Abstract

This chapter begins with experiments that measure the degree to which each chromatic scale tone fits with key-defining contexts such as scales, tonic triads, and chord cadences. The results show that a context defining a major or minor key imposes on the set of tones a well-defined ordering of structural significance or stability. This ordering is called a tonal hierarchy. The tonal hierarchies of different keys can be used to produce a quantitative measure of the degree to which the keys are related to one another. The argument is based on the idea that keys are related to the extent that their tonal hierarchies are similar. The analysis that produces a spatial representation of key distances from the tonal hierarchies completes the chapter.