The Rabbanite Midrash relates that when God said to Moses "This month (HODESH) shall be for you the beginning of months" (Ex 12,2) the Almighty pointed up into the heavens at the crescent New Moon and said "When you see like this, sanctify! [=declare New Moon day]". This Rabbinic fairy-tale highlights an important point, namely that the Bible never comes out and says we should determine the beginning of months based on the New Moon. The reason for this is that the term for "Month" (Hodesh) itself implies that the month begins with the crescent New Moon. As will be seen, this would have been obvious to any ancient Israelite present when Moses recited the prophecies of YHWH to the Children of Israel and therefore there was no need to elucidate this concept any more than such terms as "light" or "dark". However, due to the long exile, we have lost the use of Biblical Hebrew in day to day speech. Therefore, we will have to reconstruct the meaning of Hodesh from the usage of the word in the Biblical text using sound linguistic principles.
He Created the Moon for Holidays
There can be no doubt that the biblical Holidays are dependent on the moon. The strongest proof of this is the passage in Ps 104,19 which declares:
"He created the moon for Mo'adim [appointed times]"
The Hebrew term Mo'adim [appointed times] is the same word used to describe the Biblical Holidays. Leviticus 23, which contains a catalogue of the Biblical Holidays opens with the statement: "These are the Mo'adim [appointed times] of YHWH, holy convocations which you shall proclaim in their appointed times [Mo'adam].". So when the Psalmist tells us that God created the moon for Mo'adim [appointed times] he means that the moon was created to determine the time of the Mo'adim of YHWH, that is, the Biblical Holidays.
"Hodesh" Is Related To the Moon
The above verse clearly teaches us that the holidays are related to the moon. But when the Torah was given Ps 104 had not yet been written by the Levitical prophets, and the question still remains of how the ancient Israelites could have known this. The answer is that the Hebrew word for month (Hodesh) itself indicates a connection to the moon. We can see this connection in a number of instances in which Hodesh (month) is used interchangeably with the word "Yerah", the common Biblical Hebrew word for moon, which by extension also means "month". For example:
"...in the month (Yerah) of Ziv,
which is the Second month (Hodesh)..." (1Kings 6,1)
"...in the month (Yerah) of Ethanim... which is the Seventh month (Hodesh)..." (1Kings 8,2)
Another proof that Hodesh is related to the moon (Yerah) is the phrase "A Hodesh (month) of days" (Gen 29,14; Nu 11,20-21) [meaning a period of 29 or 30 days] which is equivalent to the phrase "A Yerah (month/ moon) of days" (Dt 21,13; 2Ki 15,13). Clearly then Hodesh is related to "Yerah", which itself literally means "moon".
"Hodesh" Means New Moon (Day)
The primary meaning of Hodesh (month) is actually "New Moon" or "New Moon Day" and it is only by extension that it came to mean "month", that is, the period between one New Moon and the next. This primary meaning is preserved in a number of passages such as 1Sam 20,5 in which Jonathan says to David "Tomorrow is the New Moon (Hodesh)". Clearly, in this verse Hodesh is used to refer to the specific day on which the month begins and not the entire month. Another passage which uses Hodesh in its primary sense is Ez 46,1 which talks about "The Day (Yom) of the New Moon (Ha-Hodesh)". Clearly in this verse Hodesh (New Moon) is a specific event and the beginning of the month is the day on which this event (New Moon) occurs.
The Biblical New Moon is the "First Crescent"
"Hodesh" (New Moon), is derived from the root H.D.SH. 
meaning "new" or "to make new/ renew". The Crescent New Moon is called Hodesh because it is the first time the moon is seen anew after being concealed for several days at the end of the lunar cycle. At the end of the lunar month the moon is close to the sun 1 and eventually reaches the point of "conjunction" when it passes between the Sun and the Earth.2 As a result, around the time of conjunction very little of the moon's illuminated surface faces the Earth and it is not visible through the infinitely brighter glare of the sun. After the moon moves past the sun it continues towards the opposite side of the Earth. As it gets farther away from the sun the percentage of its illuminated surface facing the Earth increases and one evening shortly after sunset the moon is seen anew after being invisible for 1.5-3.5 days. Because the moon is seen anew after a period of invisibility the ancients called it a "New Moon" or "Hodesh" (from Hadash meaning "new").
