According to the old Japanese lunar calendar, January was called “Mutsuki”, which meant something like a month of family gathering and feasting. In January there are some days related to specific traditions and customs.
After New Year’s Day, January 2 is noted for the day of your “first dreaming.” If you have a bad dream it will indicate a bad year ahead, a sort of fortunetelling.
Then comes January 7, when we have rice porridge cooked with seven different kinds of vegetables. This is supposedly meant to keep you free from diseases; nowadays people welcome porridge which is “gentle to the stomach” especially after having heavy meals and a lot to drink during New Year.
Lastly, there is January 11 on which we eat rice cakes that have been offered to Shinto gods at home. Incidentally, January 4 is the birthday of my younger son and January 31 is that of my own.