Could a third interval be seen as a step?

Question

In the context of common practice music we study (or at least I studied) that a non-chord tone is said a neighbor tone if it's between two notes with the same pitch and differs from them for a step, that is for an interval of a second. Also I studied that there are no non-chord tones of the type skip-tone-skip.

Now let's say I have a V-I chord progression, that in the upper voice I have a B and a C and that to make things less boring I want to put an C-E in the middle. I also believe that C-E-C sounds quite good but that C and E are a non-chord tones I cannot classify, though they sound good to me and classical, too, in a way. I'd say that it sounds way better than something like C-F-C, although F would be in the chord.

So how do you think we can call that non-chord tone? Is it a "mistake" if I put that there? Am I missing something?

Answer 1

If you like the way it sounds, do it! You can explain it away, if you want to, by conceptualizing that V chord as a V13 chord; that way the C and E are both conceptualized as chord tones.

To answer your question more generally, some scales do have thirds in them. Take, for instance, a pentatonic scale: C D E G A C. Although E and G are a minor third apart, they are only a step apart within the context of the pentatonic scale. So this is one way in which a third can be considered a step.

Answer 2

The interval C-E is not a step. It is a major third; thirds and larger intervals are leaps, not steps.

But I think the pitch E would go well with the chord IV. It converts it to IV7.

In jazz chord notation, that would be Fmaj7 or FM7 or F^Δ7.