There is nowhere in the Torah that specifically mentions that the calendar cycle is to be based mainly on a lunar cycle. (I'm intentionally omitting the notion of the solar / seasonal influence of adding an extra month, occasionally, as I understand why this is done.)

The Gregorian calendar and many other calendars are primarily solar based. The Gregorian uses the solar orbit as its base for defining a year and divides it into 12 segments with each segment called a "month".

In contrast, the Judaic calendar is based on the molad which is based on the actual calculation of the lunar orbit. (I'm not talking about the additional requirement to visibly see the 1st crescent, witnesses, Sanhedrin, etc. That's derived separately. But the basis is still the molad which is based on the lunar orbit.)

How is this requirement derived or is this halacha Lemoshe Misinai? (part of Masorah)

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    Wouldn't the pasuk Shmos 12:2 show how Moshe is being told how the months are determined? From there we see that it is lunar based and how he was given the halacha. – sabbahillel Feb 2 '17 at 16:34
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    Do you realize the gregorian calendar splitting a year into 12 parts is based on the moon? They just got tired of actually paying attention to the moon. Why do you think they split it to 12 sections? – Double AA Feb 2 '17 at 16:37
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    @DanF A chodesh is a month. A month is the moon. There's nothing else to it. It's just what the words mean. Everyone had lunar months. What other way was there to split up the year? You aren't presenting any viable alternative that isn't totally arbitrary or fundamentally mimicking the moon. – Double AA Feb 2 '17 at 16:37
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    @DanF הַחֹדֶשׁ הַזֶּה לָכֶם means Hashem showed Moshe the moon as he was declaring that it would be the basis for the period of time defined as "chodesh" which is translated as "month". See the Rashi on that pasuk. Since he was shown the moon and told exactly what it meant, then the pasuk is saying that this is the basis of the calendar. SInce the pasuk is saying that Moshe was shown it, then we see the halacha leMoshe being established (though before Sinai). – sabbahillel Feb 2 '17 at 18:59
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    In the Book of Esther, months are identified with Persian luni-solar calendar months. – A L Feb 2 '17 at 19:46

Rashi on Shmos 13:2 explicitly says that Hashem showed Moshe the moon and explained how the calendar was based and how the new month was to be determined. This explanation would include the rules for the chagim, the year (including leap year) and the specific times. It would be like a halacha leMoshe miSinai, except that it was at Yetzias Mitzraim.

Shmos 12:2

This month: Heb. הַחֹדֶשׁ הַזֶה, lit., this renewal. He [God] showed him [Moses] the moon in its renewal and said to him, “When the moon renews itself, you will have a new month” (Mechilta). Nevertheless, [despite this rendering,] a biblical verse does not lose its simple meaning (Shab. 63a). Concerning the month of Nissan, He said to him, “This shall be the first of the order of the number of the months, so Iyar shall be called the second [month], and Sivan the third [month].”

This: Moses found difficulty [determining] the [precise moment of the] renewal of the moon, in what size it should appear before it is fit for sanctification. So He showed him with His finger the moon in the sky and said to him, “You must see a moon like this and sanctify [the month].” Now how did He show it to him? Did He not speak to him only by day, as it says: “Now it came to pass on the day that the Lord spoke” (Exod. 6:28); “on the day He commanded” (Lev. 7:38); “from the day that the Lord commanded and on” (Num. 15:23) ? Rather, just before sunset, this chapter was said to him, and He showed him [the moon] when it became dark. — [from Mechilta]

  • may be that the word chodesh points a renewing of a natural phenomenon observed at the time of the statement החודש הזה לכם ראש חודשים – kouty Feb 2 '17 at 20:19

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