Koshogatsu (小正月)
Koshogatsu is the day of mochi no hi in the New Year (January 15th of the old lunar calendar, or the first full moon of the New Year). Today, koshogatsu may be celebrated on January 15th of the new calendar (solar calendar). This term is used in contrast to Ooshogatsu (the big or primary New Year's Day), which refers to New Year's Day. It is considered that the term is a relic of the time when the mochi no hi was regarded as the first day of a month, before the Chinese-style lunar calendar was introduced. Normally, matsu no uchi (the period in which matsu kazari (pine decoration) is displayed during the New Year) should last up to Koshogatsu; even today, matsu no uchi lasts until Koshogatsu of January 15th in the Kansai and Kinki regions.
There was a custom of eating azukigayu (adzuki beans and rice gruel) on the morning of Koshogatsu. It is recorded in writings such as "Tosa Nikki" (Tosa Diary) and "Makura no Soshi" (The Pillow Book) that azukigayu was eaten on Koshogatsu in bygone days. Even today, in some areas such as the farming villages of the Tohoku region, there is a custom of eating azukigayu before the sagicho (ritual bonfire of New Year's decorations). In these regions, it is considered taboo to eat an adzuki bean (or red food in general, including meat) during the period from New Year's Day until Koshogatsu.
In contrast to Ooshogatsu, which is full of events for welcoming Toshigami (god of the incoming year) and Sorei (ancestral spirit, being the collective of ancestral spirits that have lost their individuality), Koshogatsu is centered around homey events and events relating to agriculture, such as praying for a good harvest. In some regions, Koshogatsu is called Onna-shogatsu (Women's New Year, also called Me-shogatsu) to thank housewives for their hard work over matsu no uchi, during which they weren't supposed to have to work in the kitchen until Jinjitsu (in the lunar calendar, the seventh day after New Year's Day).
Since genpuku no gi (the ceremony of attaining manhood) was conducted in Koshogatsu, January 15th became a national holiday called Coming-of-Age Day. However, since it's difficult to relate Coming-of-Age Day to Koshogatsu based on the name of the holiday, and because people had lost their familiarity with Koshogatsu, in 2000 Coming-of-Age Day was changed to the second Monday of January.
China's Yuan Xiao Jie
Yuan Xiao Jie (the Chinese lantern festival held on the 15th of the first month of the lunar calendar, called Genshosetsu in Japanese) is also called Shang Yuan Festival (Jogensetsu in Japanese) and is celebrated according to the old calendar. This is the fifteenth significant day counting from the New Year's Day, which is Ooshogatsu, and this period is called Chinese New Year. Because Koshogatsu falls on the night with a full moon, people celebrate Koshogatsu at night by installing chochin (Japanese paper lanterns) and objects such as dragons containing lights (also referred to as lanterns). Further, people boil and eat round rice dumplings called 'Yuan Xiao' (glutinous rice balls), which represent the full moon.
For young people in Malaysia, this is also a night on which to have romantic conversations with members of the opposite sex.