On my blacksmith, I can craft blue 463 weapons that require Harmonies, and some of these weapons sell for a fair bit of gold. Blacksmiths can also use Harmonies to craft epic 496 gear if they buy the somewhat expensive patterns off the AH (or get them in a raid or the Black Market Auction House). All these epic recipes take Blood Spirits, which are still somewhat rare and expensive, but much more attainable now that many realms have guilds with normal mode raids on farm. Item level 496 gear is still good enough that people will want it in patch 5.2. That said, this epic gear sells fairly slowly, so your major Harmony-soak is going to be weapons and maybe the 476 epic armor. These recipes are gated behind being honored with The Klaxxi, but if you hit 90 in that zone like most people do, you're likely to have enough reputation to get them without doing dailies. If you didn't get to them before hitting 90, just go and do all their non-blue quests and you'll be rewarded with enough reputation for the recipes.
On a tailor, you can turn Harmonies into Imperial Silk which are the base ingredient for your gear enhancements and epic gloves and chest pieces, as well as the best bag in the game. The Golden Lotus is unfortunately the reputation you need for Tailoring recipes, and you won't have any lead on them by leveling. That said, it's only a few days of dailies to get honored, and that's when you'll learn all the 476 BoE crafted gear and your Spellthreads. If you keep going and get August Celestials rep up to exalted, then you'll be able to make that bag.
edit: If items made from Imperial Silk are not profitable on your realm, then you're better off farming Enigma Seeds, because the only thing Tailors can do with Harmonies is make more Imperial Silk.
As a leatherworker, you can make blue 450 cloaks which will generally sell quite well. Once you get Golden Lotus honored, you can make the 476 epic armor, and you can make the 496 epic armor any time you're willing to invest in a pattern.
An engineer can make a bunch of items with Harmonies, none of which require rep grinding. Mist-Piercing Goggles are in constant demand by new gatherers, the new weapon scope will be purchased every time a hunter gets a weapon upgrade, this gun is generally the first thing these hunters want to buy when they hit 90, and there are a pair of mounts that will sell so rarely that they basically won't count.
Scribes can use Harmonies to make a blue 424 caster offhand and blue 424 staves for casters and agility users. These blues are usable by non-scribes, and the offhands can be upgraded to 476 healing and dps epics which are also usable by non-scribes. The staves can be upgraded by a scribe, but the upgrade is not something you can sell. If you have no other use for your Harmonies, you can make more Darkmoon Cards with 10 of them.
edit: I took out the part about the weekly quest -- I can't see it on my scribe because he's not max level, but I'm being told that it never made it to live.
Jewelcrafters can craft pets, but mostly skip the daily cooldown on research. Alchemists can only use it to skip the daily cooldown on (and reduce the materials of) making a Living Steel.
As you can see, the daily 1.6 Spirits of Harmony you can farm can end up being wildly different profit for you, depending on which professions you have. If you can't use Harmonies profitably, the other option is to use them to buy things from your Spirit of Harmony vendor. Golden Lotus used to be the obvious best deal here, however in patch 5.1, the number of Lotus you get for a Harmony was reduced to 2 from 3. If you're trying to get Lotus, you're better off planting Enigma Seeds, however the Lotus has gone way down in price lately.
If you can't make a Spirit of Harmony into something more valuable than the average of a stack of herbs on your realm, then consider Enigma Seeds. These will turn into a stack of a random herb, or a Golden Lotus. Average out the value of a stack of herbs (add up the price for Fool's Cap, Green Tea Leaf, Silkweed, Rain Poppy, and Snow Lily, then divide by 6), and then assuming you're getting one Lotus about every 8 Seeds, divide the price of a Lotus by 8. If those two numbers together are higher than what you can make with a mote of Harmony, then Enigma Seeds are the way to go.
My farmer is a blacksmith, so I still come ahead making Harmonies. They're worth a lot less now than they were last patch, but so are the Golden Lotus and herbs I'm giving up by not farming Enigma Seeds. I check frequently, though.
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