What are butsumetsu (Buddha's death) and tomobiki (trail days)?

These days originated from the rokuyo (siz days) cycle, a concept from the Edo period (1600-1868) in which six different fortunes succeed each other in this order: Sensho, tomobiki, Sempu, Butsurnetsu, Taian, and Shakku.
This is a kind of fortune-telling calendar which came from China.
Each day has its advantages and disadvantages, but butsumetsu is considered the worst day, so people avoid holding weddings on that day.
The number of weddings on butsumetsu is about a third of those held on the good luck day of taian.
Tomobiki is neither a good nor a bad day, but it literally means "pull away friends," so people do not like to have funerals on this day.
There are no scientific grounds for these folk beliefs, but they have a deep-rooted influence, even today.