In an earlier note I mentioned the idea of the Pre-Islamic calendar using the Octaeteris (8 years with 3 leap months) during the 200 years it was lunisolar. This would fit in well with the idea of each leap month occurring after each regular
month in turn as suggested in
These two differ by the placing of only 4 of the 21 leap years, of which 2 are one year early and two are one year late.
I reckon the jitter of the corrected Octaeterides by taking the ‘ssLssLssLssLss’, which begins with the corrected 4th octaeteris. These 14 years have 4 leap years compared to 14*7/19 = 5.15789…. on average for 14 years. So
the jitter is 1.15789… months or exactly 22/19 months, which is 4/19 months more than the 18/19 months jitter of the Metonic cycle.
The 4/19 suggests that the above alignment with 4 leap years not synchronised is the best alignment one can get.