<p>In 1582, when the Gregorian calendar was instituted, in addition to removing ten days from the month of October, four days were subtracted from the age of the Moon. Was this number observed or computed? My computation is that in the 12x1257 (= 15084) months between the council of Nicea in 325 and the Gregorian reform in 1582, the discrepancy between the nominal synodic month (29.5 days) and the astronomical synodic month (29.53059 days) would amount to a difference of 461 days (= .03*15084)! Even allowing for the loss of full synodic months, the difference is on the order of 18 days (= Mod[461, 29.5]). If the four-day discrepancy was observed, is there any way to reconcile it with the 18 day value? That is, can the four days be explained computationally?</p>

CC BY-SA 4.0
2024-11-25T23:21:03.413Z
It would mostly likely be some of both observation and computation.  Algorithms at the time needed to be updated with recent observations to make good predictions.  I have never heard of the 4 day correction, but it's usefulness would have been short lived, as lunar predictions still needed to be updated with observations.  And the calendar was adopted at vastly different times around the world, which would have required different corrections.
Greg Miller
CC BY-SA 4.0
2024-11-26T09:18:58.353Z
The ecclesiastical calendar uses the Metonic cycle of 19 solar years = 235 lunations, with 7 intercalary months per 19 year cycle, giving a mean month length of ~29.53 days. It's a little bit messy, due to leap days.
PM 2Ring
CC BY-SA 4.0
2024-11-26T09:21:18.627Z
From https://en.wikipedia.org/wiki/Date_of_Easter#Gregorian_reform_of_the_computus "However, 19 uncorrected Julian years are a little longer than 235 lunations. The difference accumulates to one day in about 308 years [...] At the time of the reform, the epacts were changed by 7, even though 10 days were skipped, in order to make a three-day correction to the timing of the new moons". It's not clear why the correction was 3 rather than 4 days.
PM 2Ring
<history><moon-phases>
Gregorian lunar correction
Spencer Rugaber
# Gregorian lunar correction

(Asked by: username_0 on 2024-11-25)

In 1582, when the Gregorian calendar was instituted, in addition to removing ten days from the month of October, four days were subtracted from the age of the Moon. Was this number observed or computed? My computation is that in the 12x1257 (= 15084) months between the council of Nicea in 325 and the Gregorian reform in 1582, the discrepancy between the nominal synodic month (29.5 days) and the astronomical synodic month (29.53059 days) would amount to a difference of 461 days (= .03\*15084)! Even allowing for the loss of full synodic months, the difference is on the order of 18 days (= Mod[461, 29.5]). If the four-day discrepancy was observed, is there any way to reconcile it with the 18 day value? That is, can the four days be explained computationally?

**Tags:** history, moon-phases

> **Comments:**
> **username_1**: It would mostly likely be some of both observation and computation.  Algorithms at the time needed to be updated with recent observations to make good predictions.  I have never heard of the 4 day correction, but it's usefulness would have been short lived, as lunar predictions still needed to be updated with observations.  And the calendar was adopted at vastly different times around the world, which would have required different corrections.  
> **username_2**: The ecclesiastical calendar uses the Metonic cycle of 19 solar years = 235 lunations, with 7 intercalary months per 19 year cycle, giving a mean month length of ~29.53 days. It's a little bit messy, due to leap days.  
> **username_2**: From https://en.wikipedia.org/wiki/Date_of_Easter#Gregorian_reform_of_the_computus "However, 19 uncorrected Julian years are a little longer than 235 lunations. The difference accumulates to one day in about 308 years [...] At the time of the reform, the epacts were changed by 7, even though 10 days were skipped, in order to make a three-day correction to the timing of the new moons". It's not clear why the correction was 3 rather than 4 days.  

---

## 0 answers

