I think improvisation for "musu" doesn`t sound quite right. The Chinese character in verb form is "umu" which means to give birth, thus the definition of "creative" in a literal sense.
The interesting thing about the Japanese language is the ability to be incredibly vague. By saying Takemusu Aiki, the Founder was most certainly not teaching anything concrete. Grammatically, the sentence could mean, " Take gives birth to aiki" or " Aiki gives birth to take" or "creativity brings about aiki which then causes take." Each character could be looked at separately and reconfigured in different ways. Ai, ki, take, musu. Then there is kototama theory which says that each sound can be looked at separately and reconfigured. Ta, ke, mu, su, a, i, ki, plus the differing pronunciations for the characters, bu, umu ( which can be divided into u and mu)
Personally, I think it is one of those things where understanding comes with study, experience, and reflection. Louis Armstrong was once asked, what is swing? He answered something like, "If you gotta ask, you ain`t got it." This might be something similar.