I thought something with Musick in, too.

How about Heart's Ease as a name? Here's why:

The tune is made reference to in Act 4, Scene 5 of Shakespeare's Romeo and Juliet, (1597).

"Peter: Musicians, O, musicians, Heart's ease, Heart's ease; O, an you will have me live, play Hearts ease.
Fiddler: Why Hearts ease?
Peter: O, musicians, because my hart itself plays My heart is full of woe; O, play me some merry dump, to comfort me."

It the name of a tune by renaissance composer/lutenist/cittern player Anthony Holborne and also the name of a tune in Playford, baroque period (though the two tunes are unrelated - at least, my ears can't hear a connection), so the name spans two of the three periods we cover.

Wikipedia tells me, "As its name implies, Heartsease has a long history of use in herbalism. It has been recommended, among other uses, as a treatment for epilepsy, asthma, skin diseases and eczema. It has expectorant properties, and so has been used in the treatment of chest complaints such as bronchitis and whooping cough. It is also a diuretic, leading to its use in treating rheumatism and cystitis." So that would cover work in schools that would include general social history around the music - food, medicine, crime, etc.

But is it a good name for a duo?