Take the 2-minute tour ×
Mi Yodeya is a question and answer site for those who base their lives on Jewish law and tradition and anyone interested in learning more. It's 100% free, no registration required.

How can I tell if a given year is a Hebrew Leap Year? The simpler, the better.

[Assuming we are using a fixed calendar, not like the "olden days".]

share|improve this question
add comment

5 Answers 5

up vote 19 down vote accepted

If you have a piano keyboard handy, you can use it as a mnemonic aid:

              Y mod 19 =

│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│  ▐██▌  ▐██▌  │  ▐██▌  ▐██▌  ▐██▌  │
│    │    │    │    │     │    │    │
│    │    │    │    │     │    │    │
│  0 │  3 │  6 │  8 │  11 │ 14 │ 17 │
└────┴────┴────┴────┴─────┴────┴────┘
  • half step = leap years 2 years apart
  • whole step = leap years 3 years apart
share|improve this answer
1  
That's pretty cool! –  Dave Mar 23 '11 at 6:59
1  
Daniel ben Noach, Welcome to mi.yodeya, and thanks very much for the awesome mnemonic and accompanying ASCII art! I look forward to seeing you around. –  Isaac Moses Mar 23 '11 at 13:36
    
So, is there a common consideration that causes this coincidence? Is it just that you want to put your two short intervals as far apart as possible in both cases? I don't know enough about music to understand what drove the design of scales and therefore pianos. –  Isaac Moses Mar 23 '11 at 17:18
2  
According to en.wikipedia.org/wiki/…, it's just a coincidence. –  Daniel ben Noach Mar 24 '11 at 0:06
add comment

A Hebrew Leap Year (in modern times) depends on which year of the 19-year cycle we are in. The years of the 19 year cycle that are leap years are: 3, 6, 8, 11, 14, 17, and 19. (to figure out which year of the cycle you're in, find the remainder of the current year when divided by 19).

It turns out there's a simple equation you can use:

(7y+1) mod 19 < 7 

[read, 7 times year, plus 1, divided by 19 & find remainder].

if the remainder is less than 7, it's a leap year. If it's 7 or greater, it's a regular year.

For example, for 5771 (this year):

7 * 5771 = 40397
40397 + 1 = 40398
40398 / 19 = 2126 remainder 4
4 is less than 7, so it's a leap year!

OR, you can use the "old-fashioned," non-mathy method of memorizing גוחאדז"ט - which comes out to: 3, 6, 8, 1, 4, 7, 9. Adding ten to the ones after 8 gets you: 3, 6, 8, 11, 14, 17, and 19 - like we found above.

share|improve this answer
    
I once came across a different equation in an old book about the Jewish calendar: (12y+17) mod 19 > 11. –  Alex Mar 17 '11 at 22:22
3  
Note that both R'yydl's and R'Alex's formulas require you to assume the numbers modulo 19 are 0, ..., 18, not 1, ..., 19 (or anything else). In fact, they're the same formula reworded, believe it or not: Because 7=-12 and 1=-18 (mod 19), we have 7y+1=-(12y+18)=-(12y+17)-1, so when 7y+1<7, 12y+17+1>-7=12 i.e. 12y+17>11. –  msh210 Mar 18 '11 at 2:40
3  
A little shortcut: Since 5700 is evenly divisible by 19, you can just use the last two digits for recent years (e.g. 71 in 5771). –  Dave Mar 18 '11 at 4:25
1  
@Dave, years 3, 6, 8, 11, 14, 17, and 19 of each 19-year cycle are leap years. It happens to be that if you multiply each of those by 7 and add 1 you get a number whose remainder mod 19 is 0, 1, 2, 3, 4, 5, or 6, and that the same is false of the other years. I don't think there's anything deeper than that to it. I can't think of any way to discover the formula other than trial and error, but perhaps there is a way... likely someone at Mathematics will know. –  msh210 Jun 22 '11 at 15:24
1  
@msh210 - Good Idea! See here: math.stackexchange.com/questions/46964/… –  Dave Jun 22 '11 at 19:37
show 4 more comments

Simpler is 5771 / 19 = 303 remainder 14 so it is a leap year.

share|improve this answer
4  
Yep. But that requires memorizing the 7 years that are leap years. –  yydl Mar 17 '11 at 22:56
add comment

Here's a version that can be done mentally. It works for all years between 5700-5799 (1940-2039):

1) Take the last two digits of the year, and add the second digit to half of the first. If there is a remainder, add 10. If this brings the total to 19 or more, subtract 19. You now know which year in the cycle it is. [Year 19 = 0.]

2) For cycle numbers greater than 7, add 1. Then check if it's evenly divisible by 3 -- if so, it is a leap year.

Example:

The last two digits of 5771 are 71.

1 + 3 (half of 7) = 4

Since there is a remainder: 4 + 10 = 14. --> [It is year #14 in the cycle.]

14 is more than 7, so we add 1, raising it to 15.

Since 15 is divisible by 3, it is a leap year.

share|improve this answer
add comment

After dividing the year by 19, if the remainder's digits have only curves or only straight lines, it's a leap year. Otherwise, it's not.

00 - all curved
03 - all curved
06 - all curved
08 - all curved
11 - all straight
14 - all straight
17 - all straight

Of course, this depends on the font you use. We're assuming that 0,3,6,8 are curved; 1,4,7 are straight, and 2,5,9 are mixed.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.