Why did David compose this Mizmor?
Radak: It was when he brought the Aron from Beis Oved Edom ha'Giti to Ir David, and he gave it to Asaf and his brothers to sing it in front of the Aron. The first 15 verses are in Divrei ha'Yamim I, 16:8-22, with small differences. Here, David wrote it and elaborated to tell about Zera Avraham until they entered Eretz Yisrael. There (verses 23-33), it adds "Shiru la'Shem Barachu Shmo
Whom does he tell to praise Hashem?
Radak: He tells the singers and the Tzibur.
Malbim: It is His close ones, who received individual benefits.
What is the meaning of "Kir'u vi'Shmo"?
Radak #1: Pray to Him. This is like "uv'Shem Hashem Ekra" (116:17).
Ibn Ezra, Radak #2: To teach 1 people His way, like "va'Yikra Sham Avram b'Shem Hashem" (Bereishis 13:4). This is like the verse continues "Hodi'u va'Amim Alilosav."
'Rashi' (Divrei ha'Yamim I, 16:8): Call to Him to help His Aron. This is like "u'Krasem b'Shem Eloheichem va'Ani Ekra b'Shem Hashem" (Melachim I, 18:24).
Gra (Divrei ha'Yamim I, 16:8): Attribute all that you do to Him, like the Avos did - "va'Yikra Sham Avram b'Shem Hashem" (Bereishis 13:4).
The correct text of Radak is 'Lehoros', like it says in Ibn Ezra. (PF)
What are "Alilosav"?
Rashi: His deeds.
Radak: His actions against the Pelishtim due to the Aron.
Gra (Divrei ha'Yamim I, 16:8): It is the great Chesed that he conducts with Yisrael. He gives good to a Yisrael, then takes it away to atone for his sin in this world.
Malbim: They are conduct and deeds according to His Midos - "Rachum v'Chanun v'Rav Chesed" (Shemos 34:6), which is according to people's deeds, and reward and punishment.
