In music theory the consonance between two frequencies $a, b$ is said to be determined by the "simplicity" of the fraction $k = \frac{b}{a}$.
Example: A fifth ($k = \frac{3}{2}$) is sounds more consonant, then a major second ($k = \frac{9}{8}$).
I tried to formalise this notion on the set $\mathbb{Q} \cap [1,2)$ by defining the "simplicity" of a rational number as the least common multiple of the numerator and the denominator. This doesn't work since there are multiple ways to get get the same lcm. (e.g. $lcm(28, 15) = lcm(21, 20) = 420$)
Is it even possible to get a precise definition for this intuitiv notion of simplicity?