The practice of Yom Kippur Katan is held on erev Rosh Chodesh (by some) so that we can maintain the element of kapparah essential to Rosh Chodesh but not compromise the celebration of the day by injecting a tension between repentance and celebration.
Why do we avoid this tension? Yom Kippur, itself, has a dual nature as does Tish'a B'av (in that it is called a mo'ed which might have something to do with the birth of the moshiach).
If we have precedent for having a day which has two conflicting moods, why don't we import the Yom Kippur Katan aspects to Rosh Chodesh itself? Those who say vidui before tachanun could still say vidui at least, even if they omit tachanun, itself (as an example of a compromise position).
If one answers that the nature of the kapparah on Rosh Chodesh is categorically different from that on Yom Kippur (as the linked answer above explains) then why do we put traditional kapparah prayers such as the techinot and mini-neilah in mincha on Yom Kippur Katan and expect them to reflect the aspect of kapparah referenced in the musaf on Rosh Chodesh? In fact, if the nature of the kapparah is different, why should Yom Kippur Katan be related to Rosh Chodesh at all? An echo of Yom Kippur would not effect the same type of kapparah as what Rosh Chodesh was supposed to be!
It seems to me that either Y"KK addresses the kapparah of Rosh Chodesh and might as well be on Rosh Chodesh at least in part, or it has no relation to the kapparah and shouldn't be tethered to Rosh Chodesh at all. Does anyone have any insight into this?
