There is no other way to approach any presentation of God.
Just as reflected by Paul. We are to sift (critically analyze) all presentations of the Gospel through the Scriptures.
That you enjoyed it and was a blessing to you, does not remove from my analysis of it being vain repetition.
I would mention this one part. You are correct that rhythm is an element of music. The stress of the beat pattern determines much of the action the performer wants to communicate to the listener.
Putting the stress on the up and off beat of 1 and 3 enhances the sensual. Example a Sousa march stresses the 1 and 3 beat of the measure. Take a typical Sousa march and move the beat to 2 and 4 and the music becomes less of a march and more of a dance. (Once had a band do that with Stars and Strips - they eventually fell out laughing)
More to the point, is how the dominance of the rhythmic aspects were manipulative to the listener.
Rhythmically, melodically, harmonically, and by presentation it was basically vain repetition.
It appealed to the flesh, and the desires of the flesh.
In effect, the music became a distraction to the validity of the lyrics and the intellectual purposefully becoming dulled to the testimony of (or truth) of the lyrics.
The author of the lyrics was presenting a testimony of salvation, that because of ____ then ____.
Look at the lyrics and see if the testimony of the writer was clearly given in the song as presented in the OP:
How Great Thou Art Lyrics
Verse 1:
O Lord my God, When I in awesome wonder,
Consider all the worlds Thy Hands have made;
I see the stars, I hear the rolling thunder,
Thy power throughout the universe displayed.
Chorus:
Then sings my soul, My Savior God, to Thee,
How great Thou art, How great Thou art.
Then sings my soul, My Savior God, to Thee,
How great Thou art, How great Thou art!
Verse 2:
When through the woods, and forest glades I wander,
And hear the birds sing sweetly in the trees.
When I look down, from lofty mountain grandeur,
And see the brook, and feel the gentle breeze.
Chorus
Verse 3:
And when I think, that God, His Son not sparing;
Sent Him to die, I scarce can take it in;
That on the Cross, my burden gladly bearing,
He bled and died to take away my sin.
Chorus
Verse 4:
When Christ shall come, with shout of acclamation,
And take me home, what joy shall fill my heart.
Then I shall bow, in humble adoration,
And then proclaim: "My God, how great Thou art!"
Chorus