What scale repeats by every fourth?

Question

I've stumbled across this in my own compositions and I'm sure I've heard songs on the radio do this.

The simplest way to describe this is to take a regular piano and paint the keys so that there's only sets of 2 black keys (instead of the usual 2 black and then 3 black) so that the notes in the scale would be something like:

A B C D E F G A Bb C D Eb F G Ab Bb C Db Eb F Gb Ab Bb B C#

Or painted onto the current piano setup:

It's like a "mini" scale that follows the pattern of tone semi-tone tone, and repeats indefinitely.

I find that it works well when you don't change positions quickly, because I guess your ear "forgets" what scale it's in.

Is there an official name for this and has anyone else come across it?

Answer 1

This scale is an example of a non-octave repeating scale: the pattern of steps repeats within an interval other than an octave. This particular scale has been discussed previously on this stack exchange post, which references the "Super Ultra Hyper Mega Meta Lydian scale," which follows the pattern C-D-F#-G-A-B-C#-D-E-F#-G#-A-B-C#-D#-E-F#-G#-A#-.... This scale is much like yours, repeating every fifth instead of every forth. That particular scale that took the internet by storm after Jacob Collier discussed it.

That stack exchange question proposes the name "Sub Diminutive Infinitesimal Teensy Weensy Mixolydian" for the scale that you described here, although that name does not appear to be used anywhere else.