If, for example, the mineral is scratched by quartz but not by orthoclase, then its hardness is between 6 and 7.
[i] Use leap months. In the traditional Chinese and Jewish calendars most years have 12 months, but some have a 13th month. In these luni-solar calendars the length of the year varies from 354 to 384 days.
[ii] Define 12 synodic lunar months to be a year and don't worry about the length of the year. This is the solution of the Islamic calendar. Since the Islamic year has only 354 or 355 days, its length does not match the cycle of the seasons.
[iii] Observe the solar year and let the months be 12 arbitrary periods; don't worry about the Moon. This is the solution adopted by the Romans, who established the civil calendar we use today. In this calendar, all months have 30 or 31 days except the second month, February. February has 28 days in ordinary years and 29 in leap years. See also year [2].