For me, a "tertiary" would be someone who has very little regular connection with my day-to-day life. Some folks think of "Friends with Benefits" or "FwB", other use the rather more explicit term "fuck-buddy".
When I use the terms at all, I tend to think of them in terms of degree of decision-making, and sharing of resources. It has nothing to do with how much you love someone, and it most certainly has nothing to do with hierarchies.
If you're looking for a "I see you once a month, so we're tertiaries, but if I were to see you twice a month, we'd be secondaries" you are absolutely not going to find any hard-and-fast rules.
Could you tell us more about why you are interested in researching this? Maybe we can help you more.
Please check out The Birdcage - an open, friendly Polyamory forum for all parts of New York State
"Listen, or your tongue will make you deaf." - Native American Proverb