Most countries which use the Gregorian Calendar accept the 7-day-week system. So does Japan now. However, traditionally Japan used to use the 6-day-week system which originates in China.
先勝（せんしょうsenshou / さきがちsakigachi, etc）
友引（ともびきtomobiki）
先負（せんぷsenpu / さきまけsakimake, etc）
仏滅（ぶつめつbutsumetsu）
大安（たいあんtaian）
赤口（しゃっこうshakkou / せきぐちsekiguchi, etc）
They rotate in this order. However, as the first day of each month of the old lunar calendar has a particular day assigned (i.e. in the old lunar calendar, each date has the same day of the week every year), in the modern Gregorian calendar, the rotation does not look regular.
Each day of these 6 has a different jinx associated with it and some people in Japan still consults with this calendar when they decide the date for an important event such as a wedding. The jinx are:
先勝（せんしょう/さきがち, etc）: morning is lucky, so better get things done early.
友引（ともびき）: a bad day for having a funeral as it pulls friends to the other world. For this jinx, some crematoriums are closed on this day.
先負（せんぷ/さきまけ, etc）: Not suitable for urgent business and/or competition
仏滅（ぶつめつ）: the unluckiest day of the week and few people get married on this day, though because of that, many wedding venues give discounts so it is the best day to have an inexpensive wedding.
大安（たいあん）: the luckiest day of the week, so many couples get married on this day and quite a few people/companies still choose this day for starting something new.
赤口（しゃっこう/せきぐち, etc）: lucky between around 11 am and around 1 pm but the rest of the day is unlucky.
By the way, today (10 October 2018) is 仏滅 (butsumetsu).
If you want to know which day it is, you can add this calendar to MS Outlook and/or Google calendar. If you want to know how, please email me.
