the bass line. Finish with the middle line. You need to be able to block out the other lines as you proceed with this. A good way to practice this is when listening to any music (with or without score), just pick one of the more accompanying instruments and try and follow it whilst blocking out the others - it is easy when listening to just concentrate on the melody, avoid this.
