melody with no root note / chord?

[macmanmatty]

I was having a conversation about vocal melodies and that if someone has less than one octave worth of notes they could sing then they couldn't never sing in they keys out of there vocal range unless the root note of key was not present in the melody. My question is has anyone ever heard or written a song where the root note or chord of the key the song is played in was not present in the song or melody? I can't see how that would even be possible.

[JonPR]

It would be possible, but highly unlikely. I certainly can't think of examples - although it's quite easy to improvise tunes that follow that rule - i.e., to noodle around on (say) the C major scale without ever playing the C.
Sometimes when doing that, one of the other notes might suggest an alternative modal root - but equally it could just sound like random noodling in C major; or even non-random, if logical phrases are formed. It would just never sound resolved. (Unless, as I say, you made one of those other notes sound like a modal root.)
That's for an unaccompanied tune. Add chords, and that would usually suggest a key, but a melody that didn't contain the keynote would always sound unfinished. That's not a bad thing if it's an effect the composer wants!

The vocal question is slightly different. Someone whose vocal range was limited to less than an octave would be very limited in the number of songs they could sing (most songs have a range of an octave or more), but maybe less limited in the keys they could sing them in.
Where the keynote is in the melody - or even if it's missing - is of no account. What matters - what limits the singer's choice of key - is the range of the melody. They'd simply have to choose a key where the melody's range fitted within their range - and obviously if their own range is limited, that's what limits their choice of keys.

E.g. take Losing My Religion, whose melodic range is a perfect 4th (very narrow). The notes in the melody in the original key (A minor) are G-A-B-C. The keynote is in there, but that's not relevant.
Maybe our poor singer - let's say he's a guy - can't get up to that C (middle C). But as long as his vocal range is greater than a 4th, he can just lower the song's key until its 4th fits within his range; so he can hit both the high note and the low note.
Or maybe they're female and can't get down to that G; so they'd need to raise the key.

Of course, if this singer's range is only a perfect 4th, then there is only one key they could sing it in. (Eg, if our guy's range was only E to A, then he'd have to sing Losing My Religion in F# minor, notes E F# G# A.)
But the wider their range gets, the more choice of keys they have (for this song anyway).

This is all somewhat hypothetical, because even untrained singers can usually manage at least an octave in range; their problems are usually elsewhere: singing in tune, or holding a pitch, or getting enough projection or tone.
Still, because most melodies do stretch to an octave or so, that still limits the keys that most singers can choose for any particular song. Most people - given a reasonable (if untrained) voice - would be capable of singing most songs in a narrow range of keys, but would commonly go for a most comfortable central one, without too much stretching high or low.

[macmanmatty]

this was less of vocal more of a has anyone written a song in key of G major with no G note or G chord I tried using the notes A-B-C-D-E-F# to write in melody in G major with no G note but it sounds more like key of A minor than G major if you end on an E or D major if you end on a D.

[JonPR]

Originally Posted by macmanmatty

this was less of vocal more of a has anyone written a song in key of G major with no G note or G chord I tried using the notes A-B-C-D-E-F# to write in melody in G major with no G note but it sounds more like key of A minor than G major if you end on an E or D major if you end on a D.

Right.
But I think you mean "E minor if you end on E" - or "A minor if you end on A".

And to be strictly pedantic, it would be A dorian if A sounded like the keynote, and D mixolydian if D sounded like the keynote.

You could still write a melody with no G note in it, and use a chord sequence that pointed to G as the key (on the G chord you could use B or D notes in the melody). That would over-ride any modal effect of the melody. It would just not have a resolved sound at the end.