Kaparat Pasha on Rosh Chodesh

Why do we add "Kaparat Pasha" during a leap year in the Rosh Chodesh Mussaf ? What is the mistake we are asking for atonement for and why does this mistake only take place before Adar II (when the months would be the same whether it was a leap year or not). I have heard that the mistake is that if this year were not a leap year, then Adar II would really be Nisan and we therefore would be eating Chomtetz on "Pesach". However, this mistake begins at Rosh Chodesh Adar II not before it, and we STOP adding Kaporas Poshah from Nisan onwards.

The Musaf of Rosh Chodesh contains a series of blessings for the new month, beginning with: "Chadesh aleinu et ha'chodesh hazeh...". The original version (pre-13th century - ashkenaz), to be rcited each and every Rosh Chodesh - leap year not withstanding - concluded with:"limchilat cheit, v'lislichat avon, u'lchaparat pasha". From our Yom Kippur machzor (as well as from multiude of Tanachic sources), we learn that three categories of sin exist in Halacha: cheit, avon, and pesha. Each are remedied individually by: "selicha, mechila, and kapparah". (See, Rav Soloveitchik, On Repentance, for analysis). The "Chassidei Ashkenaz" of the 13th century (not at all to be confused with modern Chassidism) "fine-tuned" certain Tefillot to conform to appropriate numerical categories. Simply counting up the series of blessings found in "Chadesh aleinu...", one discovers that there are 13 blessings. The innovation in the siddur had to do with artificially placing prarenthesis around the 13th blessing (which just happens to be "u'lchaparat pasha"), and reciting monthly only 12 blessings -obviously corresponding to the number of months throughout the year - while maintaining the 13th "in reserve" for the leap year, which carries the 13th month, and hence that year's Rosh Chodesh Musaf deserves the extra blessing. Actually, we were to begin adding the 13th blessing (i.e. "u'lichapart pasha) as early as Rosh Chodesh Nisan. However, as Chazal teach us (Sanhedrin1:-14:) that Bet Din would only publicize the leap year to the masses only from Rosh Chodesh Cheshvon onwards, we, therefore, have incorporated a rememberance to this Halacha by only "upgrading" the leap year Musaf from Cheshvon onwards until (and including) the end of the lunar year: Adar Sheni. Rabbi Aaron Adler