The diminished scale

Major's steps come in an uneven, homey order. The diminished scale is pure clockwork: W H W H W H W H. Compare the walk, then hear the machine over its own chord.

Because the pattern repeats every minor third, starting the scale on C or on E♭ gives the same shape, and nearly the same notes. Like the °7 chord that lives inside it, it has no single root: four doors into one room.

Count them: eight notes, one more than any key owns. That extra tooth is the giveaway that this scale answers to symmetry, not to a tonic.