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When we say hallel on days like Rosh chodesh, we don't say parts of two prakim of tehillim. This is often called "chatzi" hallel, or half hallel. In fact, according to http://www.5tjt.com/local-news/13099-our-better-halves the hallel we are left with is closer to 85% of the full hallel. Some siddurim refer to saying the "whole hallel" as "gomrim" we finish the hallel (as in http://www.daat.ac.il/daat/sidurim/mizrah/hol/rosh.htm) , and this makes more sense. The gemara in taanis 28b uses the phrase "gomer bahem et hahalel" and later refers to the shorter version as subject to "medalgin", skipping, but not half (though there might be other places in the gemara which use the word "half")

I understand that "chatzi" does not always mean an exact 50% but I'm wondering when the texts (either liturguical or halachic) began referring to the incomplete hallel as chatzi. Is there a talmudic phrase which would source this (and thus give it semantic value within the context of the gemara's language and use of the word "chatzi") or is it simply a linguistic shortcut introduced later?

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gomrim can also be translated as "we complete". –  Menachem Apr 20 '12 at 16:42
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The earliest I can find for calling the abreviated Halel "Half Halel" is the Levush (c. 1600):

לבוש אורח חיים סימן תפח

וכשאומרים חצי הלל כגון בראש חודש וחול המועד

Even after him, it is not the standard way of referring to it. Everyone else calls it "Halel BeDilug" which means "Halel with skipping."

Note also that the phrase is used earlier at least to the time of the Terumat Hadeshen, c 1450 (Leket Yosher 1:91) to refer to the two 'halves' of halel said at the seder: one during maggid and one during halel. Possibly the phrase was later borrowed to describe Halel BeDilug.

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I find this very interesting - it suggests that the phrase is relatively modern. I like the possibility that it develops from the seder a la the Trumat Hadeshen, and this gives a good textual precedent but as a note, even there, the first "half" is tehillim 113 and 114, significantly less than 50%. –  Danno Apr 22 '12 at 1:48
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I would propose that it is known as Chatzi Hallel even though it is 85% since the 2 parts we do not say are both approximately 1/2 a chapter of Tehilim (Lo Lanu is Tehilim 115 verses 1-11, and Ohavti is Tehilim 116 verse 1-11) which we say the other 1/2 (Hashem Zecharanu is Tehilim 115 verses 12-18, and Ma Ashiv is Tehilim 116 verses 12-19).

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I saw that answer on the site which I included but it is neither persuasive (because the adjective "half" modifies the noun "hallel" not "perek" or any other implied noun) nor historically precedented as far as I have found. Do you have any source (siddur or otherwise) which gives this logic or is a firm starting point for this convention? –  Danno Apr 20 '12 at 13:45
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As I said this was my own proposal. –  Gershon Gold Apr 20 '12 at 13:48
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If I had to guess, it is probably because the other way "incomplete" things are generally referred to is "חסר" (literally, "missing"), which sort of sounds weak or even deficient or, I dunno, inferior. "Half-Kaddish" is also much more than half of the Kaddish, and I would venture to guess (unless someone can provide a source indicating otherwise) that it is for a similar reason.

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I made a count on kaddish and found that the "half kaddish" is actually 59.4 percent. I haven't done any textual investigation but I wonder what the source of "chatzi kaddish" is textually. –  Danno Apr 22 '12 at 1:40
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I can't provide the provenance of the term חצי הלל as sought, but there are examples of חצי's meaning "divided" rather than "halved". E.g., "חצי שיעור אסור מן התורה", which רש״י (to יומא ע״ג ע״ב‎) explains as meaning "פחות מכשיעור".

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Also, for example, the Torah often refers to חצי שבט מנשה having received territory on the east side of the Jordan, but from Josh. 17:1-2 we see that in fact most of the tribe (six subfamilies of Gilead) were assigned to the west side (Eretz Yisrael proper). –  Alex Apr 20 '12 at 16:39
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Are you sure Rashi means that chatzi=part and not that half is being used as an example for the general case of part? We see in the torah (for instance Ex38:26 Nu31:27) that sometimes it means exactly half. –  Double AA Apr 22 '12 at 1:52
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@DoubleAA (2nd comment): מחצית isn't necessarily the same as חצי. But anyway, of course חצי often enough means exactly half (as in the measurements of the Mishkan and for the korbanos, etc.); but conversely, think of Aharon's plea ויאכל חצי בשרו (Num. 12:12) or חצי הר הגלעד, where it doesn't necessarily have to mean 50% precisely. –  Alex Apr 22 '12 at 2:28
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And about Menashe: the list in the second census (Num. 26) lists a family of Machir, a family of his son Gilead, and six families of his children. These last six are the ones mentioned in Joshua. Since, as Rashi (to Num. 26:24,36) points out, separate family listings for parent and child mean that the parent had other children but that the named ones had particularly large families of their own, then that would seem to imply that Gilead's descendants were >50% of Machir's, and the descendants of his six sons were >50% of Gilead's. In any case, it's highly unlikely that they were exactly 50%. –  Alex Apr 22 '12 at 2:32
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The question assumes that chazi in Mishnaic Hebrew means half (which it does in Modern Hebrew). As one of the previous answers mentions, chazi shiur is another place where it seems that chazi means "part of a whole" (or "a fraction") rather than 50%.

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