Praise him for his mighty acts - See the notes at Psalms 145:4 : “One generation shall praise thy works to another, and shall declare thy mighty acts.” The Hebrew word is the same. The reference is to that which displays the power of God; the things which manifest his omnipotence.
Praise him according to his excellent greatness - Hebrew, the multitude of his greatness. Let the praise in elevation correspond with this; let it be such as shall properly express this; let all be employed that will contribute to make this known, or that will be appropriate to this. Hence, the psalmist proceeds to call on all to make use of everything, by instrument and voice, that would in any manner set forth the praise of God.