The Alternating 8th Month

What have hitherto been called solar months have been twelfths of a solar year. I don't know if a "solar yerm" and a "natural solar yerm" have been defined but it can't be other than;

N = 1 / ( [ 61 / W ] - 2 ),  W = Y / 12

N = 1 / ( [ 732 / Y ] - 2 )

a period of about 241 days. Anyway, I found the pattern of the alternating 8th solar month

30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( -- )

and the intervention after 103 months.