The symmetrical scales
Two scales built from a repeating step pattern, so they look the same starting from any of their notes. That symmetry is their whole character: no note is more "home" than another, so the ear floats, unmoored. Composers use them for exactly that — dreams, magic, menace, disorientation.
Whole-tone — all whole steps
Six notes, every step a whole step. No half steps means no leading tone, no tonic pull. Debussy's signature sound.
There are only two whole-tone scales in all of music — one starting on C, one on C♯ — because after six whole steps you're back where you started.
Octatonic (diminished) — alternating whole and half
Eight notes, alternating whole step, half step, whole, half… It has a jumpy, eerie, "which key is this?" quality. Stravinsky and countless film composers use it for menace and the supernatural.
There are only three distinct octatonic scales, for the same symmetry reason.
The augmented scale (a note)
One more symmetrical scale you'll see named: the augmented (or hexatonic) scale — alternating minor 3rd, half step (C E♭ E G A♭ B, back to C). Six notes, built from two augmented triads (C–E–G♯ and E♭–G–B). Used for a similar floating, uncanny effect. Recognise the name; don't drill it.
Try it
Try
Play the whole-tone scale from D against a D drone. Every note sits the same distance from its neighbour, and against the drone none of them "click" the way ^1, ^3, ^5 do in a major scale. It's like standing in a room with no walls — no reference point. That's the sound Debussy wanted.
The usual mistake
Trying to hear these as "wrong major scales" and correcting the odd notes. They're supposed to have no home. The whole point of a symmetrical scale is the absence of gravity — play it as it is and let it drift.