A tuning system in music is a system which describes the spacing of notes relative to the root, usually ending in the octave. The tuning system we use today is Equal Temperament, which evenly spaces the 12 notes in an octave. This results in intervals that look like this: 2^(0/12) 2^(1/12) 2^(2/12) 2^(3/12) 2^(4/12) 2^(5/12) 2^(6/12) 2^(7/12) 2^(8/12) 2^(9/12) 2^(10/12) 2^(11/12) 2^(12/12). They appear to be natural numbers, but every single one of them besides the root and octave are irrational numbers. Do not be deceived by the natural cent values. Cents as a measurement were made standard by Alexander J. Ellis in the 1800s, long after Equal Temperament was established. I could just as easily redefine cents to be a shorter interval and 2,000 in between each octave which would align well with Just Intonation. (1/3)