Quaternions for Winds

Me and the computer "wrote" this using quaternions where a = duration , b = pitch , c = dynamic, d = articulation.

I'm curious how quaternions were used to generate this.  I assume by a, b, c, and d, you mean the coefficients in a + bi + cj + dk, but I don't understand how thinking of this as a quaternion, as opposed to just a set of four values, is relevant to the composition process.