Like the twenty-third, this is a song of trust and protection in divine presence, the source of goodness and guidance. David describes God as his portion and cup, evoking familiar imagery in themes that connect well with daily life. He recognises his fortunate heritage:
6 My boundaries enclose a pleasant land; I have a goodly heritage. 7 I bless God who gives me counsel; my heart teaches me, night after night. 8 I keep God always before me; because God is at my right hand, I shall not be moved. 9 Therefore my heart is glad, and my soul rejoices; my body also rests secure.
Read more about this in the main page Psalm 16: Heritage and equity.
This page mentions an interesting setting of the psalm to the old song Precious Lord, hold my hand. For those in a classical frame of mind, an earlier setting of Psalm 16 (15 in the Vulgate) by Parisian composer Marc-Antoine Charpentier (1643-1704) will be of interest. This one is not listed in the CPDL psalms pages, but is hidden in a Mass for Four Choirs — heavy!
Many other settings may be found online, including three separate settings by Orlando Lasso addressing separately verses 1-4 (six voices), 7-8 (four voices) and 8-10 in seven parts.
And having earlier revealed the Charpentier opus magnus for four choirs, an even more obscure setting for three choirs comes to mind. This one, Bewahre mich, Herr, was written by German composer Johann Sommer, whose only other work seems to be another 12-voice piece for Psalm 8. He must have liked the dynamic range and full sound of many voices.
If you wish to be remembered for generations for your triple-choir compositional skills, you should lay down the public records more deliberately than did Johann Sommer, whose days in the Choral Public Domain are shown as 1570 to 1627.
Unless these dates are wrong, a purported link to the Wikipedia entry for this composer leads to a different Johann Sommer, an earlier theologian from Transylvania. And several others appear in different eras and centuries. So the life and times of this JS remains regrettably obscure.
In more modern usage, several good options are available in Psalms for All Seasons (including mentioned above) — though not in Together in Song. At Woden Valley we choose a refrain used previously at South Woden:
This couplet for the call-and-response antiphon is the second half of a longer composition by the cantor, to which the verses are sung — in a rather more free and lyrical style than the following sound clip: