Example 4. One subset of each set of equivalence classes for the eight equivalence relations in the IRK scope. More

Figure 4.2. A . Three-note set-class space, with regions corresponding to clustered (triangle), tertian (quadrilateral), quartal (pentagon), and equipollent (oval) set-classes. Small italic labels show equal-tempered chromatic sets; large bold labels show equiheptatonic set-classes. B . Single More

Figure 5.7. The single-semitone layer of chromatic tetrachordal set-class space, superimposing the one-step layer of diatonic tetrachordal set-class space. Circles represent generated collections. Shapes represent clustered (triangle), tertian (quadrilateral), quartal (pentagon), and equipollent More

Image 9. An English country dance set. Squares represent men and circles women. More

Example 4. Interpreting chromatic semitones in settings with three or more voices. More

Figure 7.3. Improvising by alternating a hexachord's intrinsic 024 6 sets. More

Figure A3. Categorizing small sets using the first three Fourier components. More

Figure 7.5. Improvising using hexachordal 013 6 ( top ) and 012 6 ( bottom ) sets. More

Figure 5.4. In a seven-tone scale, the M2 transform sends clusters to tertian, tertian sets to quartal, and quartal to cluster. The equipollent set-classes (open note heads = trichord, closed note heads = tetrachord) are preserved under the transform. More

Figure 7.4. The quartal hexachordal voicing chains together hexachordal 023 6 and 013 6 sets. More