What am I missing here please?
You are able to figure out what the resulting chords are, no problem there. But you're supposed to listen to it and keep what you like. :) If you don't want to make the C chord a C6, then don't add an A vocal harmony, add something else.
There are basically two styles for creating backing vocal harmonies:
- (A) Follow the steps of the melody along the scale, at a distance of a fixed interval. Change the interval if it's necessary for the chord you want to create, or keep a fixed interval if you like the way it sounds. Style A in its simplest mechanical form only needs to know the melody, a scale and a set of intervals.
- (B) Do not follow the steps of the melody. Backing vocals sing chords like an organ chord or synth pad. Lead melody goes up and down, but backing vocals only change pitch when the backing chord changes. Style B needs information about backing chord changes.
Notation examples of the two. First, style A, lead melody in black, harmony notes in blue.
Then style B, harmony notes shown in green.
Style B seems to be used more in rock music, and style A more in pop/jazz. In style B, sometimes the lead melody notes can even overlap with the backing voices, and when the lead melody steps up and down, there can be close intervals like seconds etc. In traditional classical styles this would probably have been frowned upon, but I think it can be a nice effect and is really a matter of taste.
There's also a combination of the two: sing tones of the written backing chords only, but move to a higher or lower chord tone, if the melody steps on your current note.
If you look at vocal harmonizer effect devices, they are divided in these two categories. There are scale-based harmonizers where you set a scale and supply the lead vocal into an audio input. And then there are chord-based harmonizers with a lead vocal input and a backing chords input, where you connect e.g. a guitar that plays chords. Some harmonizers have hybrid modes where you set a default scale (by specifying a key), but you can override or augment it by playing chords.