ukulele scale
E♭ whole tone
E♭1F2G3A♯4B♯5C♯♯6
Six notes, every step a whole one. There are only two of these scales in all, and every note can be heard as the tonic.
The same sounds spelled from the other side are D♯ whole tone.
Written out
Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.
The step pattern
E♭WFWGWAWBWC♯WE♭
What is true of it
E♭ whole tone is E♭, F, G, A, B and C♯, and back to E♭.
Its steps are W – W – W – W – W – W, where W is a whole step and H a half.
Across the first twelve frets of the ukulele its notes fall in 26 places, which is what makes a scale a shape rather than a list.
Chords made only of these notes
Found by testing every chord in the catalogue against these 6 sounds, not chosen.