As we said in הלל המצרי, פרקים קיד and קטו are one unit; there is no הללויה separating them and in the Allepo Codex, they are in one paragraph. Rabbi Yitzchak Etshalom, in his essay on פרק קטו (personal communication; he says it will be on yutorah.org “soon”) points out that there is an internal structure: most of the psukim are in two-fold parallelism, but some have three phrases, and those three-phrase psukim serve to divide the unit into semi-indepent sections.
I will take that idea, and assume that the “extra” phrase serves like the הללויה's that separate the other פרקים. It is the conclusion of the previous paragraph, and the introduction to the next one. In other words, the structure of פרקים קיד and קטו is:
We’ve talked about the difference between הלל and הודאה: הלל is focused on ה׳, and הודאה is focused on the human being. Our “הלל” divides into two parts; the first is delineated with הללויה and is all about הקב״ה: it starts with הללו עבדי ה׳; הללו את שם ה׳ and ends with הללו את ה׳ כל גוים; שבחוהו כל האמים. Even in these middle paragraphs, we don’t see any mention of exactly how ה׳ saved us, just glorifying Him for saving us. Those details are in the second part, הודו לה׳ כי טוב.
הללויה
While the paragraph starts with בצאת ישראל ממצרים, it isn’t about יציאת מצרים at all. It’s about the revelation of ה׳'s power at מעמד הר סיני. It is the illustration of what we said in the previous paragraph, על השמים כבודו. בצאת ישראל ממצרים means after Israel left Egypt, when they were in a land of an עם לעז, a “people of alien tongue” as Artscroll puts it. The Jews were a special people with a special mission.
The emphasis is on how בני ישראל were מצויינים שם; they kept their distinction if nothing else, as descendants of בית יעקב, in order to become קדשו and ממשלותיו of הקב״ה. Note that this distinction between ישראל and יהודה means that this line was written after they entered ארץ ישראל and the nation split into two demographic parts, from at least the time of Shaul; the political split wouldn’t come until much later, but we’ve talked about how they acted as separate nations. In בני עקיבא terms, יהודה had תורת ישראל while ישראל had עם ישראל and ארץ ישראל. And in terms of our perek, יהודה was קדשו while ישראל was ממשלותיו. That’s not a bad thing; as long as they were united, they could complement each other and be the מרכבה that carries the presence of ה׳ in the world, to be witnesses to the power of ה׳ that will be described.
That role is bookended by two events that demonstrate ה׳'s control of nature: splitting ים סוף and splitting the ירדן. And at מעמד הר סיני itself, the earth itself shook, רקדו כאילים. Nothing about giving the Torah here; it’s all הלל of גבורת ה׳.
We see the experience of מעמד הר סיני, in the shaking of the earth itself, as a common theme in תנ״ך:
מלפני אדון חולי ארץ is ambiguous; it’s usually translated as an apostrophe to the earth: “Before the Lord, tremble O earth”, or the earth’s answer to the question of מה לך…תרקדו כאילים: ”before the Lord’s Presence did I, the earth, tremble“ (Artscroll’s translation). But Rabbi Etshalom and Rabbi Sacks in his siddur take חולי as “birthpangs” and thus מְחֹלֵל as “creator”:
So מלפני אדון חולי ארץ is the answer as stated by the narrator: the mountains skipped “before the Lord, Creator of the earth”. As we’ve said many times before, in poetry, ambiguity is intentional. The message is that G-d both created the world and controls it, and the last demonstration of that is ההפכי הצור אגם מים, turning the rock to water. That episode was the introduction to מעמד הר סיני:
But it’s more than that. אין מים אלא תורה and the image of the water flowing from the rock is the image of a river flowing from הר ה׳, that takes us from הר סיני, when ה׳ is revealed to בני ישראל, to the אחרית הימים, when ה׳ will be revealed to the whole world.
And this section ends (as I am reading it) with the anaphora of לא לנו ה׳ לא לנו; the purpose of all this is not to show how great we are, but to allow us to declare מי כה׳ אלקינו המגביהי לשבת.
לא לנו ה׳ לא לנו
But לא לנו ה׳ לא לנו is also the introduction to the next section, which we skip when we say “half Hallel”. The origin of this is in the gemara:
Rosh Chodesh was not part of the תקנה of saying הלל: נְבִיאִים שֶׁבֵּינֵיהֶן תִּיקְּנוּ לָהֶם לְיִשְׂרָאֵל שֶׁיְּהוּ אוֹמְרִים אוֹתוֹ עַל כׇּל פֶּרֶק וּפֶרֶק, and just reciting Hallel without just cause is a bad thing:
(We’ll deal with this more when we discuss פסוקי דזמרא.)
But by leaving out parts, we make it clear that we’re not reciting “הלל” as celebration of an overt miracle but just saying תהילים. The part we skip over is not so much a praise of ה׳ as a prayer, and a denigration of עבודה זרה. It has a different flavor than the rest of הלל, so it isn’t missed.
