Frequency curve as a function of Galactic radius. The solid black line is the rotational frequency curve of the potential, whereas the dashed and dot-dashed lines are rotional frequency plus or minus 0.25 and 0.5 times the epicyclic frequency, ${\kappa }_0(R)=\sqrt{(2\text{Ω}/R)\text{d}\left(R^2\text{Ω}\right)/\text{d}R}$. The horizontal blue and red lines are the pattern speed of the bar and the spiral arms, respectively. The vertical dashed and dot-dashed lines are the corresponding resonances for bar and spiral arms.