I am currently analysing Someday My Prince Will Come for an oral examination on wednesday in Jazz theory. I have identified the progression in bars 19 to 21 as a Monte progression, but I'm really bad at identifying scales. The chord progression on my sheet is Eb over E half-diminished to Bb/F, with the key being Bb. What kind of scale does one use over the E half-diminished? I was thinking of mixo b13, however the E interferes with that idea.
As mentioned in my comment and also in David Bowling's answer, the standard progression would be
Eb Edim7 Bb/F with an E diminished chord instead of a half-diminished chord. This is a very common progression. You can find it for instance in bar 6 of almost any jazz blues.
Clearly, changing the half-diminished chord to a diminished chord has consequences on the appropriate chord scale. Apart from the diminished (whole-half) scale, a very natural choice is Bb melodic minor #4, which is a mode of the F harmonic major scale. The reason why this scale sounds so natural over the Edim7 chord in that context is that it requires the minimum number of alterations from the Bb major scale to accommodate for the chord tones of Edim7:
Bb C Db E F G A
It takes one natural to alter
E, and one flat to change
Db. The diminished scale and most other scale options imply more alterations of the Bb major scale, yet only those two alterations are really necessary.
When I look up Some Day My Prince Will Come in my copy of The Real Book, I see E♭ to E° to B♭/F. That E° is a diminished chord, not half-diminished (which would be written E∅). E° and E∅ can look a lot alike when handwritten, and this is one of the reasons I usually prefer to write half-diminished chords as E-7(♭5), e.g.
You can play a Diminished scale (Whole-Half scale) over a diminished chord. You could also play the 2nd mode (Locrian ♮6 scale) or the 7th mode (Altered 𝄫7 scale, Ultralocrian scale) of the Harmonic Minor scale here.
For half-diminished chords, Locrian (7th mode of the Major scale) or Locrian #2 (the 6th mode of the Melodic Minor scale, also called the Half-Diminished scale) are good choices.
I think I figured it out myself. The scale to use on the E half-diminished is a locrian scale (with one b from E onwards). The notes are: e - f - g - a - bb - c - d.