Crescent New Moon vs. Astronomical New Moon
Many people have been led astray by the inaccurate use in modern languages of the term "New Moon". Modern astronomers adopted this otherwise unused term, which had always referred to the first visible sliver, and used it to refer to conjunction (when the Moon passes between the Earth and the Sun, at which time it is not visible). The astronomers soon realized that the inaccurate use of "New Moon" to refer to conjunction would lead to confusion so to be more accurate scientists now distinguish between "Astronomical New Moon" and "Crescent New Moon". "Astronomical New Moon" means New Moon as the term is used by astronomers, i.e. conjunction. In contrast, "Crescent New Moon" uses the term in the original meaning of the first visible sliver. A good English dictionary should reflect both meanings. For example, the Random House Dictionary of the English Language, Unabridged Edition defines New Moon as: "The moon either when in conjunction with the sun or soon after being either invisible [Astronomical New Moon] or visible [Crescent New Moon] only as a slender crescent." (square brackets added by NG).
The Supposed Evidence For "Concealed Moon"
Having been confused by the use of the term New Moon in modern astronomy some people have sought Biblical support for this incorrect meaning of the term. Ps 81,3 [Heb. 81,4] is usually cited which says:
"Blow on a horn for the Hodesh (New Moon)
On the Keseh (Full Moon) for the Day of our Hag (Feast)."
According to the "Concealed Moon Theory", the term "Keseh" is derived from the root K.S.Y. meaning "to cover" and thus means "covered moon" or "concealed moon". According to this interpretation, when the verse says to blow on a horn on the day of Keseh it actually means "[blow on a horn] on the day of Concealed Moon". However, the language does not support this argument for the second half of the verse also refers to the day of Keseh as "the day of our Feast (Hag)". In the Bible, Feast (Hag) is a technical term which always refers to the three annual pilgrimage-feasts (Matzot, Shavuot, Sukkot; see Ex 23; Ex 34). New Moon Day (Hodesh) is never classified as a "Pilgrimage-Feast" so Keseh/ Hag can not possibly be synonymous with New Moon Day (Hodesh). It has further been suggested that Keseh refers to the Biblical holiday of Yom Teruah (Day of Shouting), which always falls out on New Moon Day. However, the Bible describes Yom Teruah as a Moed (appointed time) and never as a Hag (Pilgrimage-Feast) so Keseh/ Hag can not refer to Yom Teruah either.
What Does Keseh Really Mean?
It is likely that Keseh is related to the Aramaic word "Kista" and the Assyrian word "Kuseu" which mean "full moon" (see Brown-Driver-Briggs p.490b) [Hebrew, Aramaic, and Assyrian are all Semitic languages and often share common roots]. This fits in perfectly with the description of Keseh as the day of the Hag since two of the three Pilgrimage-Feasts are on the 15th of the month, which is about the time of the Full Moon!
More on "Concealed Moon"
Another point to consider is that there is no actual "day" of concealed moon. In fact the moon stays concealed anywhere from 1.5 to 3.5 days in the Middle East. It has been proposed that the "day" of concealed moon is actually the day of conjunction (when the moon passes between the Earth and Sun). However, it was only 1000 years after Moses that the Babylonian astronomers discovered how to calculate the moment of conjunction. Therefore, the ancient Israelites would have had no way of knowing when the moment of conjunction takes place and would not have known on which day to observe "Concealed Moon Day".
It has been suggested that the ancient Israelites could have looked at the "Old Moon" and determined the Day of Conjunction by when the Old Moon was no longer visible in the morning sky. However, such a method would not work in the Middle East where the so-called "concealed moon" can remain concealed for as many as 3.5 days! It is in fact common for the moon to stay concealed for 2.5 days and in such instances how would the ancient Israelites have known which day was the Day of Conjunction?
In contrast, the ancient Israelites would have been well aware of the Crescent New Moon. In ancient societies people worked from dawn to dusk and they would have noticed the Old Moon getting smaller and smaller in the morning sky. When the morning moon had disappeared the ancient Israelites would have anxiously awaited its reappearance 1.5-3.5 days later in the evening sky. Having disappeared for several days and then appearing anew in the early evening sky they would have called it the "New Moon" or "Hodesh" (from Hadash meaning "New").
from the web site of the Honorable Hazzan Nehemia Gordon