What’s interesting is that the full pasuk, לא לנו ה׳ לא לנו, כי לשמך תן כבוד על חסדך על אמתך, is in second person. It’s the only place in הלל where the psalmist is apparently addressing ה׳ directly. The gemara explains that these two psukim are a quote:
In other words, in every generation, we ask ה׳ to save us, because He is identified with us: we are בית יעקב and He is אלו־ה יעקב. Not answering us would be a חילול ה׳: למה יאמרו הגוים: איה נא אלקיהם? Moshe made that argument first:
And the word נא in this context means “now”, not “please”: the nations say: “Your G-d may have done great things (see the previous paragraph) but what has He done lately?”. But we don’t claim to deserve anything; ה׳ acts על חסדך על אמתך, a hendiadys for ה׳'s חסד של אמת.
The חילול ה׳ is that the nations have gods also, and they pray to and praise those gods. But those gods are inert and unmoving; they cannot answer. If You do not answer, then You put Yourself in the same category: one of עצביהם.
The sense of this section is that the psalmist is talking to his audience: you say לשמך תן כבוד על חסדך על אמתך; למה יאמרו הגוים, איה נא אלהיהם. But don’t worry. ה׳ did miracles before, בצאת ישראל ממצרים, and He will do so again, ישראל, בטח בה׳. Just don’t fall into the trap of looking to false gods for your salvation. They are עצבים.
עצב meaning “idol” is an interesting word. עצב means “sadness” in modern Hebrew, but in תנ״ך it has a subtly different connotation:
Artscroll translates עצבון as “toil”:
It’s a reference to the original curse of Adam:
And how technology would save them:
The Midrash puts it more poetically:
The word עצבון comes up in the curse of Chava as well:
And עצב can mean “formed” (which explicitly connects it to idols, מעשה ידי אדם):
Dr. Zornberg says that the two meanings of עצב are really the same. She notes that both curses of עצבון, of צער גידול בנים and of קוץ ודרדר תצמיח לך, are curses that despite all their toil, the results are completely out of their hands:
עצבון is the עצב, the misery, of toil: when all your effort, all your hard work, comes to nothing.
And עצבון is what G-d feels when His creation fails Him:
So that is what עצביהם are: the products of sincere hard work; עובדי עבודה זרה are truly trying to serve the forces of nature. But it is ultimately futile because those forces cannot answer, they are deaf, dumb, blind and immobile.
And this paragraph ends with לא יהגו בגרונם, just as the description of עצביהם started with פה להם ולא ידברו: the gods of other nations cannot speak, they cannot answer the prayers of those who call out to them.
לא יהגו בגרונם
The way I am reading this, לא יהגו בגרונם is also the introduction to the next section, כמוהם יהיו עשיהם כל אשר בטח בהם. I don’t think that is a prayer or a curse (“Those who make them should become like them”, as Artscroll translates it) but a statement of fact. Those who trust in the unconcious forces in nature, who pray to them expecting to be answered, will be לא יהגו בגרונם: they are effectively silent; their prayers have no meaning. As Yirmiyahu says,
The problem is that we are supposed to realize that we are created in the image of G-d. But human beings tend to get that backward:
We, in a sense, create ourselves in the image of the gods that we create in our own image. The things we worship are a reflection of the things we value.
That’s usually translated as “[the worth of] a person is measured by how others praise them”:
But the Chida reads it as “by what they praise”:
I think בתחון in עצבים is the same idea. Our purpose in creation is imitatio dei:
And it is inevitable that כמוהם יהיו…כל אשר בטח בהם. Be careful what you have faith in; it determines who you are. And so the psalmist exhorts us: ישראל בְּטַח בה׳; עזרם ומגנם הוא. בְּטַח is in the צווי, a command. It is addressed to three groups: all of ישראל, then the בית אהרן, which Rav Moshe Feinstein points out doesn’t mean כוהנים in the halachic sense, but “those who are dedicated to serving ה׳”. Even they are subject to the dangers of עצביהם כסף וזהב.
And the final group is יראי ה׳, expanding the focus to the entire world:
And we end with the assurance that our בתחון will not be in vain: ה׳ זכרנו יברך: G-d, who pays attention to us and judges us (the implication of זכרון with respect to הקב״ה; see the Rosh Hashana davening), will bless us.
ה׳ זכרנו יברך
The next section is all about that reassurance; ה׳ זכרנו יברך is the title. The same groups who are urged to have בתחון—בית ישראל, בית אהרן and יראי ה׳—will be blessed, and all of them: הקטנים עם הגדלים is a merism for “everyone”.
יסף ה׳ עליכם expresses what “ברכה” means: to increase (a בריכה is a spring).
So that becomes our הלל: the introduction said, “רם על כל גוים ה׳; על השמים כבודו” and now we declare that ה׳ has the power and the will to continuously give to those who trust in Him, who is עשה שמים וארץ.
But that ברכה comes with responsibility: השמים שמים לה׳; והארץ נתן לבני אדם. We are here, on the ארץ, with a purpose. In terms of Hallel, that purpose is less doing מצוות and more carrying the שכינה in the world, by declaring His greatness in public. Those who have בתחון in עצבים are silent, ירדי דומה; the psalmist said פה להם ולא ידברו…כמוהם יהיו עשיהם. They are like המתים, who are לא יהללו י־ה. But we are different, אנחנו נברך י־ה. ברכה here is harder to translate; how can a human being bless G-d in the sense of giving something? The Avudraham explains that “blessing” ה׳ means acknowledging Him as the source of blessing:
And so we return to the beginning: פרק קיג exhorted us יהי שם ה׳ מברך מעתה ועד עולם and now we declare that we will do so, ואנחנו נברך י־ה מעתה ועד עולם.