Commonly recited from Psalms is Chapter 118, recited in Hallel on Rosh Chodesh and Festivals. It begins (v. 1-4):
הוֹד֣וּ לַיהוָ֣ה כִּי־ט֑וֹב כִּ֖י לְעוֹלָ֣ם חַסְדּֽוֹ׃
Praise the LORD, for He is good, His steadfast love is eternal.
יֹֽאמַר־נָ֥א יִשְׂרָאֵ֑ל כִּ֖י לְעוֹלָ֣ם חַסְדּֽוֹ׃
Let Israel declare, “His steadfast love is eternal.”
יֹֽאמְרוּ־נָ֥א בֵֽית־אַהֲרֹ֑ן כִּ֖י לְעוֹלָ֣ם חַסְדּֽוֹ׃
Let the house of Aaron declare, “His steadfast love is eternal.”
יֹֽאמְרוּ־נָ֭א יִרְאֵ֣י יְהוָ֑ה כִּ֖י לְעוֹלָ֣ם חַסְדּֽוֹ׃
Let those who fear the LORD declare, “His steadfast love is eternal.”
There seems to be a progression of mentioning something about Israel, the house of Aharon, and then those who fear Hashem. I didn't think much of this, until I noticed the same progression appears earlier in Chapter 115:9-11, in the part that's only recited with full Hallel:
יִ֭שְׂרָאֵל בְּטַ֣ח בַּיהוָ֑ה עֶזְרָ֖ם וּמָגִנָּ֣ם הֽוּא׃
O Israel, trust in the LORD! He is their help and shield.
בֵּ֣ית אַ֭הֲרֹן בִּטְח֣וּ בַיהוָ֑ה עֶזְרָ֖ם וּמָגִנָּ֣ם הֽוּא׃
O house of Aaron, trust in the LORD! He is their help and shield.
יִרְאֵ֣י יְ֭הוָה בִּטְח֣וּ בַיהוָ֑ה עֶזְרָ֖ם וּמָגִנָּ֣ם הֽוּא׃
O you who fear the LORD, trust in the LORD! He is their help and shield.
Again, it mentions Israel, the house of Aharon, and those who fear Hashem.
Do any commentaries pick up on this and explain its significance?