Lute amplifies the 12hp regen component of cantana (55) and Nivs 5hp component (forget the level). These stack and with maestro lute gives you over 40/tick.
The 12 mana regen component is not modified but does "stack" with the flat 7 mana per 3 sec cast of the mana pulse song. You can technically get 4 pulses to land between refresh of cantana giving you 36 (12x3) + 28 (7x4) for 64 mana per 18 seconds.
Cantana with lute and 4x pulse gives 21 mana and 29hp per tic averaged
Cantana and Nivs with lute and 3x pulse gives >40hp and 19 mana per tic averaged
Gypsy lute still lets you put out ~36hp and 25hp per tick
As it relates to this conversation - the healing potential of a bard alone demonstrates the potency of using your instruments more often. With breath of harmony click you can still keep up 17 a tic (both songs without mod) - so depending on your level and gear weapons use is still reasonable, just don't trick yourself into thinking you're putting out good damage. I've parsed myself many times and even at 60 it's not pretty.
Epic changes everything. 1.8 song mod while meleeing is fantastic and the proc haste for group is amazing.
For the lower level bards - don't be quick to adopt the lower level cantana too quickly. Level 6 hymn of restoration scales up a bit higher than even the 55 cantana. From levels 6 through 50 I'd argue that in all but a very few cases bards with one song and a 100p lute outheal every other class. We have no burst healing but I know I've almost put more than a few healers to sleep even in my 50s in KC because they didn't have to cast a heal in over a half hour. At best you can heal for the group exclusively, at worst you save your healer (especially useful for Druids healing) a ton of mana - more mana than you would have given them with lower level cantana.
Cantana of Soothing caps at 4hp/tic. It does give 5 mana a tic but if healer mana is what you're most worried about you would likely save them mana (a lot) in the long run by using hymn of restoration.
Sorry for any autocorrect spelling issues - on phone right now.
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