In case anyone cares, in addition to dealing additional damage, Heavenward Howl will also cause melee attacks to feed mobs twice the amount of TP that melee attacks would otherwise give. Tested on MNK/RUN using Fermion Sword and no gear in all other slots. Used Virelai on a Bull Dhalmel and <pettp> after each swing. Each attack without HH was giving it 30 TP, and each attack with HH was giving it 60 TP,
even if the HP drained was 0. Used a Hoe afterwards to make sure it's actually "TPx2" for HH hits, and got the same result. 67 TP per hit with HH down, 134 TP per hit with HH up.
I tested this because I noticed Imps in this month's Ambuscade seemed to be building TP more rapidly while I was using Heavenward Howl during HP drain moon phase. Don't know if this was already common knowledge or not, but the BG page didn't mention anything about the additional damage also causing additional TP to be fed.