Is Morse code binary, ternary or quinary?

I see it as tetrary (4 components)

short beep short silence (usually defined as the length of one short beep) long beep (usually defined as the length of 3 short beeps) long silence (longer than two short silences)

TLDR: "We can thus conclude that the Morse code can be understood, and easily analyzed, as the composition of a prefix binary encoding of a 3 symbols alphabet {dot, dash, sep} into a binary alphabet, and a prefix encoding of a 58 symbol alphabet (57 characters and one space) into the 3 letters alphabet.

The composition itself is a prefix encoding of the 58 symbols into a binary representation."