The Gregorian system in a new conception and layout, as a new style which combines solar and lunar cycles. The gregorian year is structured in 12 "holy nights" (the time between the 25 of December and 6 of January) and 12 real lunar month (synodic). This new calendar recombine loyalty to seasons with genuine lunar months, soothes the blurring of all other systems by the month "hug" of the 12 nights rounding.
The year starts on 6 January. 12 synodic months follow with alternately 30 and 29 days, ending on 25 December - more 12 nights (11 days) to complete the year. Imagine that throughout this layout the Gregorian calendar becomes acceptable for Muslims and Jewish people? Its real that lunar months do not start with new moon in every year, but are real lunar months at all...