time and frequency

I always love to ask a provoking questions.

We use various musical tunings and scales. Logarithmic (12-TET), pythagorean, harmonic, and so on, We use various reference notes to "connect" the scales (like A=432Hz or A=440Hz and more).

And we use "cycles per second" to describe the frequencies.

But no matter what kind of a system we use - my question is - why we use a sexagesimall system of time? Why we use the system in which the basic time unit equals 1 second as a calculus of 1 / (24 x 60 x 60) ? Where did it really came from, and what meaning it has for our consciousness setting?

It is interesting, because some people refer often to the pythagorean scale as to the "sacred one", based on whole numbers and mathematic relations of numbers. C=256Hz is an octavisation of 1Hz.

But... still, 1Hz = 1 second = a certain quality of pitch if you go a few octaves higher.

What kind of other time unit would be more useful? Or - perhaps - paralel to the law of octave = 2:1 there is some other 12-TET meaningful system, that is based on different ratio? I need check how the equivalent of notes will look like, if the calculus was based on sexagesimall system, 60:1 (-;