What should be used to describe music that involves notes progressing by semitones?

The term that best describes music progressing by semitones is "chromatic." In musical terms, a chromatic scale consists of twelve pitches, each a semitone apart, which means that every adjacent note represents a half-step increment. This results in a rich, nuanced sound palette, as chromatic movement is defined by the inclusion of all notes within an octave, without restriction to a specific key or scale.

In contrast, the term "melodic" refers more broadly to the overall contour and motion of a melody, which may not necessarily involve semitonal progressions. "Diatonic" refers to notes that belong to a specific scale, typically comprising whole steps and half steps but not exclusively focusing on semitones. "Intervallic" pertains to the distance between two pitches rather than the specific progression of notes. Therefore, the choice of "chromatic" accurately captures the essence of music that involves movement through semitones.