Abarim Publications' online Biblical Hebrew Dictionary
There are two separate verbs קטר (qatar) that either have nothing to do with each other, or there aren't two roots at all; just one:
The denominative verb קטר (qatar I) means to burn incense, or sacrifice something that will result in lots of pleasing smoke (Exodus 29:13, Isaiah 6:4, Jeremiah 19:13). Essentially this verb means "to make to rise up in smoke". According to HAW Theological Wordbook of the Old Testament, a similar verb in Babylonian means simply to rise. And according to BDB Theological Dictionary the Assyrian cognate means to smoke.
It should be noted that turning something into smoke and letting it waft about mimics the non-discriminatory or non-selective distribution of energy and blessings that mark God, and his sun and rain and even his Spirit (Matthew 5:45, Joel 2:28). Modern philanthropy imagines it can do better than God, and tends to select to whom it gives. But giving life to one is the same as taking it from another, and the best intentions of the most generous selective givers have the exact same effect as the purifying efforts of people like Hitler. Godly people give to whomever comes along, without testing them first on their merit and virtue. Ungodly and evil people use their own standards to try their visitors, and reward them to the degree of similarity to themselves. Godly people use their wealth to bring forth a godly diversity in a grateful world. Evil people use their wealth to forge a desperate world into their own image.
In the Biblical symbolic structure, incense burning or otherwise producing a pleasing smoke, is much more than just pleasant. Converting an item into smoke allowed it to "rise" into heaven as a sort of smoke-mail, so to speak. But this not simply because smoke rises but because it dissipates and seems to disappear into another dimension. God, after all, is everywhere and not only "up there". Uniquely in the religiously arena, the Hebrew prophets campaigned vehemently against the old illusion that heaven was "up there," and that high places would be closer to God than any location on sea level. Hence the Tower of Babel, which reached into the sky, was destroyed - Genesis 11:4; Lifting eyes to heaven and worshipping stars was condemned - Deuteronomy 4:19, Jeremiah 8:2, Zephaniah 1:5; So called high-places were condemned - Deuteronomy 12:2, Psalm 78:58; The Word is not on a high mountain but in us - Deuteronomy 30:14; And the Kingdom of God is not in outer space but in our midst - Luke 17:21.
Creating smoke has a very strong spiritual dimension. Hence David sings, "may my prayer be counted as incense before Thee" (Psalm 141:2), and John the Revelator sees golden bowls full of incense that represent the prayers of the saints (Revelation 5:8, 8:3). Paul speaks of the sweet aroma of the knowledge of Him, and "us" being the aroma of Christ to God (2 Corinthians 2:14-15). And when Jesus "rose," his disciples were gazing intently into the sky, only to be told off by the angels (Acts 1:11). Yes, clouds took Jesus from sight, but it is by no means implied that he sailed off into space.
Other derivations of this root all have to do with incense or smoke:
- The feminine noun קטרת (qetoret), meaning incense or perfume (Ezekiel 16:18).
- The masculine noun קיטור (qitor), meaning thick smoke (Genesis 19:28, Psalm 119:83).
- The feminine noun קטר (qitter), meaning incense (Jeremiah 44:21 only).
- The masculine noun מקטר (miqtar), place of sacrificial smoke (Exodus 30:1 only).
- The similar masculine noun מקטר (muqtar), incense (Malachi 1:11 only).
- The feminine noun מקטרת (miqteret), censer (Ezekiel 8:11).
- The feminine noun מקטרה (meqattera), incense altar (2 Chronicles 30:14).
- A variant that isn't treated by HAW Theological Wordbook of the Old Testament but is by BDB Theological Dictionary is קטורה (qtwrh). It means incense, is used only in Deuteronomy 33:10 and is pretty much identical to the name Keturah
The verb קטר (qatar II) is a dubious word, according to BDB Theological Dictionary, which also submits that it apparently means to shut in or enclose. It occurs in the Bible only once, in Ezekiel 46:22 in the plural construction קטרות חצרות (qeterot haserot), meaning "enclosed(?) courts".
Some scholars have proposed that this verb doesn't really exist and that Ezekiel 46:22 contains a typo and the author meant קטנות (qatonot) from the verb קטן (qaton), meaning to be small.
None of the consulted sources, however, proposes that this "second" verb קטר (qatar) is really not a second but still the first one, and that it means smoky or nice smelling courts. After all, Ezekiel's host explains that "these are the boiling places, where the ministers of the house shall boil the sacrifices of the people" (Ezekiel 46:24).