Alternating Periodic Sequences

I can make a batch of these "mean yerm" formulas. I think they work because 730 = 2*365. There's a sort of range between 727 and 733 which are prime numbers. So, there are certain subdivisions of the year and a "mean yerm" to each...

mean yerm of 8ths = 1 / [  2 - ( 728 / Y ) ]

mean yerm of 3rds = 1 / [  2 - ( 729 / Y ) ]

mean yerm of 10ths = 1 / [  2 - ( 730 / Y ) ]

mean yerm of 17ths = 1 / [ ( 731 / Y ) - 2 ]

mean yerm of 12ths = 1 / [ ( 732 / Y ) - 2 ]

Some years lead to integer mean yerms. These 5 "elegant" years are

365 & 71 / 293
365 & 119 / 491
365 & 365 / 1507
365 & 8 / 33
365 & 39 / 161

and all cycles are odd numbered. These cycles are then described by their alternating periodic sequence,

8ths = 46, 45, ...
3rds = 122, 121, ...
10ths = 37, 36, ...
17ths = 21, 22, ...
12ths = 30, 31, ...