cool info, psy...
i don't know for sure if this is along the same lines, but...
in my experience, while it's not absolute (as psy said), if you play two notes together (like an A and a C), you'll 'hear' the higher note (the C), and it will 'fit into' the melody like a C would. if you play 3 notes, same rule applies... a C/E/G (cmaj) chord fits a melody similar to a lone G.
it's not absolute... there are probably reasons for this; i think the ear latches on to the most 'energetic' note and follows it; 'energy' of a note is tied to both volume and frequency (higher frequency at same volume = higher energy).
so, if you are working this out, and the upper note works but the chord doesn't, keep the upper note and change the chord.
a chord DOES sound different from a single note; this tone difference is why we have chord theory. but you are talking about if a patch for instance just sounds 'right' when you play an interval (say your third above) for instance. sometimes i have played patches that somehow just sounded more 'right' on some intervals and chords than others.
sometimes that 'sound' will travel up and down the keyboard with you, and you can just transpose the whole chord to one that fits in your progression. other times, it doesn't move.. it's only the C/E/G right here on this octave, and no other notes nearby. so what could cause that?
if you think about it in 'absolute' terms, for example, let's use a sawtooth... a major chord at any note should have the exact same harmonic relationships; i.e. the 'sound' should be the same, in the way all piano keys 'sound' the same, just at different pitches. but for some sounds, maybe it doesn't. that means something is keeping them from having the same harmonic relationships.
on many acoustic instruments, the intervals between notes aren't 'exactly' a 12th... a piano (just intonation) has a couple notes per octave 'tweaked' for instance; so transposing across those notes may be slightly off, and not have the exact same relationships; a slight change might take away the 'magic' you heard, who knows. try sampling & transposing then.
for electronic instruments, we have even more going on, lots of complex things that can affect harmonic relationships. for example, a resonant filter will emphasize harmonics near the cutoff frequency. maybe if the cutoff is set right near the E, a C/E/G might have one or two of the C harmonics emphasized, and the G de-emphasized, and you don't even realize it but it sounds 'good'. if your filter is not keytracking at exactly 1:1, perhaps going up an octave will not have the cutoff right near the E anymore, and the C harmonics will not be emphasized, and the actual 'tone' changes. if you can figure out what might be causing the change, you can adjust the patch programming to compensate.
if you can't, you might be able to sample the 'magic' notes, and use a sampler to transpose them. this still won't necessarily help with making it fit your chord progression though... an A and a C will always be a minor third (which you can probably fit somewhere, but maybe not); a C/E/G will always be a major chord (and if your progression needs a minor, well it just won't work), etc.
if there are errors, please correct them.