Ring oscillators are not really resonant, I wonder whether
you are just setting yourself a task with no useful result.
They certainly are not small-signal resonant once you get
to a significant number of stages - at some point the
signals become bang-bang, square, and there is nothing
linear going on except momentarily as stages cross the
inverter's linear region one after the other.
Ask yourself what use any calculated Q number would
have.
If you want to get at phase noise, you should look to
stage edge-rates and supply / ground rejection (slim
to none), the edge rate slope transforms voltage noise to
"time noise" (jitter, phase noise depending on how you
care to express it) during the linear intervals of the
stage's cycle.
I wouldn't expect (but could be wrong) a Q
N relation
based on a small signal linear type tank oscillator to
hold much relevance to a RO's behaviors. Transistor
noise is going to be dwarfed by all of the thrashing.