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I'm trying to pin down an algorithm for calculating when to start saying ותן טל ומטר in diaspora. (In Israel it begins 7 Cheshvan.) I've gotten that we need to know how many centuries passed since 1500 on the Gregorian calendar, but I'm confused how to factor in the fact that three years every 400 years was treated differently.

How would you calculate Tekufat Tishri for any given year?

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Near-duplicate of judaism.stackexchange.com/questions/11985. Really, this question is lacking in motivation: you don't indicate why you want to know about t'kufas Tishre, why it's important to the calculation of when to start saying "v'sen tal umatar". –  msh210 Mar 13 '12 at 15:36
    
@msh210 I'm getting the feeling Moshe wants a formula to use in one of his famous apps (as evidenced by his user profile). –  Double AA Mar 14 '12 at 2:32
    
@DoubleAA - Haha, and right you are. I studied this in a few places, but I was feeling a bit lazy while coding and decided it makes a good question for this site regardless. –  Moshe Mar 14 '12 at 2:49
    
@Moshe Which is why I tried to write out a formula in my answer that would be useful in code, even if no one else will really benefit by reading it. –  Double AA Mar 14 '12 at 3:05
    
@DoubleAA I'm going to have to go over it again, but thanks for the starting point. Too tired to look at the moment. Also, Ultimate Omer 2 just got an update approved. Please email me for a promo code as thanks for your help. moshberm {at} gmail, thanks. –  Moshe Mar 14 '12 at 3:19
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2 Answers

This past tekufat tishrei was October 7, 2011 at 9 PM. To calculate the next tekufat tishrei: add six hours to the previous year's time, while subtracting 24 hours for every civil leap year passed in between tekufot tishrei.

Source

To generalize, tekufat tishrei for future years is on October 7 at time: ((6 hours*(year mod 4)) - 3 hours) + (24 hours * (ceiling (0.75*(floor ((year - 2000) / 100)))))

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I'm not sure now if my math works out. I think I'm on the right track, but maybe that aspect of the question better belongs on mathematics.SE –  Double AA Mar 13 '12 at 17:47
    
Ok I think that should do it. –  Double AA Mar 13 '12 at 17:50
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Since your need seems to be to figure out "when to start saying ותן טל ומטר in diaspora", I'll just focus on that (and ignore the mention of the tekufah in the title):

To simplify things, start with the date November 21.

You will then need to adjust based on two rules:

  1. If the following year is a Gregorian leap year, push the day off by one (i.e. November 22).
  2. Then add days based on the drift between the Julian and Gregorian calendars [see the chart]. This drift increases by 1 day every 100 years, except where the 100th year is divisible by 4 (e.g. 2000).

For example: This year (2011) is the year before a leap year. It also happens to be that we are running a 13 day difference between Julian and Gregorian. So take November 22, add 13 days, and voila: December 5, 2011 emerges.

And you should definitely read this for more.

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Is there a way to figure out that chart algorithmically? Number of centuries since "year 500"? –  Moshe Mar 30 '12 at 4:45
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