Basically, I'm interested in calendars. A lot of the worldbuilding community seems convinced the lunisolar one is the best out there. I tend to somewhat diasagree, even if it is neat since you have at the same time an account of the moon and an account of the Sun. Problem is of course that it's so variable, having 7/19 years of 29 days longer is problematic to me.
I'm proposing an alternat Lunisolar calendar here. It avoids some of the querks of adding a full month. Instead of adding a full month every no and then you add a week roughly equivalent to a fourth of the phase period.
Thus you have still month aligned to the phases but every now and then the month start with a half, full or new moon. if we made the calculation (i'll do it more carefully though) you would have : 12*29.54059+29.54059/4=361.8722275 days And adding the intercalary week you would have : 12*29.54059+2*29.54059/4=369.257375.
Using the Metonic cycle (19 ☉years≅235 ☽ months≅6940 days) we can calculate when those intercalary weeks should be placed : Let say we aproximate the normal year as being 362 days so if we count only with them : 19*362= 6878 Then let's subtract this time to the Metonic cycle : 6940-6878= 62
Then let's devide this duration by the lunar week.
(29.54059/4= 7.3851475) 62/7.3851475=8.3952283959 8*7= 56 9*7= 63 7*8=56 8*8=64
So now a bunch of solutions can be chosen :
1) Not doing one of the 9 intercalary weeks some Metonic cycles so that the average of total leap days is 62
2) Do an intercalary weeks one day shorter.
3) Having 7 intercalary weeks and 1 intercallary half month of 13 days
4) Another general solution is to make sure the normal years are closer to their total duration using their true length of 361.8722275 days*19= 6 875.5723225 so 6875 or 6876 so the number of days that need to be put upon the intercalary weeks is then 64-65 which is slightly better since then you can have 8 intercalary weeks of 8 days. I'm pretty sure we can come up with even better solutions but i think it's a good compromise.