In Ancient Greek grammar, a barytone is a word without any accent on the last syllable. Words with an acute or circumflex on the second-to-last or third-from-last syllable are barytones, as well as words with no accent on any syllable:
Like the word baritone, it comes from Ancient Greek barýtonos, from barýs 'heavy; low' and tónos 'pitch; sound'.
Herbert Weir Smyth. Greek Grammar. paragraph 158.