The core here is setting something into proper order. Fix a broken object and you repair it; set a thing in place and you install it; agree on the right order for everyone and you have a standard or a regulation. The same root gives tikkun, the deep idea of repair, and taknon, the dry word for a set of rules. Each word below is a different way of putting things right, verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
No pa'al is in use for this root; the work is shared between pi'el (correcting what is wrong) and hif'il (installing/arranging from scratch). The hitpa'el לְהִתַּקֵּן carries the reflexive-passive sense: a thing that gets put right. That is why so many nouns here come in pi'el and hif'il pairs.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.