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One user named Maika Sakuranomiya had posted this answer to a question:

Cadence for Phrygian mode: v^(no5)_(no3) - i

A ^(no5)_(no3) means an octave chord, which indicates a power chord without the fifth - two or more same notes being played in different octaves.

However, then another user named User45266 had commented like this on the answer:

V^(no5)_(no3)? I'm sorry, but what? That is literally just a single note. I see why you wrote that, but I can't quite convince myself that a single note can be part of a cadence.

A user named Dom had posted a similar comment:

Concepts like V^(no5)_(no3) are not real.

Does that mean octave chords are not part of standard usage?

Each age in music history had its own standards and uses, rules and theorists. But an octave chord will be possible in all periods of music. Today and also in earlier days it is used to evoke a certain effect. Actually it’s just a tone in unison. But mind the overtones! The 5th and 3rd will still be heard.

Disclaimer: I am user45266. You're not entirely wrong about octave chords:

Sure, an octave chord could be considered its own chord, if it helps. The doubled-up-an-octave note definitely achieves a different effect than just a single note, and I could totally see it becoming an entity similar to a power chord.

The problem is that V(no3 no5) doesn't mean an octave chord.

In C major, we'd start with G-B-D, take away the B, then take away the D. What have we got left? Just the note G. No definition of a chord I've ever heard allows for one-note chords, and what would be the point of calling that single note a V(no3 no5) anyway? The whole idea of a one-note chord is pretty useless.

Sure, just from looking at the chord symbol, you could argue that V(no3 no5) implies that the root is doubled at the octave, forming a two-note chord. But why would it make any sense to even describe that as a modification to a triad anyway? It would be much more efficient to just call it an octave, or some other descriptive term that gets that idea across.

And I especially want to mention that it makes zero sense to include them in any list of chords, because every list of chords would have to be inundated with octave chords. And since they're so simple, any performer reading that chord symbol as a modification to a triad would immediately have the exact same objections I do. I can hear it now: "Wait,... drop the 3 and the 5 ... isn't that just one note?!". And boom, you just lost the respect of the performers, because you inadvertently made their lives harder by using ridiculous non-standard chord symbols for simple concepts. (Imagine reading sheet music written in G♯ major. That, but much worse.)

In conclusion, octave chords could be and are used as real things. Go ahead, call them octave chords (if that's how they're being used), and use them to their fullest.

But don't call them V(no3 no5).