Fig.~\ref{rad_turb} is a plot of turbulent line width on a 1 pc scale as a function of surface density, $\Sigma$, described by Eq.~\ref{density}. 

\begin{equation}
\Sigma = \frac{M_{\mathrm{lum}}}{\mathrm{\pi} R^2}.
\label{density}
\end{equation}

From Fig.~\ref{rad_sig} and Fig.~\ref{rad_turb}, and confirmed in Table \ref{means}, which presents the geometric mean of turbulent line width on a 1 pc scale, $\overline{\sigma_0}$, and the corresponding standard error, $SE(\sigma_0)$, nuclear clouds tend to be more turbulent and dense than disk clouds, but there is no statistical difference in the average turbulence of arm versus inter-arm populations. Though, the inter-arm clouds do tend to have lower surface densities than both arm and nuclear clouds as shown in Fig.~\ref{r_sigma} and Fig.~\ref{rad_turb}. Note that we ignored arm datum with abnormally large values of $\Sigma > 10^3~M_{\odot}\ \mathrm{pc}^{-2}$ after finding that their surface densities were an order of magnitude smaller when calculated with area derived radii rather than $\sigma$ derived radii. Though the turbulent properties are changing among GMAs, the agreement with a single line suggests that the GMAs are all virialized and thus their virial mass is consistent with their luminous mass.
