The hymn is sung to the tune "Vienna." Here's the first musical phrase:
In the first verse, the text here is "Come, my soul, with ev'ry care." The phrase "ev'ry care" is sung to notes of all different pitches (D C B), giving a sense of breadth.
Way back in October, my weekly hymn tune was "Vienna," paired with the text "Lord, We Come Before Thee Now" (The Lutheran Hymnal #18). I noticed a couple instances where the tune connects to the text.
The end of the second phrase descends:
This descent musically represents "At Thy feet we humbly bow" in the first verse and "In compassion now descend" in the second.
Although this tune is also in LSB, I wasn't familiar with it. The first phrase here reminds me of the penultimate phrase in an-other hymn tune, but since I can't place that other tune, I can't compare them.