So a common term in Ireland and UK when I was there (tertiary education). When I talk with Americans, the pronunciation is different or is it a word they do not know? (is it like Quay, a word Americans mostly do not know the correct pronunciation)
Seems to differ, not being critical here, but I notice Google seems to have a new feature for pronunciation, you should see the 2 variants
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Tertiary, four syllables to identify #3 
I’ve only ever used it, and first encountered, in material science/engineering settings.
An alloy or ceramic compound can exhibit multiple phases (structures) of approximately the same chemistry, within a bulk specimen
I’ve wondered, but apparently quaternary is in fact a word.
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It seems to be consistent among words ending in -tiary
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I say Ter she airy
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