Much of Old Testament poetry is focusing on praising God, especially the Book of Psalms. Several of our hymns today are inspired by the language in ancient psalms. We don't have a similar book in the Book of Mormon, but sometimes we find these poetic exclamations of praise, like 1 Nephi 1:14 or 2 Nephi 4:20-25. Another notable example is found in Alma 26, when Ammon rejoices in the fruit of their labors. He uses language very reminiscent of Psalms
be the name of our God; let us to his praise, yea, let us give to his holy name, for he doth work righteousness forever...Yea, we have reason to praise him forever, for he is the Most High God (Alma 26:8, 14)
I will praise the Lord according to his righteousness: and will sing praise to the name of the Lord most high. (Psalm 7:17)
This is only one example. There is not a direct quote of complete verses for instance, but recurring themes and terms that are found not only in this example but several others as I have compared Ammon's words with Psalms, for instance "Most High" God, "sing praise", "his holy name", "give thanks forever". When Ammon talks about singing, I wonder how literal that should be understood. I find it likely that the Nephites had the Book of Psalms on the brass plates (Lord Wilmore wrote extensively about Book of Mormon quotes from Psalms). But perhaps the Nephites also wrote music to accompany the sort of praise that Ammon gives in Alma 26. ("let us sing to his praise").
Ammon specifically mentions "the song of redeeming love" that we also read about in Alma 5. This could only be a metaphor but also an actual hymn. LeGrand Baker speculates if this could be referring to Psalm 21. In that case, it was sung at the temple as an invitation to enter in. As mentioned previously, the concept of redemption is connected to meeting God.
Music was a part of temple worship in ancient Israel.
The Levites ministered before the LORD, offering up thanks and praise with instrument and voice. The Levites accompanied and aided worshippers in keeping divine commands to remember and offer thanksgiving to the LORD. Using their lyric text, the Psalms, the Israelites gathered in holy places and invoked the name of the LORD, literally requesting his presence. The psalms accompanied ritual acts. A Levitical temple orchestra, composed of lyres, harps, cymbals, and trumpets accompanied the daily sacrifices.
Israelite worshippers sang songs of ascent as they would journey up to the house of the LORD. Music was a medium through which the Israelites were able to worship, expressing thanks and praise, as well as publicly announced the LORD’s presence.
This is for instance seen in 2 Chronicles 7:6, right after Solomon dedicated the temple.
And the priests waited on their offices: the Levites also with instruments of musick of the Lord, which David the king had made to praise the Lord, because his mercy endureth for ever, when David praised by their ministry; and the priests sounded trumpets before them, and all Israel stood.
David had composed many of those songs "to praise the Lord, because his mercy endureth forever". This is typical language in Psalms, but seeing how Ammon uses similar language, it is not hard to imagine that these traditions carried over into Nephite culture and religious worship.
Therefore, let us , yea, we will in the Lord; yea, we will rejoice, for our joy is full; yea, we will praise our God forever. (Alma 26:16)