Recent work on Ligeti’s use of complementary collections in his late works, which Richard Steinitz refers to as “Combinatorial Tonality,” presented at the 2017 Conference on Mathematics and Computation in Music. (An earlier version presented at the 2017 Joint Mathematics Meeting of the American Mathematical Society and Mathematical Association of America.) These works exploit the intervallic content both within and between collections. The intra- and inter-harmonic potentials are analytically useful and exhibit nice mathematical properties. Analysis of Ligeti’s Désordre develops ideas in Lawrence Quinnett’s FSU doctoral treatise Harmony and Counterpoint in Ligeti Études.