Speculation and Discussion
Taken from the Magical Speculation thread in the forums:
- possibly bardic magic "kill, kill, kill, the big ogre!"
 Speculation from page
Being as it's pure speculation, I'm tossing it here for now.
The magic of Rhyme-o-mancy may be connected to the underlying mechanics of dance fighting, such that the forces of Rhyme and Rhythm cause units to be more effective in combat. If so, Rhyme-o-mancers could be give increase the bonus units receive for in dance fighting. This would be similar to the bonus that golems created by a Dirtamancer receive when stacked with a dirtamancer, and the "huge" bonus that uncroaked receive when stacked with a Croakamancer.
This bonus could be permenent. A Rhyme-o-mancer might be involved in training units so that they can dance fight. If the RCC had no Rhyme-o-mancer, then that could explain why so few of their units could lead a dance fight. Alternatively, training might increase a unit's dance fight stat, but only work on units with some basic skill.
If their bonus was large enough, it might be worth using Rhyme-o-mancers in actual battle, despite the risk. However, given the shortage of casters, their bonus would have to be large.
It is also possible that they provide out of combat bonuses. Construction, for instance, might proceed faster if the workers dance to a song crafted by a Rhyme-o-mancer for that purpose.
Rhyme-o-mancy is pretty wide-open as far as its effects, but we can probably guess that it depends on rhymed incantations. Commander I. Heartly Noah June 3 2009
 Element and Axis
Rhyme-o-mancy is Stagemancy, magic of all three elements. It is aligned to the axis of Numbers. It is possible that using Matter, Motion, and Life together with Numbers one generates music. Perhaps the three elements together improve the Numbers? All that is clear is that the result is not concerned with Fate or the Erf. Commander I. Heartly Noah June 3 2009
 Rhyming Appearances
There's a third: page 111, by Transylvito against Stanley on the way to Faq. --Darren 12:18, 1 September 2009 (UTC)
Rhyme-o-mancy may simply be an equivalent to bardic magic. A rhyme-o-mancer may be a bard. This would include the "rocking out" ability that The Arkenhammer grants The Tool.