I learned that segments in worms are called annuli. In music, they're called scale-nulli.

Just kidding -- they're not called that. Usually they are called tetrachords, but those are groupings of four pitches. The following are groupings of 3 and 4 pitches.

The segments below are groupings that make horizontal Major and Minor scales easy to see and hear on the fretboard (they work on the piano too, but seems like they mess up scale fingerings on the keyboard -- I'll have to investigate that a little further and/or ask a pianist friend what they think.)