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.

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.

Each row of the spreadsheet corresponds to a cycle defined by its first three columns (A, B and C). Here I define the columns.

Defining Columns

A: Years

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.

C: Abundant

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).

Derived Columns

E: Leap Years

This is the number of leap years in the same cycle of the equivalent solar calendar.
```E = C + 30B - 11A
```

F: Yerms

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.

I: Days

This is the total number of days in one cycle.
```I = 354A + 30B + C
I = 365A + E
```

J: Months

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.

Lunisolar_391_334_315

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.

In Lunisolar_391_334_315_A.htm, this is done for many accurate lunisolar cycles (ordered by length).

Lunisolar_333

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