What would you suggest in the way of mantras? I'm not really familiar with that concept.
Right, let's flesh out an example list here:
Beaiigi: Warmth self.
Benuigi: Warmth other.
Take a look at those, and you'll notice they both have "Be--igi". That means one of those is "Good" and one is "Fire." Ai is self, and Nu is other. Be, in this case, is the Beneficial, and igi is the classic fire.
Of course, having two-letter strings would probably be a bad idea, since it can result in strings of short-strings that spell out something in three-letter strings if you don't choose the lettering of it all very carfully.
The mantras clearly follow the rune idea, only less ordered, less varied, etc. You would have a lower amount of strings, though tying them together can result in interesting things.
Ma-be-nu-igi, under the assumption that Ma is Malicious, for example: what would this do? Maybe it's a cauterizing effect--burn out a wound or debuff at the cost of health.
Negigi: If Neg is Negative/Anti, this results in the opposite effect than fire, which, under logic would be water or ice, though on a magic wheel it could be something else. Or maybe negative does the opposite logic effect instead of magic.
Say the opposite is water, and aqu is water. Aqu-neg-igi would result in a double-strength water spell. Why would you want to do this? Because AquAqu might do something entirely different. Manuaqu might punch the enemy with water, and Manuaqunegigi punch them even harder, but manuaquaqu could instead punch them at level one strength with a knockback.
Additionally, using the same mantra could result in an exponential cost increase. If Aqu and Igi cost 3, and Neg costs 1, AquAqu could cost 9, whereas AquNegIgi costs 7. With this logic, even if AquAqu is the same as AquNegIgi, it's cheaper to use Aqunegigi. AquAquAqu would cost 27, AquAquNegIgi 13, and AquNegIgiNegIgi also 13. (If Neg was more than 1, then it would cost more than only having one neg)