A Neo-Riepelian Key-Distance Theory

In Sect. 13.1 the (implied) key-distance theories of Heinichen, Kellner, and Weber are contrasted with the (incomplete) theory of Riepel. For Riepel, the parallel key, the tonic of which is chromatic relative to the home key, is more distant from the home key than a key (for example, the relative) the tonic of which is diatonic. Section 13.2 examines the prevalent belief that Weber’s theory has been empirically validated by Krumhansl and her associates. Finally, Sect. 13.3 posits a “neo-Riepelian” theory of key distance. Unlike other theories, by neo-Riepelian theory a distance between two keys does not necessarily exist; as a result, except for diatonic key relations, key distances in general do not conform to what is known in algebra as “metric space.”