There are more Psalms that are considered Penitentiary Psalms. But these 7 are the standards: 6, 32, 38, 51, 102, 130, 143.
Psalm 6
I will do direct study of the text first. Then when I have time, I will investigate the historical account of it.
Psa 6:1 To the chief Musician on Neginoth upon Sheminith, A Psalm of David. O LORD, rebuke me not in thine anger, neither chasten me in thy hot displeasure.
This is about David's sins. Our sins. God would not be anger with us if not for our sins. He disciplines those whom he loves. However, the rebuking and chastening are not desired here. When we are well, we pray conveniently for God's discipline; while in sorrow, we ask for the relieve of such, for we say that: the discipline is too heavy, or that we have learned our lesson. Here David, while admitting his corruption, appeals to God's mercy using the intended human value God has created.
"Anger" here has to do with the countenance of God. It is enough when anger is revealed upon His face, further rebuking would prove too much, though not undeserving. "Displeasure" has to do with heat. It could be greater terror than anger and thus, the chastening instead of mere rebuke. I am not certain of the importance of the order for "rebuke" and "chasten" here, however, it is clear David did not find the types of God's anger (אף & חָמא) gradually uncomfortable by degree. He is willing to face God's anger, but not the discipline, and he begs (not demands) for the relieve of these.
Psa 6:2 Have mercy upon me, O LORD; for I am weak: O LORD, heal me; for my bones are vexed.
Psa 6:3 My soul is also sore vexed: but thou, O LORD, how long?
"Weak" here is similar to sick. "Bones" maybe refer to the physical foundation of one's life. The result of a corrupt lifestyle. David is diagnosing himself from outward corruption to the inner sorrow of the soul in the next verse. Divine mercy (in all aspect of one's fallen life) and time! are crucial for this prayer.
Psa 6:4 Return, O LORD, deliver my soul: oh save me for thy mercies' sake.
"Return" - The Lord was once in our presence and He has turned away because of our sins. In essence, we have turned away from God to our own ways. First and foremost, the salvation and deliverance of the strangled soul comes first over all other temporal material sufferings. This is not by demand. Love is not demanded, neither is mercy. God's mercy, is David's first most appeal. The second is teleological, in the next verse. Ultimately, the reconciliation of the relationship with God is the primary concern.
Psa 6:5 For in death there is no remembrance of thee: in the grave who shall give thee thanks?
The only outcome of God's continuous anger towards us is our death. Some define "death" as separation (from God). David recognizes the chief purpose of man - to praise God. Only living things are capable of giving thanks. This is not a reminder to God of what He would miss (God lacks nothing) and certainly not blackmailing God. David is admitting that he is tumbling down an unnatural path which defeats his created purpose, and he desired the recovery of such, and thus, appeal to God's mercy.
Psa 6:6 I am weary with my groaning; all the night make I my bed to swim; I water my couch with my tears.
Here David confesses his humility. He does not seek worldly pleasure to cover his sorrow, and we shouldn't. Instead, David cried in secret. One can only imagine how such a man endure sorrow in public. Was it shame? I am sure it is. Shame is required for our repentance, not just the feeling of guilt. Some have despised shame. It is embarrassing to cry in public. But without it, we would not care about the value of relationships with anyone. We would only care about a guiltless path rather than dignity in others. The only solution to shame is to confront it with tears in private with God as the only audience. All else matters not: Not proclaiming to others, the need for their sympathy (or that they need to show sympathy). When necessary, we ask for nothing more than the context of mercy from others. Shame should only be directed to God, not others, though others may inadvertently witness one's shame. For only the Creator is responsible for our chief purpose, should we repent of our ways.
Often times, people like to tell others: "You need to repent!" This often wrong because they appear to demand shame, yet they are no God. However, they would justify themselves one way or another.
Psa 6:7 Mine eye is consumed because of grief; it waxeth old because of all mine enemies.
Here, "enemies" refers to those who justifies themselves for everything they do. So, they do not think they need mercy nor to show mercy. Perhaps David's enemies think their action against David is just due to David's sin, and he deserves no mercy, God will not hear him. Mercy is not in their dictionary. Jealousy is among many of the roots of their enmity.
David now elaborates the cause of his sorrow. God's punishment usually entails using workers of iniquity.
Psa 6:8 Depart from me, all ye workers of iniquity; for the LORD hath heard the voice of my weeping.
Psa 6:9 The LORD hath heard my supplication; the LORD will receive my prayer.
"The LORD will receive my prayer" - Hope is aligned with attributes of God. A prayer is a crucial aspect of executing our hope. The right supplication performs repentance when necessary.
"Depart from me..." Performative utterance against all obstacles is required in the process of reconciliation with God.
Psa 6:10 Let all mine enemies be ashamed and sore vexed: let them return and be ashamed suddenly.
David does not demand the shame of his enemies. He does hope for their repentance and their shame be felt at home in God's presence. The first "ashamed" is not a vengeful utterance. It is out of disappointment. The second one is out of hope for their repentance.