Why is the smallest 2nd, that can be written, negative?

If we are to write two notes a 2nd apart, we need to use 2 consecutive letters of the alphabet (such as AtoB or EtoF) or GtoA (note names repeat after G)

The smallest 2nds are then B-C and E-F, being both 1/2 steps apart. And they're minor 2nds.

Now if we use flats and sharps we can make those 2nds even smaller and they will still be 2nds

So B#-C and B-Cb are 2nds and there notes are cero steps apart (B# is enharmonic for C, and Cb is enharmonic for B).

Now if we use both alterations at the same time we have:
B#-Cb which are -1 half step apart. (minus 1 half step , that's a negative number!)

mDecks