Which interval notation is correct

Standard notation for one octave

There is octave notation for pitches only. C4 is middle C. C5 is an octave higher, etc.

But when you're talking about chords, the Am could be any octave you want. And if you want to specifically play an octave, like in an A arranged as A3 and A4, I don't think there is any other chord symbol other than writing octave, oct, etc.

Usually the chord indicates the bass and pitches to be used for harmony. The arrangement (octave, inversion, etc.) is up to you.

An octave almost always only indicates the bass. And usually your harmony is a little more robust than a single note. Even though you are playing an octave bass, the chord for that beat or some beats, etc. is usually 3 or 4 notes that make the entire phrase "fit". Chances are you'll find a 3rd, 5th, etc. at some point.

TO UPDATE:

Oh hey, I just checked out my own little piano practice program.

I've listed these chord types: 1 + 8, unison, and octave.

jjmusicnotes

To be clear, both the question and this answer seem to imply macroanalytical notation (which is used for chord notation). Different notation must be used for certain pitch classes. For Stephen: In fact, cases where the bass doubles in the octave are usually only used in strategic moments and so actually make up a very small percentage of the music.

Cathedral ♦

That doesn't really carry over to some musicians as an interval. Think about whether we would put the notation on a lead sheet.

jjmusicnotes

@Dom - what does musician not really pass on?

Cathedral ♦

@jjmusicnotes the C4 to C5 as a simple idea for an interval. If anyone should write that it looks like you're playing a C4, it's a C5.

jjmusicnotes

@ Dom - I get it, I was referring to using the "standard" 5 line notation more than I commented on the pitch class.