I've been practicing singing scales with a piano, but I'm confused about whether it can teach me to sing a melody. When singing scales, I match the pitch of the individual piano note with my voice. However when singing actual songs, you're not singing to a specific note but to a chord. So in an actual song, if the piano or guitar plays a C chord, my voice would sing either a C, E or G note, right? (ideally, something other than C). So if singing songs requires you to sing a different note than the main note, how do you effectively practice scales? I mean what's the point of learning to match pitch when in practice you're trying to avoid singing the same pitch as the chord?
Pitch matching and ear training is very useful for learning. One of the primary goals is simply to accustom your voice and your ear to a consistent set of pitches or intervals, enabling you to reproduce them with ease and recognize if you're singing off-key. Singing along with scales also helps with things like quick note transitions when doing runs of notes.
So in an actual song, if the piano or guitar plays a C chord, my voice would sing either a C, E or G note, right?
No. The melody and backing chords are (usually) related, but the melody very frequently strays from the notes of the chord.
I mean what's the point of learning to match pitch when in practice you're trying to avoid singing the same pitch as the chord?
If you were to learn a song by ear, you'd be matching pitch to the melody — whether it's played by an instrument or sung by someone else. Instrumental music is not purely comprised of chords! There can be multiple in(ter)dependent melodic and harmonic lines.
Ultimately, the melody notes you will sing are notes that are drawn from scales. You should also practise intervals, arpeggios, etc. in order to learn other orders of the notes and other techniques, but learning scales is far from useless.
It's true that over a C chord, the main notes you'll sing are from that C chord (CEG), but other notes are bound to be in there somewhere. Otherwise it'll start to sound like arpeggio practice time. By main notes, I mean the ones that are more emphasised - often 1 and 3 in the bar. For example, if there were a D,E,F,and G as 4 crotchets in a particular bar, yes, there's E and G, but the underlying chord certainly wouldn't be a C - it'd be more likely Dm.
You're not actually trying to avoid singing the same pitches as a chord produces. Think about it - if the notes to be sung in a particular bar didn't fit to the underlyiong chord, either the chord's wrong, or the notes are wrong! Most times, the notes will be at least part matched to the chord, it happens at least 9 times out of ten. Don't believe me - check a few melodies and look at the chord make up. They'll match.
Your question relates to practising. Why not get the accompanist to play a series of chords. C, Dm, Em, F, G, Am, Bo (or G7) back to C. Then you can practise singing the root of each, the 3 or 5 of each. Taking it further, you can sing, say, 1-3-1, or 1-2-3, or 1-2-3-2-1 on each chord, etc.When sufficiently experienced, listen to a triad, and sing 4-3-2-3, so you're actually putting a sus 4 and sus 2 into the played chord. The combinations, with timing changes, are endless. Bit like real songs, actually...