I will praise the Lord according to his righteousness - That is, particularly as manifested in the treatment of the righteous and the wicked, protecting the one, and bringing deeserved punishment upon the other. The purpose of the psalm is to show this. In the course of the psalm the author had declared his full conviction that this was the character of God, and now, in view of this, he says that he will render to him the praise and glory which such a character deserves. He will acknowledge him by public acts of praise as such a God; and will at all times ascribe these attributes to him.
And will sing praise to the name of the Lord - To the name of Jehovah; that is, to Yahweh himself, the “name” being often used to designate a person, or that by which he is known; and also, in many cases, as in this, being significant, or designating the essential nature of him to whom it is applied.
Most high - Exalted above all other beings; exalted above all worlds. The purpose here declared of praising God may refer either to the act which he was then performing in the composition of the psalm, or it may be a purpose in respect to the future, declaring his intention to be to retain in future life the memory of those characteristics of the divine nature now disclosed to him, and to celebrate them in all time to come. The great truth taught is, that God is to be adored for what he is, and that his holy character, manifested alike in the treatment of the righteous and the wicked, lays the foundation for exalted praise.