The Bible seems to indicate that angels say or proclaim, and do not sing. In Job 38:7 it says that the stars sang and the sons of God shouted. In Job 1:6 the sons of God are identified as angels.

W.A. Criswell, in his Expository Sermons on Revelation had this to say about angels not singing:
“Another thing which is astonishing to me is that angels never sing. Never! When I stumbled into that fact, it was an amazing discovery! I had already made up my mind, before I say these things, that I am going to keep referring to angels singing, even though it is not true. To do so is traditional. After all, did they not sing when Jesus was born? Always people have spoken about the angels singing when Jesus was born. ‘Glory to God in the highest and on earth…’you know the angels song. So I turned to Luke 2:13 and read, ‘ And suddenly there was with the angel a multitude of the heavenly host SAYING Glory to God in the highest’. So it was in the book of Revelation too. ‘And there was a great host of angels SAYING with a loud voice’. Never in the Bible do angels sing. Never! They always SAY. They are in a doxology, in a chorus, they are in a recitative, they are all together, SAYING, but never in the Bible do the angels sing!That was an astonishing discovery to me. So I began reading, studying, probing and trying to find out why angels do not sing, and this is the best reason that I can find. Always the redeemed sing. God’s blood-washed sing. God’s children sing. But angels do not sing. Here is my conclusion: Music is made up of major and minor chords. The minor chords speak of wretchedness, death and sorrow of this fallen creation. Most of nature moans and groans in a plaintive minor key. The sound of the wind through the forest, the sound of the storm, the sound of the wind around the house, is always in a minor key. It wails…Even the nightingales’ song, the sweetest song of the birds, is the saddest. All this reflects the wretchedness, the despair, the hurt, the agony, the travail of this fallen creation. But an angel knows nothing of this. The major key and major chords are chords of triumph and victory. Surely God has taken us out of the miry clay. He has taken us out of the horrible pit. He has set our feet on the solid rock and put a new song in our souls and new praises on our lips. The angels know nothing of this! An angel has never been redeemed. An angel has never been saved…they see it, they watch it, but they know nothing about it (experientially)…it takes a saved soul to sing!”
– W.A. Criswell, Expository Sermons on Revelation, Volume III, p. 82-83)