A chromaticism is a note that doesn’t belong to the mode. In the modal approach I learned, there are two types, and they behave differently.
Passing tone chromaticisms
Passing tone chromaticisms sit between two diatonic degrees that are a whole step apart, connecting them. They enrich the melody by splitting the mode’s whole steps into half steps. You can insert them between any two diatonic notes a whole step apart.
In D Dorian (D–E–F–G–A–B–C), for example, D♯ can pass between D and E. E and F are already a half step apart, so there’s no room for one there.
Leading tone chromaticisms
Leading tone chromaticisms sit a half step below a diatonic degree and create tension that resolves upward into that degree. They don’t connect two notes; they create a pull. The same pitch can be either kind. What matters is whether it passes between two notes or leans into one. Note that the leading tone to a diatonic degree isn’t necessarily a chromaticism. The 2 to ♭3 in Dorian is just part of the scale. Blue notes can work as leading tone chromaticisms: in Mixolydian, the raised second (or flat third) resolves into the third, and the raised fourth (or flat fifth) resolves into the fifth.
Which way it resolves
In the modal approach I learned from Enrique Vargas, leading tone chromaticisms resolve upward, and a chromatic note a half step above a diatonic degree that resolves downward doesn’t give you the same clean tension and release. That’s a rule of this approach, not of harmony in general. Tonal music resolves lowered notes downward all the time (♭6 to 5 in a major key is a common example).
A diatonic note can also function as a leading tone if it happens to sit a half step below another diatonic degree. B is a leading tone for C even though B is diatonic in C Ionian.
Too much chromaticism dilutes the mode
The caution: the more chromaticisms you add, the more the modal flavor dilutes. In a seven-note diatonic mode, add all five possible passing tones between diatonic degrees and you’ve essentially converted the mode into a chromatic scale. In flamenco, as Enrique Vargas teaches, chromaticisms should be used sparingly; the genre’s power depends on strong modal identity.
Chromaticism is a spice, not a sauce. The mode has to be audible for the chromatic additions to mean anything.
Related: Modal Notes and Primary and Secondary Chords in Modal Music.
Acknowledgment
I learned this approach to modal theory from Enrique Vargas, my teacher for over twelve years.

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