ἀείδω compare the morphological problems with ἀείρω
I.to sing, Il., etc.:—then of any sound, to twang, of the bowstring, Od.; to whistle, of the wind, Mosch.; to ring, of a stone struck, Theocr.
II.trans.,
1.c. acc. rei, to sing, chant, μῆνιν, παιήονα, κλέα ἀνδρῶν Hom.:—absol., ἀείδειν ἀμφί τινος to sing in one's praise, Od.:—Pass., of songs, to be sung, Hdt.; ᾆσμα καλῶς ᾀσθέν Xen.
2.c. acc. pers. to sing, praise, attic