I have not yet seen Harp Dreams, but I think I recognize what you are describing. I learned this system in skills classes in my undergrad. We all cursed its existence at the time, but I have actually returned to it frequently since then.
Quarter Note: Ta
Two eighths: Ta-di
Four sixteenths: Ta-ka-di-mi (you’ll notice that the syllables line up)
Triplets: Ta-ki-da
Six sixteenths: Ta-va-ki-di-da-ma
I would love to hear if anyone has any more information!