Why we Add ולכפרת פשע on Rosh Chodesh of a leap year until Chodesh Nissan

On Rosh Chodesh  of a leap year we added in the Shemona Esreh of Mussaf  the words  ולכפרת פשע
In a Leap Year, in addition to praying for good and for blessing, for joy and for gladness, for salvation and comfort, for sustenance and maintenance, for life and peace, for pardon of sin and forgiveness of iniquity”, we add a 13th request in respect of the additional month: “ולכפרת פשע-and for atonement of transgression”.

A possible reason suggested is that in case the Leap Year was mistakenly designated, and in consequence Chametz was eaten on Pesach, we pray for forgiveness. (טעמי המנהגים)
The 13 pleas are corresponding to the 12 expressions of praise “הללוי’ה-הללו-הללוהו”, and the last sentence “כל הנשמה” is said twice, in respect of the Leap Year. (תהלים קנ – תניא רבתי)