In the present day, the most common time signature is $\begin{smallmatrix}4\\4\end{smallmatrix}$ (also known as “common time”). It makes sense to introduce durational symbols in the context of $\begin{smallmatrix}4\\4\end{smallmatrix}$ because a whole note takes up a whole measure in $\begin{smallmatrix}4\\4\end{smallmatrix}$, a half note takes up half a measure of $\begin{smallmatrix}4\\4\end{smallmatrix}$, a quarter note takes up ${1\over 4}$ of a measure, and so on.