This is a hauntingly beautiful melody but very difficult to make melodic.
It is certainly typical of Martin Luther and is very reminiscent of his
much better known, "A Mighty Fortress Is Our God." 

The version in the hymnal is arranged by Johann Sebastian Bach, circa 1740,
and is virtually impossible to figure out, much less sing, because the
harmonies are so complex. Hopefully this version is more accessible.

OUT OF THE DEPTHS
Psalm 130 - Martin Luther, 1524
Aus Tiefer Not (8.7.8.7.8.8.7) - Martin Luther, 1524

Out of the depths to Thee I raise
The voice of lamentation;
Lord, turn a gracious ear to me,
And hear my supplication.
If Thou shouldst count our every sin,
Each evil deed or thought within
O who could stand before Thee?

To wash away the crimson stain
Grace, grace alone prevaileth.
Our works, alas! are all in vain; 
In much the bests life faileth.
For none can glory in Thy sight,
All must alike confess Thy might
And live alone by mercy.

Therefore my trust is in the Lord,
And not in mine own merit.
On God my soul shall rest; God's word
Upholds my fainting spirit.
God's promised mercy is my fort,
My comfort, and my strong support;
I wait for it with patience.

What though I wait the live-long night,
And till the dawn appeareth,
My heart still trusteth in God's might;
It doubteth not nor feareth.
So let the Israelites in heart,
Born of the Spirit, do their part,
And wait till God appeareth.