Abarim Publications' online Biblical Greek Dictionary
υμην υμνος υμνεω
The familiar Greek words υμην (humen), meaning skin or membrane (hence our English word "hymen") and υμνος (humos), meaning song (hence our word "hymn"), are related in a beautiful and surprising fashion, and even in such a way that it's not quite clear at which point in linguistic evolution these words assumed their independent meanings, and thus until which juncture they expressed mere nuances of one essential meaning.
The noun υμην (humen), meaning skin or membrane, is not used in the New Testament, but ancient Greek writers used it to describe the membrane that envelops organs such as the brain, heart, bowels and even eyes and fetuses. The word ultimately stems from a Proto-Indo-European root syu-, which meant to bind (hence our modern verb "to sew"), and that's probably how it came to be applied to marriage and finally to the Greek god of marriage, aptly dubbed Hymen (means "one who joins" and is comparable to the Hebrew name Levi. The word παρθενος, parthenos, meaning virgin girl, is of unclear etymology but may share its root with the Latin partior or to divide, and thus literally means one who is not joined).
The ancient Greeks surmised that the god Hymen somehow had to be enticed to visit the marriage ceremony, and that was accomplished by singing an ode called υμεναιος (humenaios), which swiftly became synonymous to the ceremony at large. The noun υμνος (humos) came to denote any song dedicated to any deity, and its derived verb υμνεω (humneo) described the act of singing such a song. The Greek word υμεναιος (humenaios) also became the Latin name for the nuptial song: Hymenaeus (literally meaning: of or belonging to Hymen), and subsequently came to denote god of marriage all together.
The noun υμνος (humnos) doesn't merely denote a kind of song but literally describes the joyful joining within which a hymn is sung. A hymn is a collectively sang song. The noun occurs only twice in the New Testament, namely in Ephesians 5:19 and Colossians 3:16. The derived verb υμνεω (humneo) occurs 4 times; see full concordance.