The Hobbit Calendar is such:
2 Yule
Afteryule
Solmath
Rethe
Astron
Thrimidge
Forelithe
1 Lithe
Midsummer's Day
(Overlithe)
2 Lithe
Afterlithe
Wedmath
Halimath
Winterfilth
Blotmath
Foreyule
1 Yule
The two Yules and two Lithe, and Midsummer's Day are singular days. All of the months had 30 days. Overlithe is their leap day.
There's an in depth discussion of this in Appen. D in LotR. You can find Gondorian and Elvish calendars there too. I must say Appen. D was the hardest of the Appendices for me to read, but it's still interesting.
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