Ritual impurity and physical impurity

“The Israelites do not receive purity from their physical ritual impurities on the Day of Atonement, presumably because they have already received it directly through rituals earlier in the year. But remedying sin is another matter. First it requires sacrificial כפר, then divinely granted forgiveness (סלח), and finally communal purification (טהר) on the Day of Atonement. Therefore, on the Day of Atonement the people reach the טהר stage of כפר with regard to their sins that is equivalent to the טהר stage reached earlier in the year with regard to their ritual impurities. This is evident in the striking parallel between Num 8:21, expressing the טהר goal of an outer-altar purification offering that removes physical ritual impurity from the Levites, and Lev 16:30, stating the טהר benefit of the communal Day of Atonement rituals with regard to sins of the entire community:
Num 8:21: ‏וַיְכַפֵּ֧ר עֲלֵיהֶ֛ם אַהֲרֹ֖ן לְטַהֲרָֽם, and Aaron effected purgation on their behalf to purify them.
Lev 16:30: ‏יְכַפֵּ֥ר עֲלֵיכֶ֖ם לְטַהֵ֣ר אֶתְכֶ֑ם, . . . shall purgation be effected on your behalf to purify you.
In each of these verses, כפר for the collective offerer (Levites or whole community) cleanses (pi`el of טהר) them.”—Cult and Character, pages 231-232

<idle musing>
Did you follow that? I didn't think so :) It is difficult to follow without the context. What Gane is arguing is that physical impurities were cleansed through offerings at a higher level throughout the year than ritual impurities, which includes sins of omission and commission, were. So,טהר cleansing had to be reached for both of them in order for forgiveness (סלח) to happen. At least, I think that is what he is saying...
</idle musing>