2nds are supplementary intervals.
In chords 2nds are marked with 2. For instance, C D G is marked as C sus2. The 2 is for D. Seconds are also half steps and whole steps, which is the best way to refer to the sound and feel.
2nds sound quite ugly to students. By themselves, major 2nds sound better than minor 2nds, but both are a bit harsh alone. However, when combined into chords they are quite beautiful, and without them we would not have inversions of seven chords. We also need 2nds for scales. Here are the 2nds we need for written music:
- 2 or M2
- b2 or m2
- #2 or aug 2