There is a remarkable resemblance between this psalm and Psalm 14:1-7. Both are ascribed to the same author, David; and each pursues the same line of thought - the folly and wickedness of Atheism. They both show that the belief that there is no God is not a harmless idea, or a mere speculation, but that it has important consequences on the life, and is naturally connected with a wicked life, Psalm 53:3-4.
The difference in the two compositions is (a) in the title; and (b) in the psalm itself.
(a) In the title. Both psalms are ascribed to David, and both are dedicated to the "Chief Musician." But in the title to the psalm before us, there is this addition: "Upon Mahalath, Maschil." On the meaning of the term Maschil, see Introduction to Psalm 32:1-11. The term here would seem to imply that the psalm was designed to give instruction on an important subject, but why it is prefixed to this psalm, and not to the others, we have no means of determining. The word, rendered "Mahalath" - מחלת machălath - occurs only here and in the title to Ps. 88. It is supposed by Gesenius to denote a stringed instrument, as a lute or guitar, that was designed to be accompanied with the voice. DeWette renders it "flute." Luther renders it "for a choir, to be sung by one another;" that is, a responsive choir. The Septuagint and the Latin Vulgate retain the original word with no attempt to translate it. Prof. Alexander renders it disease, because a form of the word "almost identical" occurs Exodus 15:26; Proverbs 18:14; 2-Chronicles 21:15 meaning "disease," and he supposes reference is to "the spiritual malady with which all mankind are infected, and which is really the theme or subject of the composition." It is true that there is a word - מחלה machăleh - similar to this, meaning "disease," but it is also true that the word used here is never employed in that sense, and equally true that such a construction here is forced and unnatural. The obvious supposition is that it refers to an instrument of music.
(b) The difference in the psalms themselves is mainly that in Psalm 53:1-6 Psalm 14:6 is omitted, and that in the other parts of the psalm there are enlargements designed to illustrate or to explain more fully the course of thought in the psalm. It is not known by whom these changes were made. They are, as DeWette remarks, such as could not have occurred by an error in transcribing, and they must have been made by design. Whether the changes were made by the author, or by someone who collected and arranged the psalms, and who, adopting the main thoughts of Psalm 14:1-7, inserted additions conveying new phases of thought, though without intending to supersede the use of the original composition, it is not possible now to determine. It is by no means an improbable supposition that the author of the psalm - David - may have revised it himself, and made these changes as expressing more fully his idea, while, as embodying valuable thoughts, it was deemed not undesirable to retain the original psalm in the collection as proper to be used in the service of God. Similar changes occur in Ps. 18, as compared with 2 Sam. 22, where that psalm occurs in the original form of composition. There is no evidence that the alteration was made by a later writer; we may doubt whether a later writer would alter a composition of David, and publish it under his name.
For an analysis of the psalm, see Introduction to Psalm 14:1-7.

The sentiments of atheists and deists, who deny Divine Providence; their character: they are corrupt, foolish, abominable, and cruel, Psalm 53:1-4; God fills them with terror, Psalm 53:5; reproaches these for their oppression of the poor, Psalm 53:5. The psalmist prays for the restoration of Israel, Psalm 53:6.
The title, To the chief Musician upon Mahalath, an instructive Psalm of David. The word מחלת machalath, some translate the president; others, the master or leader of the dance; others, hollow instruments; others, the chorus. A flute pipe, or wind instrument with holes, appears to be what is intended. "To the chief player on the flute;" or, "To the master of the band of pipers."

