A chord with duplicate pitch classes is permutationally symmetrical (Psymmetrical),
since there is some nontrivial permutation of its notes that is a trivial voice
leading. These chords lie on the singular boundaries of the orbifolds. Nearly Psymmetrical
chords, such as {E, F, Gf}, are near these chords, and contain several notes
that are clustered close together. Efficient voice leadings permuting the clustered notes
bounce off the nearby boundaries (Fig. 2. Movies S2 and S4). Such voice leadings can be
efficient, independent, and non-trivial. Since trivial voice leadings are musically inert,
composers have reason to prefer near P-symmetry to exact P-symmetry.