ukulele scale
E major
E1F♯2G♯3A4B5C♯6D♯7
The seven-note scale everything else is measured against: two whole steps, a half, three whole steps, a half.
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
EWF♯WG♯HAWBWC♯WD♯HE
What is true of it
E major is E, F♯, G♯, A, B, C♯ and D♯, and back to E.
Its steps are W – W – H – W – W – W – H, where W is a whole step and H a half.
On the same tonic, E melodic minor differs from it by exactly one note.
Across the first twelve frets of the ukulele its notes fall in 30 places, which is what makes a scale a shape rather than a list.
Chords made only of these notes
C♯mminorC♯m7minor seventhD♯dimdiminishedD♯m7♭5half-diminished seventhEmajorEmaj7major seventhF♯mminorF♯m7minor seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.