INTRODUCTION TO PSALM 53
To the chief Musician upon Mahalath, Maschil, A Psalm of David. The word "mahalath" is only used here and in Psalm 88:1. Some, with Aben Ezra, take it to be the first word of a song, to the tune of which this psalm was set; others, with Jarchi, that it is the name of a musical instrument on which it was sung; a hollow instrument; of the same nature with "nehiloth", See Gill on Psalm 5:1, title. Though it may relate to the argument or subject matter of the psalm, and be rendered, "concerning sickness" or "infirmity" (e); and, as Jarchi observes, some interpret it, "concerning the sickness or weakness of Israel", when the temple was destroyed. But it seems much better to understand it of the sickness and disease of sin, and the weakness following upon that, to which all mankind are subject; since the psalm manifestly treats of the general corruption and depravity of human nature. This psalm is the same with Psalm 14:1, and is expressed in the same words, with some little difference; the reason of its repetition is variously conjectured. Some think that the compiler of the book of Psalm, observing various readings in it occasioned by copying, thought fit to insert it both ways; but it is most likely to be composed by David himself, at different times, and it may be on different occasions, and with different views. Some think the former, namely the fourteenth psalm, was written concerning Nabal, and this concerning Doeg; according to Jarchi, that was concerning Nebuchadnezzar, this concerning Titus Vespasian; or, as others think, Antiochus Epiphanes. Kimchi is of opinion that this psalm, being placed between one that relates to Doeg, and another that refers to the Ziphites, points at the likeness there is between the case of David and the Messiah; that as David had many who sought to ensnare him, yet God rewarded them, and established him in the kingdom; so it will be with the Messiah: but it is much more reasonable with others to conclude, that it is repeated either because of the importance of it; because that as the former may refer to the corruption of the Jews in the times of David, this to the corruption of men in the times of Christ and his apostles, and under the Gospel dispensation, until the second coming of Christ, especially under the reign of antichrist. The argument of the psalm, according to the Syriac version, is concerning Ahithophel, who gave counsel to Absalom to pursue his father David and kill him: and, according to the Arabic version, it is a prophecy concerning Babel and Sennacherib; so Theodoret: but rather concerning mystical Babylon, and the man of sin.
(e) "de miseria", Tigurine version, "vel infirmitate"; so Ainsworth.

The corruption of man by nature.

Elohimic Variation of the Jahve - Psalm 14:1-7
Psalm 52:1-9 and Psalm 53:1-6, which are most closely related by occasion, contents, and expression, are separated by the insertion of Psalm 53:1-6, in which the individual character of Psalm 52:1-9, the description of moral corruption and the announcement of the divine curse, is generalized. Psalm 53:1-6 also belongs to this series according to its species of poetic composition; for the inscription runs: To the Precentor, after Machalath, a Maskı̂l of David. The formula על־מחלת recurs in Psalm 88:1 with the addition of לענּות. Since Ps 88 is the gloomiest of all the Psalm, and Psalm 53:1-6, although having a bright border, is still also a dark picture, the signification of מחלה, laxness (root חל, opp. מר), sickness, sorrow, which is capable of being supported by Exodus 15:26, must be retained. על־מחלת signifies after a sad tone or manner; whether it be that מחלת itself (with the ancient dialectic feminine termination, like נגינת, Psalm 61:1) is a name for such an elegiac kind of melody, or that it was thereby designed to indicate the initial word of some popular song. In the latter case מחלת is the construct form, the standard song beginning מחלת לב or some such way. The signification to be sweet (Aramaic) and melodious (Aethiopic), which the root חלי obtains in the dialects, is foreign to Hebrew. It is altogether inadmissible to combine מחלת with Arab. mahlt, ease, comfort (Germ. Gemהchlichkeit, cf. mהchlich, easily, slowly, with mהhlich, by degrees), as Hitzig does; since מחל, Rabbinic, to pardon, coincides more readily with מחה, Psalm 51:3, Psalm 51:11. So that we may regard machalath as equivalent to mesto, not piano or andante.
That the two texts, Psalm 14:1-7 and Psalm 53:1-6, are "vestiges of an original identity" (Hupfeld) is not established: Psalm 53:1-6 is a later variation of Psalm 14:1-7. The musical designation, common only to the earlier Psalm, at once dissuades one from coming down beyond the time of Jehoshaphat or Hezekiah. Moreover, we have here a manifest instance that even Psalm which are composed upon the model of, or are variations of Davidic Psalm, were without any hesitation inscribed לדוד.
Beside the critical problem, all that remains here for the exegesis is merely the discussion of anything peculiar in the deviations in the form of the text.