computer architecture – Does a Turing machine tape must be binary?

I once asked why does computer data bits are usually organized on binary (base 2) sets, rather than on unary (base 1) sets, aiming to also understand why its not also ternary (base 3), heptary (base 7), ennary (base 9) or even decimal (base 10).

One programmer commented that Turing machines are always binary because the tape includes at least one stage to go to and at least one stage to go back to (or something of that sort; translating from Hebrew without knowing the professional terminology in English).

Does a Turing machine tape must be binary? — Can’t it be unary in any situation?
Was there an attempt to create a “similar” model which is unary just for the sake of research (putting efficiency aside)?

Thanks,