A Guide to the Lunisolar Spreadsheets
The are some spreadsheets that describe various possible cycles for a
rule-based lunsolar calendar.
Each cycle has a fixed number of years, months and days.
The spreadsheets are
You need Microsoft X-cell or emulator of such to read the xls spreadsheets.
Each row in the spreadsheet corresponds to a lunisolar cycle.
You can create your own cycle by saving your own copy of the spreadsheet,
then modifying the figures in the first three colums of a row.
The other figures in the row change to their correct values for the new cycle.
You may copy a row before modifying its copy.
The Speadsheeet Columns
Each row of the spreadsheet corresponds to a cycle
defined by its first three columns (A, B and C).
Here I define the columns.
This is the total number of years in the cycle.
B: Long Years
This is the number of years in the cycle that have an intercalary month.
This is the number of days in excess of what would occur
if all 12-month years had 354 days
and all 13-month years had 384 days.
If the basic year has 12 months of 354 days and
the intercalary month has 30 days,
then the abundance is the number of years with an additional day (abundant years).
E: Leap Years
This is the number of leap years in the
same cycle of the equivalent solar calendar.
E = C + 30B - 11A
This is the number of half days in excess of 29.5 per month,
which is the same as the number of Yerms in the
same cycle of the equivalent lunar yerm calendar.
F = B + 2C
G: Mean Year
The mean number of days in a year of the cycle.
G = 365 + E/A
G = I/A
In an accurate cycle this is between 365.2416 to 365.2427.
H: Mean Month
The mean number of days in a month of the cycle.
H = 29.5 + F/(24A + 2B)
H = 29.5 + F/(2J)
H = I/J
In an accurate cycle this is between 29.53055 to 29.5306.
This is the total number of days in one cycle.
I = 354A + 30B + C
I = 365A + E
This is the total number of months in one cycle.
J = 12A + B
K: Saltus Lunae
This is the number of Saltus Lunae corrections needed
for Epacts or Ogam Wheel in one cycle.
K = 30B - 11A
K = E - C
L: Truncated Metonic Cycles
The 19-year Metonic cycle of 235 months is out by about 2 hours.
For longer cycles this accumulates to over a day.
The Metonic cycle can be corrected by occasionally truncating it to
11 years of which 4 have an intercalary month.
L = 7A - 19B
This is a name or brief description of the cycle in the row.
It is not calculated.
Other Spread Sheets
The spreadsheet Lunisolar_391_334_315.xls
calculates the number of 391-year, 334-year and 315-year cycles for a
given lunisolar cycle.
The defining columns are the same as before (Years, Long, Abundant)
and the derived columns are the
number of 391-year (E), 334-year (F) and 315-year (G) cycles.
These are calculated thus:
E = -37A +101B -C
F = +32A -89B +4C
G = +12A -31B -3C
Then there are columns for the number of months and days and then the mean year and mean month.
this is done for many accurate lunisolar cycles (ordered by length).
Spreadsheet Lunisolar_333.xls with
web page shows various lunisolar cycles
made up of 391-year, 334-year and 315-year cycles.
The defining columns are the numbers of 391-year (A), 334-year (B) and 315-year (C) cycles
and the derived columns are
- E: Years (
= 391*A + 334*B + 315*C)
- F: Long Years (
= 144*A + 123*B + 116*C)
- G: Abundant (
= 76*A + 65*B + 61*C)
- I: Months
- J: Days
- K: Mean Year
- L: Mean Month
- N: Leap Years
- O: Yerms
- P: Saltus Lunae
- Q: Truncated Metonic Cycles
Karl Palmen April 2011