${\gamma_A}$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. ${\gamma_B}$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{{{\gamma _A}}}{{{\gamma _B}}} = \left( {1 + \frac{1}{n}} \right)$, then the value of n is ____