The charged particle multiplicities of two- and
three-jet events from the reaction
e$^+$e$^- \rightarrow {\mathrm Z}^0 \rightarrow$hadrons
are measured for Z$^0$ decays to light quark (uds) flavors.
Using recent theoretical expressions to account for
biases from event selection,
results corresponding to unbiased gluon jets are extracted
over a range of jet energies from about 11 to 30~GeV.
We find consistency between these results and direct measurements
of unbiased gluon jet multiplicity from $\Upsilon$ 
and Z$^0$ decays.
The unbiased gluon jet data
including the direct measurements
are compared to corresponding results for quark jets.
We perform fits based on analytic expressions for particle
multiplicity in jets to determine
the ratio $r \equiv {\mathrm N}_g/{\mathrm N}_q$
of multiplicities between
gluon and quark jets as a function of energy.
We also determine the ratio of slopes,
$r^{(1)}$$\,\equiv\,$$({\mathrm{d}}{\mathrm N}_g/{\mathrm{d}}y)
/({\mathrm{d}}{\mathrm N}_q / {\mathrm{d}}y)$,
and of curvatures,
$r^{(2)}$$\,\equiv\,$$({\mathrm{d}}^2{\mathrm N}_g /{\mathrm{d}}y^2)
/({\mathrm{d}}^2{\mathrm N}_q / {\mathrm{d}}y^2)$,
where $y$ specifies the energy scale.
At 30~GeV,
we find $r$$\,=\,$$1.422\pm0.051$,
$r^{(1)}$$\,=\,$$1.761\pm0.071$ and
$r^{(2)}$$\,=\,$$1.98\pm0.13$,
where the uncertainties are the statistical and systematic
terms added in quadrature.
These results are in general agreement with theoretical
predictions.
In addition,
we use the measurements of the energy dependence of
N$_g$ and N$_q$ to determine an effective value
of the ratio of QCD color factors,
C$_A /$C$_F$.
Our result,
C$_A/$C$_F=2.23\pm0.14$~(total),
is consistent with the QCD value of 2.25.