It is very interesting. I've learned another pronunciation.
Gay-rah-sko ah-ay dee-dah-sko-meh-nos
"r" is rolled.
I know it is mostly guess work anyway, but is this the most recent "scholarly" version? Do you have an article for me to read or a reference work?
Since Timothy quoted the short version (the one that's current in Greece today), I assumed he wanted the modern Greek pronunciation, and that's what I gave him.
The pronunciation you cite, Euterpe, would be the theoretical "Erasmian" pronunciation, i.e., the way Greek sounded (supposedly) in the classical period. Ordinarily, I give only the modern Greek pronunciation, since it's the only authentic one we actually have.
The ancient Greek form of the quotation from Solon is Γηράσκω δ' ἀεὶ πολλά διδασκόμενος "Βut I grow old always learning many things."
A decent, fairly comprehensive article on Greek pronunciation through the ages is by R. Whitney Tucker, "Chronology of Greek Sound Changes,"
American Journal of Philology 90 (1969), 36-47.