"And on your day of gladness, and on your festivals, and on your new moons…." (Num. 10:10)
Rosh Chodesh, the first day of the lunar month, is called literally "the head of the month" and not the "beginning of the month", because just as the head contains the life-force for all the limbs, so does the first day of each month represent the spiritual "life-force" for the rest of the month. The second part of the name, "Chodesh", is related to the word "chadash", meaning "new". In simple terms, this refers to the renewal of the moon, the birth of the new moon. In Kabbalistic sources, however, it is explained that every Rosh Chodesh brings a new spiritual light, one that never illuminated before throughout time. This light derives from a completely new general revelation that takes place every Rosh Hashanah and that is divided up for the twelve months of the year. When each Rosh Chodesh arrives, its particular new light illuminates.
The renewal of the moon itself has a Kabbalistic dimension. The moon corresponds to the sefira of malchut in that it "has no light of its own" and shines with reflected light from the sun. Similarly, the spiritual "light" of malchut is only what it receives from the sefirot above it. Just as the moon becomes smaller and smaller until it is not visible immediately before its rebirth, similarly malchut receives its light from the sefirot above it by "nullifying itself" in its yearning to receive this light. In the same way, the Jewish people (who are compared to the moon) are able to become a vessel for G‑d's light through exhibiting the trait of self-nullification.
Rosh Chodesh…represents drawing down the spiritual into the earthly and mundane….
The association of newness with the word "chodesh" has important implications for a person's spiritual service. The Jewish people are compared to the moon, and "reckon by the moon" and "are destined to be renewed like it" (Liturgy, Kiddush Lavanah; Sanhedrin 42a). Through the "chidush", the new spiritual element that is accomplished in the world through the service of the Jewish people, the Jewish people achieve a new level higher than the one they occupied before coming down into the physical world. This will be finally revealed in the future redemption. One might say that each Rosh Chodesh there is revealed in each individual Jew the spark of Mashiach that is within him, the level of Yechida, which is a spark from the level of general Yechida, the soul of Mashiach. (See Me'or Einayim, parashat Pinchas) This revelation accomplishes a chidush in the person's whole existence and everything that pertains to him; the level of Yechida permeates him.
The spiritual character of Rosh Chodesh can best be explained by contrasting it with Shabbat. Each of these two days expresses one mode of a basic two-fold pattern in spiritual service, a pattern that is also built into the structure of Creation: elevation and drawing down. Rosh Chodesh, on which work is permitted, represents drawing down the spiritual into the earthly and mundane; Shabbat, on which work is forbidden, represents elevation, as the mundane and the earthly become more spiritual.
The two modes of this pattern also have a reciprocal relation: An elevation brings a corresponding drawing down, and a drawing down brings a corresponding elevation. The Shabbat elevation of the physical world and all the levels of the spiritual realm is followed by the drawing down of spiritual delight. The drawing down of a higher level of G‑dliness on Rosh Chodesh brings an elevation to the life-force creating the world.
On Rosh Chodesh, nature itself is on a higher level….
Although Rosh Chodesh is unlike Shabbat and Yom Tov in that work is permitted, Rosh Chodesh is not considered a regular work day and retains a separate identity. It is actually on a higher level than an ordinary weekday, which is why an additional sacrifice was brought in the days of the Temple, called the Musaf offering, to which the Musaf Standing prayer that we say now corresponds. This is also the reason we say the prayer of Hallel. In Kabbalistic terms this means causing a descent of malchut into the midot, corresponding to the work of sifting and purifying, and contrary to the spiritual character of Shabbat, when malchut ascends to chochma (Torat Shmuel 5630).
On Shabbat, by contrast, it is forbidden to do work, for spiritually Shabbat is higher than the level of "in six days G‑d created, etc." Then a divine light shines that is not clothed in nature. By violating the prohibition of work on Shabbat, we cause G‑d to contract Himself.
In contrast, on Rosh Chodesh, nature itself is on a higher level. In other words, Shabbat represents a mode that is higher than nature, a weekday represents a mode that accords with nature, and Rosh Chodesh elicits that which is higher than nature and allows it to permeate nature.
On Shabbat, the world exists directly from G‑d's thoughts - the level of thought is not hidden in the garments of nature. This is why we are not allowed to work on Shabbat, since by working we cause a descent in the world so that G‑dliness is expressed through speech, which is a condensed light that is clothed in nature.
On Rosh Chodesh the miraculous permeates the natural….
On Rosh Chodesh, nature is created by a higher form of G‑d's speech so that nature itself takes on a higher form.
This is why we say the Hallel prayer on Rosh Chodesh, but not during the week or on Shabbat. The verses of Hallel speak of how G‑d conducts Himself through miracles. During the week G‑d wants us to conduct ourselves according to nature, making a vessel, a natural way for G‑d's blessings to be manifested. We are not allowed to rely on miracles and therefore the Talmud compares saying Hallel on a weekday to "cursing and blaspheming".
On a regular Shabbat we don't say Hallel since we are not allowed to work. Shabbat is a result of preparation (the work is already completed), as indicated by the saying that "one who works before Shabbat is able to eat on Shabbat". Rosh Chodesh, however, is an intermediate between Shabbat and weekdays. We say Hallel to ask G‑d to allow our work and weekday concerns to be permeated with the spiritual, a uniting of the physical and the spiritual, which is associated with miracles.
On Rosh Chodesh the saying of Hallel is a custom, unlike the recitation of Hallel on Chanukah and Yom Tov, when it is a law. The reason is that on Rosh Chodesh the miraculous permeates the natural and weekday activities so that the weekday activities are revealed and the miraculous is hidden. This is in contrast to Yom Tov and Chanukah, which are associated with visible miracles, the military victory of the few over the many on Chanukah for instance.
The ultimate objective is to draw down G‑dliness into this world….
Chassidic philosophy explains that Rosh Chodesh and Shabbat each have an advantage over the other. The advantage of Shabbat is that it is spiritually loftier than any weekday, and therefore it is forbidden to work. On the other hand, that in itself is the advantage of Rosh Chodesh over Shabbat: It is permitted to work, and the elicitation of G‑dliness reaches farther, all the way down into the workday world. This gives it an advantage in achieving the goal of a "dwelling here below". On Shabbat, time and space themselves are elevated, as if Shabbat is a different world, but the ultimate objective is to draw down G‑dliness into this world.
This concept is identical to the advantage of Purim over the rest of the holidays. Even though from one perspective there is something lacking in a miracle clothed in nature (and therefore we do not say Hallel), from another perspective there is an advantage to this kind of miracle: Since it is clothed in nature, it shows the greatness of the divine light in even being able to permeate nature itself, and therefore the joy of Purim is greater than on any other holiday.
The differences we have been talking about between Shabbat and Rosh Chodesh apply to these two days as they exist now. However, in the future, when Mashiach comes, the Torah states, "Then all flesh will come to bow down before Me every Rosh Chodesh and Shabbat." (Isaiah 66:23) This means that the pilgrimage up to the holy Temple associated with the holidays in the days of the Temple will take place every Shabbat and Rosh Chodesh. The spiritual revelation of Shabbat and Rosh Chodesh will have reached a new and higher level.
[From The Jewish Holy Days in Chassidic Philosophy (Jason Aronson)]