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All these words refer to the hierarchical organization of the society.
"Tlatoani" was the title of the ruler. The word derives from the local "nahuatl" language and denotes a spokesman. Huey tlatoani was the really highest one.
"Altepetl" was the city state, a local ethnically based province. The word is a combination of words for "water" and "mountain".
These city states were divided to "calpulli" ("suburbs") whose top executives were known as "calpuleque". There were also additional pipiltin (noblemen).